diff --git a/.gitattributes b/.gitattributes index bed0738c7eeb449bca98b5d2f33c89a1ee56349a..e4b51cd13013121617787b33fa9681be52c46c9c 100644 --- a/.gitattributes +++ b/.gitattributes @@ -58,3 +58,7 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text # Video files - compressed *.mp4 filter=lfs diff=lfs merge=lfs -text *.webm filter=lfs diff=lfs merge=lfs -text +papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_layout.pdf filter=lfs diff=lfs merge=lfs -text +papers/markdown/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation/hybrid_auto/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation_layout.pdf filter=lfs diff=lfs merge=lfs -text +papers/markdown/2405.20853_MeshXL_Neural_Coordinate_Field_for_Generative_3D_Foundation_Models/hybrid_auto/2405.20853_MeshXL_Neural_Coordinate_Field_for_Generative_3D_Foundation_Models_layout.pdf filter=lfs diff=lfs merge=lfs -text +papers/markdown/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers/hybrid_auto/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers_layout.pdf filter=lfs diff=lfs merge=lfs -text diff --git a/MINERU_SETUP.md b/MINERU_SETUP.md new file mode 100644 index 0000000000000000000000000000000000000000..7b9655365524df5bbe8ba5e8c74c0a05b67a9e48 --- /dev/null +++ b/MINERU_SETUP.md @@ -0,0 +1,32 @@ +# MinerU deployment notes + +- Source: `tools/MinerU`, commit `79d6d8d79fb8f3ddba5cc34c07a16f0ec36f56c7` +- Environment: `tools/.envs/mineru` (Python 3.12) +- Versions: MinerU 3.4.4, PyTorch 2.11.0+cu130, vLLM 0.20.2 +- Model cache: `tools/model_cache` +- Tested hardware: 8 x NVIDIA H100 NVL 96GB; driver 595.71.05 +- Smoke output: `mineru_test_output/smoke_meshgpt` +- Smoke log: `mineru_test_output/logs/smoke_meshgpt.log` + +Highest-quality local command for research PDFs: + +```bash +CUDA_VISIBLE_DEVICES=0 \ +HF_HOME=/data/chenxing/code/docs/tools/model_cache \ +MODELSCOPE_CACHE=/data/chenxing/code/docs/tools/model_cache/modelscope \ +/data/chenxing/code/docs/tools/.envs/mineru/bin/mineru \ + -p INPUT.pdf -o OUTPUT \ + -b hybrid-engine --effort high --image-analysis true \ + --formula true --table true +``` + +Eight-GPU batch conversion (one persistent process and model instance per shard): + +```bash +./mineru_convert_8gpu.sh papers/pdfs papers/markdown +``` + +`hybrid-engine` is preferable for born-digital papers: native text extraction limits +OCR/VLM hallucination, while the high-effort VLM path analyzes figures/charts and +retains formulas and tables. Outputs include Markdown, extracted images, content-list +JSON, middle JSON, and a layout PDF for visual QA. diff --git a/README.md b/README.md new file mode 100644 index 0000000000000000000000000000000000000000..722e845bbc68c7034bb7f6776d9887d2cef384b4 --- /dev/null +++ b/README.md @@ -0,0 +1,81 @@ +--- +language: +- en +- zh +license: other +pretty_name: Mesh Foundation Papers — MinerU Parsed Corpus +tags: +- 3d +- mesh-generation +- quadrilateral-mesh +- triangle-mesh +- document-ai +- mineru +--- + +# Mesh Foundation Papers — MinerU Parsed Corpus + +This repository contains a research corpus of 37 public mesh-generation and +quad-meshing papers published between November 2023 and July 2026, together +with high-quality MinerU parsing outputs. + +本仓库收录 37 篇 Mesh 生成、三角网格和四边网格相关公开论文，以及使用 +MinerU 高质量模式生成的 Markdown、图片、结构化 JSON 和版面校验文件，便于 +异地下载、全文检索和后续综述研究。 + +## Contents + +- `papers/pdfs/`: 37 source PDFs downloaded from official arXiv endpoints. +- `papers/markdown/`: one directory per paper containing: + - parsed Markdown; + - extracted figures and tables under `images/`; + - `content_list` / `content_list_v2` JSON; + - intermediate and model JSON; + - original and layout-check PDFs. +- `papers/manifest.csv`: title, arXiv metadata, source URL and local filename. +- `papers/README.md`: download and integrity notes. +- `research/`: Chinese research notes covering the 2023–2026 timeline, + triangle-vs-quad modeling differences and a curated figure index. +- `scripts/fetch_papers.py`: reproducible downloader. +- `MINERU_SETUP.md` and `mineru_convert_8gpu.sh`: parsing environment notes and + the eight-GPU batch command. MinerU itself, model weights and environments + are intentionally not included. + +## Parsing configuration + +- MinerU 3.4.4 +- Model: MinerU2.5-Pro-2605-1.2B +- Backend: `hybrid-engine` +- Quality: `--effort high` +- Figure analysis, formulas and tables enabled +- Hardware used: 8 × NVIDIA H100 NVL 96GB + +## Integrity summary + +- 37/37 source PDFs verified with readable PDF metadata +- 643 source pages in total +- 37 non-empty Markdown documents +- 37 `content_list_v2` JSON files +- 37 layout-check PDFs +- 1,904 extracted JPG assets +- no broken local image references detected in the generated Markdown + +## Notes and limitations + +- The papers and figures remain copyrighted by their respective authors and + publishers. Consult each arXiv record and paper for its applicable license + before redistribution or commercial use. +- This repository is provided as a research convenience and does not relicense + the source papers. +- Many 2026 entries are preprints. Claims in `research/` should be treated as a + literature synthesis rather than independently verified consensus. +- MinerU output may contain extraction errors. Verify exact quotations, + equations and numerical results against the source PDF/layout PDF. + +## Reproduce + +```bash +python scripts/fetch_papers.py +./mineru_convert_8gpu.sh papers/pdfs papers/markdown +``` + diff --git a/mineru_convert_8gpu.sh b/mineru_convert_8gpu.sh new file mode 100644 index 0000000000000000000000000000000000000000..abf09ac2f2caee9f1a9dd5eab104ff2135ccb4b3 --- /dev/null +++ b/mineru_convert_8gpu.sh @@ -0,0 +1,64 @@ +#!/usr/bin/env bash +set -euo pipefail + +if [[ $# -ne 2 ]]; then + echo "Usage: $0 INPUT_PDF_DIR OUTPUT_DIR" >&2 + exit 2 +fi + +input_dir=$(realpath "$1") +output_dir=$(realpath -m "$2") +env_dir=/data/chenxing/code/docs/tools/.envs/mineru +cache_dir=/data/chenxing/code/docs/tools/model_cache + +mkdir -p "$output_dir" "$output_dir/logs" +work_dir=$(mktemp -d "$output_dir/.shards.XXXXXXXX") +trap 'rm -rf -- "$work_dir"' EXIT + +mapfile -d '' pdfs < <(find "$input_dir" -maxdepth 1 -type f -iname '*.pdf' -print0 | sort -z) +if [[ ${#pdfs[@]} -eq 0 ]]; then + echo "No PDFs found in $input_dir" >&2 + exit 1 +fi + +for gpu in {0..7}; do + mkdir -p "$work_dir/$gpu" +done + +for i in "${!pdfs[@]}"; do + gpu=$((i % 8)) + ln -s "${pdfs[$i]}" "$work_dir/$gpu/$(basename "${pdfs[$i]}")" +done + +pids=() +for gpu in {0..7}; do + if find "$work_dir/$gpu" -type l -print -quit | grep -q .; then + env CUDA_VISIBLE_DEVICES="$gpu" \ + HF_HOME="$cache_dir" \ + MODELSCOPE_CACHE="$cache_dir/modelscope" \ + "$env_dir/bin/mineru" \ + -p "$work_dir/$gpu" \ + -o "$output_dir" \ + -b hybrid-engine \ + --effort high \ + --image-analysis true \ + --formula true \ + --table true \ + >"$output_dir/logs/gpu-$gpu.log" 2>&1 & + pids+=("$!") + fi +done + +status=0 +for pid in "${pids[@]}"; do + if ! wait "$pid"; then + status=1 + fi +done + +if [[ $status -ne 0 ]]; then + echo "At least one shard failed; inspect $output_dir/logs/gpu-*.log" >&2 + exit "$status" +fi + +echo "Converted ${#pdfs[@]} PDFs into $output_dir" diff --git a/papers/README.md b/papers/README.md new file mode 100644 index 0000000000000000000000000000000000000000..ea14874f63a2c7ed177d9d93eebc35d5944acae7 --- /dev/null +++ b/papers/README.md @@ -0,0 +1,33 @@ +# Mesh 论文 PDF 语料 + +本目录收录用户清单中的 37 篇论文，来源均为 arXiv 官方页面与 PDF 端点。 + +## 目录 + +- `pdfs/`：37 个 PDF，以 `arXiv_ID_规范题名.pdf` 命名。 +- `manifest.csv`：逐篇记录请求日期、请求题名、arXiv 规范题名、首次发布日期、下载状态、来源 URL、文件名和题名匹配度。 +- 下载及核验脚本位于仓库的 `scripts/fetch_papers.py`。 + +## 完整性核验 + +- 清单记录：37 条；状态全部为 `downloaded`。 +- 唯一性：37 个 arXiv ID/source URL 均不重复，37 个文件名均不重复。 +- 文件签名：全部以 `%PDF-` 开始，文件末尾均含 `%%EOF`。 +- 可读性：全部 37 个文件可由 Poppler `pdfinfo` 解析，合计 643 页；单篇 10–36 页，无零页或解析失败文件。 +- 当前总大小约 886 MiB。 + +## 日期说明 + +清单括号日期被视为用户提供的归档月份，而 `published` 是 arXiv API 返回的首次发布日期。唯一跨月差异是 **Mesh-Pro**：请求月份为 `26.03`，arXiv 首次发布日期为 `2026-02-28`。题名精确一致，因此仍确认是目标论文。 + +## 复跑 + +在仓库根目录执行： + +```bash +python3 scripts/fetch_papers.py +``` + +脚本通过 arXiv 官方 API 按题名查询，仅接受规范化题名相似度至少 0.72 的结果，并维护 `manifest.csv`。已存在的 PDF 不会重复下载。 + +后续 Markdown 转换应以 `manifest.csv` 作为索引，建议每篇输出到以 arXiv ID 命名的独立目录，保留图片、表格和页码映射，避免同名论文（尤其两篇 MeshFlow）输出互相覆盖。 diff --git a/papers/manifest.csv b/papers/manifest.csv new file mode 100644 index 0000000000000000000000000000000000000000..1c3a5a6a3ec864d19dea59322a3ffe13a8c37f26 --- /dev/null +++ b/papers/manifest.csv @@ -0,0 +1,38 @@ +requested_date,requested_title,verified_title,published,status,source_url,filename,note +23.11,MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers,MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers,2023-11-27,downloaded,https://arxiv.org/abs/2311.15475,2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers.pdf,match=1.000 +24.05,NeurCross: a neural approach to computing cross fields for quad mesh generation,NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation,2024-05-22,downloaded,https://arxiv.org/abs/2405.13745,2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation.pdf,match=1.000 +24.05,MeshXL: neural coordinate field for generative 3D foundation models,MeshXL: Neural Coordinate Field for Generative 3D Foundation Models,2024-05-31,downloaded,https://arxiv.org/abs/2405.20853,2405.20853_MeshXL_Neural_Coordinate_Field_for_Generative_3D_Foundation_Models.pdf,match=1.000 +24.06,MeshAnything: artist-created mesh generation with autoregressive transformers,MeshAnything: Artist-Created Mesh Generation with Autoregressive Transformers,2024-06-14,downloaded,https://arxiv.org/abs/2406.10163,2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers.pdf,match=1.000 +24.08,MeshAnything V2: artist-created mesh generation with adjacent mesh tokenization,MeshAnything V2: Artist-Created Mesh Generation With Adjacent Mesh Tokenization,2024-08-05,downloaded,https://arxiv.org/abs/2408.02555,2408.02555_MeshAnything_V2_Artist-Created_Mesh_Generation_With_Adjacent_Mesh_Tokenization.pdf,match=1.000 +24.09,EdgeRunner: auto-regressive auto-encoder for artistic mesh generation,EdgeRunner: Auto-regressive Auto-encoder for Artistic Mesh Generation,2024-09-26,downloaded,https://arxiv.org/abs/2409.18114,2409.18114_EdgeRunner_Auto-regressive_Auto-encoder_for_Artistic_Mesh_Generation.pdf,match=1.000 +24.11,Scaling mesh generation via compressive tokenization,Scaling Mesh Generation via Compressive Tokenization,2024-11-11,downloaded,https://arxiv.org/abs/2411.07025,2411.07025_Scaling_Mesh_Generation_via_Compressive_Tokenization.pdf,match=1.000 +24.12,"Meshtron: high-fidelity, artist-like 3D mesh generation at scale","Meshtron: High-Fidelity, Artist-Like 3D Mesh Generation at Scale",2024-12-12,downloaded,https://arxiv.org/abs/2412.09548,2412.09548_Meshtron_High-Fidelity_Artist-Like_3D_Mesh_Generation_at_Scale.pdf,match=1.000 +25.01,Nautilus: locality-aware autoencoder for scalable mesh generation,Nautilus: Locality-aware Autoencoder for Scalable Mesh Generation,2025-01-24,downloaded,https://arxiv.org/abs/2501.14317,2501.14317_Nautilus_Locality-aware_Autoencoder_for_Scalable_Mesh_Generation.pdf,match=1.000 +25.03,TreeMeshGPT: artistic mesh generation with autoregressive tree sequencing,TreeMeshGPT: Artistic Mesh Generation with Autoregressive Tree Sequencing,2025-03-14,downloaded,https://arxiv.org/abs/2503.11629,2503.11629_TreeMeshGPT_Artistic_Mesh_Generation_with_Autoregressive_Tree_Sequencing.pdf,match=1.000 +25.03,DeepMesh: auto-regressive artist-mesh creation with reinforcement learning,DeepMesh: Auto-Regressive Artist-mesh Creation with Reinforcement Learning,2025-03-19,downloaded,https://arxiv.org/abs/2503.15265,2503.15265_DeepMesh_Auto-Regressive_Artist-mesh_Creation_with_Reinforcement_Learning.pdf,match=1.000 +25.03,MeshCraft: exploring efficient and controllable mesh generation with flow-based DiTs,MeshCraft: Exploring Efficient and Controllable Mesh Generation with Flow-based DiTs,2025-03-29,downloaded,https://arxiv.org/abs/2503.23022,2503.23022_MeshCraft_Exploring_Efficient_and_Controllable_Mesh_Generation_with_Flow-based_DiTs.pdf,match=1.000 +25.05,Mesh-RFT: enhancing mesh generation via fine-grained reinforcement fine-tuning,Mesh-RFT: Enhancing Mesh Generation via Fine-grained Reinforcement Fine-Tuning,2025-05-22,downloaded,https://arxiv.org/abs/2505.16761,2505.16761_Mesh-RFT_Enhancing_Mesh_Generation_via_Fine-grained_Reinforcement_Fine-Tuning.pdf,match=1.000 +25.06,CrossGen: learning and generating cross fields for quad meshing,CrossGen: Learning and Generating Cross Fields for Quad Meshing,2025-06-08,downloaded,https://arxiv.org/abs/2506.07020,2506.07020_CrossGen_Learning_and_Generating_Cross_Fields_for_Quad_Meshing.pdf,match=1.000 +25.07,Topology-preserved auto-regressive mesh generation in the manner of weaving silk,Topology-Preserved Auto-regressive Mesh Generation in the Manner of Weaving Silk,2025-07-03,downloaded,https://arxiv.org/abs/2507.02477,2507.02477_Topology-Preserved_Auto-regressive_Mesh_Generation_in_the_Manner_of_Weaving_Silk.pdf,match=1.000 +25.08,VertexRegen: mesh generation with continuous level of detail,VertexRegen: Mesh Generation with Continuous Level of Detail,2025-08-12,downloaded,https://arxiv.org/abs/2508.09062,2508.09062_VertexRegen_Mesh_Generation_with_Continuous_Level_of_Detail.pdf,match=1.000 +25.08,FastMesh: Efficient Artistic Mesh Generation via Component Decoupling,FastMesh: Efficient Artistic Mesh Generation via Component Decoupling,2025-08-26,downloaded,https://arxiv.org/abs/2508.19188,2508.19188_FastMesh_Efficient_Artistic_Mesh_Generation_via_Component_Decoupling.pdf,match=1.000 +25.09,QuadGPT: Native Quadrilateral Mesh Generation with Autoregressive Models,QuadGPT: Native Quadrilateral Mesh Generation with Autoregressive Models,2025-09-25,downloaded,https://arxiv.org/abs/2509.21420,2509.21420_QuadGPT_Native_Quadrilateral_Mesh_Generation_with_Autoregressive_Models.pdf,match=1.000 +25.09,ARMesh: autoregressive mesh generation via next-level-of-detail prediction,ARMesh: Autoregressive Mesh Generation via Next-Level-of-Detail Prediction,2025-09-25,downloaded,https://arxiv.org/abs/2509.20824,2509.20824_ARMesh_Autoregressive_Mesh_Generation_via_Next-Level-of-Detail_Prediction.pdf,match=1.000 +25.09,MeshMosaic: scaling artist mesh generation via local-to-global assembly,MeshMosaic: Scaling Artist Mesh Generation via Local-to-Global Assembly,2025-09-24,downloaded,https://arxiv.org/abs/2509.19995,2509.19995_MeshMosaic_Scaling_Artist_Mesh_Generation_via_Local-to-Global_Assembly.pdf,match=1.000 +25.10,"Topology sculptor, shape refiner: discrete diffusion model for high-fidelity 3D meshes generation","Topology Sculptor, Shape Refiner: Discrete Diffusion Model for High-Fidelity 3D Meshes Generation",2025-10-24,downloaded,https://arxiv.org/abs/2510.21264,2510.21264_Topology_Sculptor_Shape_Refiner_Discrete_Diffusion_Model_for_High-Fidelity_3D_Meshes_Generation.pdf,match=1.000 +25.12,MeshRipple: structured autoregressive generation of artist-meshes,MeshRipple: Structured Autoregressive Generation of Artist-Meshes,2025-12-08,downloaded,https://arxiv.org/abs/2512.07514,2512.07514_MeshRipple_Structured_Autoregressive_Generation_of_Artist-Meshes.pdf,match=1.000 +26.03,LATO: 3D Mesh Flow Matching with Structured TOpology Preserving LAtents,LATO: 3D Mesh Flow Matching with Structured TOpology Preserving LAtents,2026-03-06,downloaded,https://arxiv.org/abs/2603.06357,2603.06357_LATO_3D_Mesh_Flow_Matching_with_Structured_TOpology_Preserving_LAtents.pdf,match=1.000 +26.03,Mesh-pro: asynchronous advantage-guided ranking preference optimization for artist-style quadrilateral mesh generation,Mesh-Pro: Asynchronous Advantage-guided Ranking Preference Optimization for Artist-style Quadrilateral Mesh Generation,2026-02-28,downloaded,https://arxiv.org/abs/2603.00526,2603.00526_Mesh-Pro_Asynchronous_Advantage-guided_Ranking_Preference_Optimization_for_Artist-style_Quadrilateral_Mesh_Generation.pdf,match=1.000 +26.03,FACE: a face-based autoregressive representation for high-fidelity and efficient mesh generation,FACE: A Face-based Autoregressive Representation for High-Fidelity and Efficient Mesh Generation,2026-03-02,downloaded,https://arxiv.org/abs/2603.01515,2603.01515_FACE_A_Face-based_Autoregressive_Representation_for_High-Fidelity_and_Efficient_Mesh_Generation.pdf,match=1.000 +26.03,TopGen: learning structural layouts and cross-fields for quadrilateral mesh generation,TopGen: Learning Structural Layouts and Cross-Fields for Quadrilateral Mesh Generation,2026-03-11,downloaded,https://arxiv.org/abs/2603.10606,2603.10606_TopGen_Learning_Structural_Layouts_and_Cross-Fields_for_Quadrilateral_Mesh_Generation.pdf,match=1.000 +26.03,TopoMesh: high-fidelity mesh autoencoding via topological unification,TopoMesh: High-Fidelity Mesh Autoencoding via Topological Unification,2026-03-25,downloaded,https://arxiv.org/abs/2603.24278,2603.24278_TopoMesh_High-Fidelity_Mesh_Autoencoding_via_Topological_Unification.pdf,match=1.000 +26.04,Strips as tokens: artist mesh generation with native UV segmentation,Strips as Tokens: Artist Mesh Generation with Native UV Segmentation,2026-04-10,downloaded,https://arxiv.org/abs/2604.09132,2604.09132_Strips_as_Tokens_Artist_Mesh_Generation_with_Native_UV_Segmentation.pdf,match=1.000 +26.04,SQuadGen: generating simple quad layouts via chart distance fields,SQuadGen: Generating Simple Quad Layouts via Chart Distance Fields,2026-04-30,downloaded,https://arxiv.org/abs/2604.27329,2604.27329_SQuadGen_Generating_Simple_Quad_Layouts_via_Chart_Distance_Fields.pdf,match=1.000 +26.05,QuadLink: autoregressive quad-dominant mesh generation via point-relation learning,QuadLink: Autoregressive Quad-Dominant Mesh Generation via Point-Relation Learning,2026-05-16,downloaded,https://arxiv.org/abs/2605.16813,2605.16813_QuadLink_Autoregressive_Quad-Dominant_Mesh_Generation_via_Point-Relation_Learning.pdf,match=1.000 +26.06,MeshFlow: Efficient Artistic Mesh Generation via MeshVAE and Flow-based Diffusion Transformer,MeshFlow: Efficient Artistic Mesh Generation via MeshVAE and Flow-based Diffusion Transformer,2026-06-03,downloaded,https://arxiv.org/abs/2606.04621,2606.04621_MeshFlow_Efficient_Artistic_Mesh_Generation_via_MeshVAE_and_Flow-based_Diffusion_Transformer.pdf,match=1.000 +26.06,TriFlow: generating artist-like 3D mesh topology via nearest-vertex vector fields,TriFlow: Generating Artist-Like 3D Mesh Topology via Nearest-Vertex Vector Fields,2026-06-18,downloaded,https://arxiv.org/abs/2606.20131,2606.20131_TriFlow_Generating_Artist-Like_3D_Mesh_Topology_via_Nearest-Vertex_Vector_Fields.pdf,match=1.000 +26.06,MeshFlow: mesh generation with equivariant flow matching,MeshFlow: Mesh Generation with Equivariant Flow Matching,2026-06-22,downloaded,https://arxiv.org/abs/2606.23489,2606.23489_MeshFlow_Mesh_Generation_with_Equivariant_Flow_Matching.pdf,match=1.000 +26.06,Mesh BDF: barycentric dominance field for 3D native mesh generation,Mesh BDF: Barycentric Dominance Field for 3D Native Mesh Generation,2026-06-30,downloaded,https://arxiv.org/abs/2606.31777,2606.31777_Mesh_BDF_Barycentric_Dominance_Field_for_3D_Native_Mesh_Generation.pdf,match=1.000 +26.07,Nexus: native mesh generation with diffusion,Nexus: Native Mesh Generation with Diffusion,2026-07-15,downloaded,https://arxiv.org/abs/2607.13563,2607.13563_Nexus_Native_Mesh_Generation_with_Diffusion.pdf,match=1.000 +26.07,LATO.2: factorized 3D mesh generation with vertex and topology flow,LATO.2: Factorized 3D Mesh Generation with Vertex and Topology Flow,2026-07-12,downloaded,https://arxiv.org/abs/2607.10623,2607.10623_LATO.2_Factorized_3D_Mesh_Generation_with_Vertex_and_Topology_Flow.pdf,match=1.000 +26.07,Meshy T2: fast native mesh generation with flow matching,Meshy T2: Fast Native Mesh Generation with Flow Matching,2026-07-28,downloaded,https://arxiv.org/abs/2607.28675,2607.28675_Meshy_T2_Fast_Native_Mesh_Generation_with_Flow_Matching.pdf,match=1.000 diff --git a/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers.md b/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers.md new file mode 100644 index 0000000000000000000000000000000000000000..38af66d36232725f0f5e036efe63e9d61a06da44 --- /dev/null +++ b/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers.md @@ -0,0 +1,642 @@ +# MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers + +Yawar Siddiqui1 Antonio Alliegro2 Alexey Artemov1 + +Tatiana Tommasi2 Daniele Sirigatti3 Vladislav Rosov3 Angela Dai1 Matthias Nießner1 + +Technical University of Munich1 Politecnico di Torino2 AUDI AG3 + +![](images/3545e4e678461da72e464d2647815436fc502f261b64157952c11a9676ecbf7e.jpg) + +
+flowchart + +```mermaid +graph LR + A["Shape Dataset"] --> B["Face Encoder"] + B --> C["Embedding Codebook"] + C --> D["Token Decoder"] + D --> E["GPT-Style Transformer"] + E --> F["MeshGPT: Autoregressive Mesh Generation"] +``` +
+ +Figure 1. Our method creates triangle meshes by autoregressively sampling from a transformer model that has been trained to produce tokens from a learned geometric vocabulary. These tokens can then be decoded into the faces of a triangle mesh. Our method generates clean, coherent, and compact meshes, characterized by sharp edges and high fidelity. + +## Abstract + +We introduce MeshGPT, a new approach for generating triangle meshes that reflects the compactness typical of artist-created meshes, in contrast to dense triangle meshes extracted by iso-surfacing methods from neural fields. Inspired by recent advances in powerful large language models, we adopt a sequence-based approach to autoregressively generate triangle meshes as sequences of triangles. Wefirst learn a vocabulary oflatent quantized embeddings, using graph convolutions, which inform these embeddings ofthe local mesh geometry and topology. These embeddings are sequenced and decoded into triangles by a decoder, ensuring that they can effectively reconstruct the mesh. A transformer is then trained on this learned vocabulary to predict the index of the next embedding given previous embeddings. Once trained, our model can be autoregressively sampled to generate new triangle meshes, directly generating compact meshes with sharp edges, more closely imitating the efficient triangulation patterns of human-crafted meshes. MeshGPT demonstrates a notable improvement over state of the art mesh generation methods, with a 9% increase in shape coverage and a 30-point enhancement in FID scores across various categories. + +## 1. Introduction + +Triangle meshes are the main representation for 3D geometry in computer graphics. They are the predominant representation for 3D assets used in video games, movies, and virtual reality interfaces. Compared to alternative 3D shape representations such as point clouds or voxels, meshes provide a more coherent surface representation; they are more controllable, easier to manipulate, more compact, and fit directly into modern rendering pipelines, attaining high visual quality with far fewer primitives. In this paper, we tackle the task of automated generation of triangle meshes, streamlining the process of crafting 3D assets. + +Recently, 3D vision research has seen great interest in generative 3D models using representations such as voxels [3, 62], point clouds [37, 67, 68], and neural fields [14, 19, 31, 35, 41]. However, these representations must then be converted into meshes through a post-process for use in downstream applications, for instance by iso-surfacing with Marching Cubes [36]. Unfortunately, this results in dense, over-tessellated meshes that often exhibit oversmoothing and bumpy artifacts from the iso-surfacing, as shown in Figure 2. In contrast, artist-modeled 3D meshes are compact in representation, while maintaining sharp details with much fewer triangles. + +Thus, we propose MeshGPT1 to generate a mesh representation directly, as a set of triangles. Inspired by powerful recent advances in generative models for language, we adopt a direct sequence generation approach to synthesize triangle meshes as sequences of triangles. Following text generation paradigms, we first learn a vocabulary of triangles. Triangles are encoded into latent quantized embeddings through an encoder. To encourage learned triangle embeddings to maintain local geometric and topological features, we employ a graph convolutional encoder. These triangle embeddings are then decoded by a ResNet [22] decoder that processes the sequence of tokens representing a triangle to produce its vertex coordinates. We can then train a GPT-based architecture on this learned vocabulary to autoregressively produce sequences of triangles representing a mesh. Experiments across multiple categories of the ShapeNet dataset demonstrate that our method significantly improves 3D mesh generation quality in comparison with state of the art, with an average 9% increase in shape coverage and a 30-point improvement in FID scores. + +![](images/9c49a05ead13fc277ddba7a5d49bbf787caf1c0d5ba8613e0e8d8d464e85ac30.jpg) +Figure 2. Meshes generated by our method (top) for chairs, tables, benches, and lamps when trained on ShapeNet [5]. MeshGPT meshes tend to be compact, with the ability to represent both sharp details and curved boundaries. This contrasts with neural fieldbased approaches that yield dense triangulations not easily simplified through decimation (bottom). + +In summary, our contributions are: + +• A new generative formulation for meshes as a sequence of triangles, tailoring a GPT-inspired decoder-only transformer, to produce compact meshes with sharp edges. +• Triangles are represented as a vocabulary of latent geometric tokens to enable coherent mesh generation in an autoregressive fashion. + +## 2. Related Work + +Voxel-based 3D Shape Generation. Early shape generation approaches generated shapes as a grid of low-resolution voxels [3, 9, 26, 62] or, more recently, as high-resolution grids using efficient representations such as Octrees [57] and sparse voxels [50], with generative models such as GANs [17]. These methods pioneered the extension of 2D generative techniques into the 3D domain. However, the voxel representation inherently constrains them with gridlike artifacts and high memory requirements, limiting their practical utility in capturing fine details and complex geometries. + +Point Cloud Generation. Methods in this category represent 3D shapes by point samples on their surfaces, aiming to learn point distributions across shape datasets. Early works involved GANs for synthesizing point locations [30, 54, 59] and latent shape codes [1]. Flow-based [64] and gradient field-based models [4] also yield impressive results. Recently, diffusion-based techniques have been adapted for point cloud generation [44, 67, 68], showing competitive performance in shape generation. However, point clouds, while useful, are not the ideal format for downstream applications requiring 3D content, as converting them to meshes, which apart from being non-trivial [42, 47, 51, 65], can often fail to accurately reflect the characteristics of the underlying mesh datasets. + +Neural Implicit Fields. Implicit representation of shapes as volumetric functions (e.g., signed distance functions) has become popular for encoding arbitrary topologies at any resolution [39, 45]. Various implicit generative methods have shown impressive performance using adversarial [6, 53] and diffusion-based [8, 14, 41] models. Diffusion-based neural field synthesis in MLP weight spaces [13] and triplanes [55] have also been explored, alongside leveraging image-based models for optimizing NeRFs [25, 34, 48, 63]. However, like point clouds, these methods require mesh conversion [12, 32, 36, 49, 53] for downstream applications, often leading to dense meshes that don’t capture the properties of the underlying datasets (e.g., edge lengths, dihedral angles). In contrast, we directly fit a generative model to triangulated meshes, explicitly modeling the training data, resulting in clean, compact and coherent meshes as outputs. + +3D Mesh Generation. While several discriminative approaches capable of learning signals directly on mesh structure were proposed over the recent years [16, 21, 23, 33, 40, 52, 56], direct mesh generation remains underexplored. Mesh generation has been approached with various learning-based methods [7, 11, 18, 43]. AtlasNet [18] and BSPNet [7], for example, produce mesh patches and compact meshes through binary space partitioning, respectively. However, as we demonstrate in Sec. 4, these struggle with accurately capturing shape detail. + +Closely related to our work, PolyGen [43] employs two autoregressively trained networks to create explicit mesh structures. In contrast, our method utilizes a single decoderonly network, representing triangles through learned tokens for a more streamlined generation process compared to PolyGen’s separate vertex-and-face sequence approach. Additionally, we observe that PolyGen’s vertex generator, oblivious to face generation, and the face generator, not exposed to the generated vertex distribution during training, exhibit limited robustness during inference. + +## 3. Method + +Inspired by advancements in large language models, we develop a sequence-based approach to autoregressively generate triangle meshes as sequences of triangles. We first learn a vocabulary of geometric embeddings from a large collection of 3D object meshes, enabling triangles to be encoded to and decoded from this embedding. We then train a transformer for mesh generation as autoregressive nextindex prediction over the learned vocabulary embeddings. + +To learn the triangle vocabulary, we employ a graph convolution encoder operating on triangles of a mesh and their neighborhood to extract geometrically rich features that capture the intricate details of 3D shapes. These features are quantized as embeddings of a codebook using residual quantization [27, 38], effectively reducing sequence lengths of the mesh representation. These embeddings are sequenced and then decoded by a 1D ResNet [22] guided by a reconstruction loss. This phase lays the groundwork for the subsequent training of the transformer. + +We then train a GPT-style decoder-only transformer, which leverages these quantized geometric embeddings. Given a sequence of geometric embeddings extracted from the triangles of a mesh, the transformer is trained to predict the codebook index of the next embedding in the sequence. Once trained, the transformer can be auto-regressively sampled to predict sequences of embeddings. These embeddings can then be decoded to generate novel and diverse mesh structures that display efficient, irregular triangulations similar to human-crafted meshes. + +## 3.1. Learning Quantized Triangle Embeddings + +Autoregressive generative models, such as transformers, synthesize sequences of tokens where each new token is conditioned on previously generated tokens. For generating meshes using transformers, we must then define the ordering convention of generation, along with the tokens. + +For sequence ordering, Polygen [43] suggests a convention where faces are ordered based on their lowest vertex index, followed by the next lowest, and so forth. Vertices are sorted in $z - y - x$ order (z representing the vertical axis), progressing from lowest to highest. Within each face, indices are cyclically permuted to place the lowest index first. In our method, we also adopt this sequencing approach. + +To define the tokens to generate, we consider a practical approach to represent a mesh M for autoregressive generation: a sequence of triangles, + +$$ +\mathcal {M} := (f _ {1}, f _ {2}, f _ {3}, \dots , f _ {N}), \tag {1} +$$ + +with N faces (triangles), $f _ { i } \in \mathbb { R } ^ { n _ { \mathrm { i n } } }$ having $n _ { \mathrm { i n } }$ features. A simple approach to describe each triangle is as its three vertices, comprising nine total coordinates. Upon discretization, these coordinates can be treated as tokens. The sequence length in this case would be 9N. + +![](images/68bf00eef4f292ec6f6d2b982ffb3ea487e15df8e5bbe5ed3e13d7f0d3653820.jpg) + +
+flowchart + +```mermaid +graph LR + InputMesh["Input Mesh"] -->|"| F| × C_in"| GraphConv["Graph Convolutional Encoder"] + ReconstructedMesh["Reconstructed Mesh"] -->|"| F| × 9"| ResNetDecoder["ResNet Decoder"] + GraphConv -->|"| F| × C_e"| ResidualFaceQuant["Residual Face Quantization Module"] + ResNetDecoder --> SequenceOfFaces["Sequence Of Faces"] + SequenceOfFaces -->|"| F| × C_e"| ResidualFaceQuant + ResidualFaceQuant -->|"| F| ×"| ResidualFaceQuantModule["Residual Face Quantization Module"] + ResidualFaceQuantModule -->|"C_e"| SumResidualFeatures["Sum Residual Features"] + ResidualFaceQuantModule -->|"D × C_e"| Reshape["Reshape"] + Reshape --> FeatureCodebook["Feature Codebook"] + FeatureCodebook --> MeanAcrossSharedVertices["Mean across Shared Vertices"] + MeanAcrossSharedVertices --> SplitFeature["Split Feature"] + SplitFeature -->|"C_e"| SumResidualFeatures +``` +
+ +Figure 3. We employ a graph convolutional encoder to process mesh faces, leveraging geometric neighborhood information to capture strong features representing intricate details of 3D shapes. These features are then quantized into codebook embeddings using residual quantization [27, 38]. In contrast to naive vector quantization, this ensures better reconstruction quality. The quantized embeddings are subsequently sequenced and decoded through a 1D ResNet [22], guided by a reconstruction loss. + +However, we observe two major challenges when using coordinates directly as tokens. First, the sequence lengths become excessively long, as each face is represented by nine values. This length does not scale well with transformer architectures, which often have limited context windows. Second, representing discrete positions of a triangle as tokens fails to capture geometric patterns effectively. This is because such a representation lacks information about neighboring triangles and does not incorporate any priors from mesh distributions. + +To address the aforementioned challenges, we propose to learn geometric embeddings from a collection of triangular meshes, utilizing an encoder-decoder architecture with residual vector quantization at its bottleneck (Fig. 3). + +The network’s encoder E employs graph convolutions on mesh faces, where each face forms a node and neighboring faces are connected by undirected edges. The input face node features are comprised of the nine positionally encoded coordinates of its vertices, face normal, angles between its edges, and area. These features undergo processing through a stack of SAGEConv [20] layers, extracting a feature vector for each face. This graph convolutional approach enables the extraction of geometrically enriched features $z _ { i } \in \mathbb { R } ^ { n _ { \mathrm { z } } }$ for each face, + +$$ +\mathbf {Z} = (z _ {1}, z _ {2}, \dots , z _ {N}) = E (\mathcal {M}), \tag {2} +$$ + +fusing neighborhood information into the learned embeddings. + +For quantization, we employ residual vector quantization (RQ) [38]. We found that using a single code per face is insufficient for accurate reconstruction. Instead, we use a stack of D codes per face. Further, we find that instead of directly using D codes per face, it is more effective to first divide the feature channels among the vertices, aggregate the features by shared vertex indices, and then quantize these vertex-based features, giving $\frac { \mathrm { D } } { 3 }$ codes per vertex, and therefore effectively D codes per face. This leads to sequences that are easier to learn for the transformer trained subsequently (see Tab. 3 and Fig. 10 for comparison). Formally, given a codebook C, RQ with depth D represents features Z as + +$$ +\mathbf {T} = (t _ {1}, t _ {2}, \dots , t _ {N}) = \mathrm{RQ} (\mathbf {Z}; \mathcal {C}, D), \tag {3} +$$ + +$$ +t _ {i} = (t _ {i} ^ {1}, t _ {i} ^ {2}, \dots , t _ {i} ^ {D}), \tag {4} +$$ + +where $t _ { i }$ is a stack of tokens, each token $t _ { i } ^ { d }$ being an index to an embedding $\mathbf { e } ( t _ { i } ^ { d } )$ in the codebook C. + +The decoder then decodes the quantized face embeddings to triangles. First, the stack of D features is reduced to a single feature per face through summation across embeddings and concatenation across vertices, + +$$ +\hat {\mathbf {Z}} = (\hat {z} _ {1}, \dots , \hat {z} _ {N}), \text {with} \hat {z} _ {i} = \oplus_ {v = 0} ^ {2} \sum_ {d = 1} ^ {\frac {D}{3}} \mathbf {e} (t _ {i} ^ {3. v + d}). \tag {5} +$$ + +The face embeddings are arranged in the previously described order, and a 1D ResNet34 decoding head G processes the resulting sequence to output the reconstructed mesh ${ \hat { \mathcal { M } } } = G ( { \hat { \mathbf { Z } } } )$ with 9 coordinates representing each face. We observe that predicting these coordinates as discrete variables, i.e. as a probability distribution over a set of discrete values, leads to a more accurate reconstruction compared to regressing them as real values (Fig. 4). A cross-entropy loss on the discrete mesh coordinates and a commitment loss for the embeddings guides the reconstruction process. More details can be found in supplementary. + +![](images/ee8d3956b2fa1fe0a598529c608460da65258fd9b5188ac3e5354bbc23759131.jpg) + +
+natural_image + +Three 3D wireframe models of a chair: one with real-valued outputs, one with discrete outputs, and the ground truth (no text or symbols on the models themselves) +
+ +Figure 4. Our method utilizes a ResNet [22] decoder that outputs mesh faces as a distribution over discretized coordinate values (center), as opposed to regression of continuous values (left). This significantly reduces floating face artifacts, leading to reconstructions that more closely resemble the ground truth (right). + +After training, the graph encoder E and codebook C are incorporated into the transformer training, using T from Eq. 3 as the token sequence. With $| \mathbf { T } | = D N$ , this sequence is more concise than the naive 9N-length tokenization when $D \ < \ 9 .$ Thus, we obtain geometrically rich embeddings with shorter sequence lengths, overcoming our initial challenges and paving the way for efficient mesh generation. + +## 3.2. Mesh Generation with Transformers + +![](images/72cb966cd94dd8b5076080c802a06cda11de1a0168b09a46a1aa9944576b1ec9.jpg) + +
+flowchart + +```mermaid +graph LR + A["Face Graph + Input Features"] --> B["Graph Convolutional Encoder"] + B --> C["Residual Face Quantization Module"] + C --> D["Sequence & Flatten"] + D --> E["GPT-Style Transformer"] + E --> F["Predicted Codebook Indices"] + F --> G["GT Codebook Indices"] + G --> H["CE Loss"] +``` +
+ +Figure 5. We employ a transformer to generate mesh sequences as token indices from a pre-learned codebook vocabulary. During training, a graph encoder extracts features from mesh faces, which are quantized into a set of face embeddings. These embeddings are flattened, bookended with start and end tokens, and fed into a GPTstyle transformer. This decoder predicts the subsequent codebook index for each embedding, optimized via cross-entropy loss. + +We employ a decoder-only transformer architecture from the GPT family of models to predict meshes as sequences of indices from the learned codebook in Sec. 3.1. The input to this transformer consists of embeddings $\mathbf { e } ( t _ { i } ^ { d } )$ extracted from the mesh M using the GraphConv encoder E and quantized using RQ (Eq. 3). The embeddings are prefixed and suffixed with a learned start and end embedding. Additionally, learned discrete positional encodings are added, indicating the position of each face in the sequence and the index of each embedding within the face. The features then pass through a stack of multiheaded self-attention layers, where the transformer is trained to predict the codebook index of the next embedding in the sequence (Fig. 5). Essentially, we maximize the log probability of the training sequences with respect to the transformer parameters θ, + +$$ +\prod_ {i = 1} ^ {N} \prod_ {d = 1} ^ {D} p (t _ {i} ^ {d} \mid \mathbf {e} (t _ {< i} ^ {d}), \mathbf {e} (t _ {i} ^ {< d}); \theta). \tag {6} +$$ + +Once the transformer is trained, it can autoregressively generate a sequence of tokens, starting with a start token and continuing until a stop token is encountered using beam sampling. The codebook embeddings indexed by this sequence of tokens is then decoded by decoder G to produce the generated mesh. As this output initially forms a ‘triangle soup’ with duplicate vertices for neighboring faces, we apply a simple post-processing operation to merge close vertices (e.g., with MeshLab), to yield the final mesh. + +## 3.3. Implementation Details + +In learning the triangle vocabulary, our residual quantization layer features a depth of 2, yielding D = 6 embeddings per face, each with dimension 192. The codebook is dynamically updated using an exponential moving average of the clustered features. Following [29], we incorporate stochastic sampling of codes and employ a shared codebook across all levels. The decoder predicts the coordinates of the faces across 128 classes, resulting in a discretization of space to 1283 possible values. This encoder-decoder network is trained using 2 A100 GPUs for ≈ 2 days. + +For our transformer, we use a GPT2-medium model, equipped with a context window of up to 4608 embeddings. The model is trained on 4 A100 GPUs, for ≈ 5 days. + +Both the encoder-decoder network and the transformer are written using the Pytorch [46] and are trained utilizing the ADAM optimizer [28]. We set the learning rate at 1 × $1 0 ^ { - 4 }$ and use an effective batch size of 64. + +## 4. Experiments + +## 4.1. Dataset and Metrics + +Data. We present our results on the ShapeNetV2 dataset. Both the encoder-decoder network and the GPT model are trained across all 55 categories of this dataset. Additionally, we fine-tune the GPT model specifically on four categories: Chair, Table, Bench, and Lamp. The results are reported on these categories. During training, we employ augmentation techniques including random shifts and random scaling to enhance the diversity of the training meshes. Similar to Polygen [43], we also apply planar decimation to further augment the shapes. To ensure that the entire mesh fits into the transformer’s context window, we select only those meshes for training that have fewer than 800 faces post-decimation. Detailed information regarding the augmentation processes, decimation techniques, and data splits are provided in the supplementary material. + +Metrics. Evaluating the unconditional synthesis of 3D shapes presents challenges due to the absence of direct ground truth correspondence. Hence, we utilize established metrics for assessment, consistent with previous works [37, 67, 68]. These include Minimum Matching Distance (MMD), Coverage (COV), and 1-Nearest-Neighbor Accuracy (1-NNA). For MMD, lower is better; for COV, higher is better; for 1-NNA, 50% is the optimal. We use a Chamfer Distance (CD) distance measure for computing these metrics in 3D. More details about these metrics can be found in the supplementary. + +The aforementioned metrics effectively measure the quality of shapes but do not address the visual similarity of the generated meshes to the real distribution. To assess this aspect, we render both the generated meshes and the + +
ClassMethodCOV↑MMD↓1-NNAFID↓KID↓|V||F|
ChairAtlasNet [18]9.034.0595.13170.710.16925004050
BSPNet [7]16.483.6291.7546.730.0306731165
Polygen [43]31.224.4193.5661.100.043248603
GET3D [14]40.853.5683.0481.450.0541372527457
GET3D*38.753.5784.0778.290.065199399
MeshGPT43.283.2975.5118.460.010125228
TableAtlasNet [18]7.163.8596.30161.380.15025004050
BSPNet [7]16.833.1493.5830.780.017420699
Polygen [43]32.993.0088.6538.530.029147454
GET3D [14]41.702.7885.5493.930.0761376727537
GET3D*37.952.8581.9350.460.037199399
MeshGPT45.682.3672.886.240.00299187
BenchAtlasNet [18]20.532.4790.58189.390.16325004050
BSPNet [7]28.742.0588.4459.110.030457756
Polygen [43]51.921.9776.9849.340.031172430
MeshGPT55.231.4468.248.720.001159291
LampAtlasNet [18]19.974.6891.85177.910.13925004050
BSPNet [7]18.385.3293.13112.650.0775871011
Polygen [43]47.864.1881.4252.480.025185558
MeshGPT53.883.9465.7319.910.004150288
+ +Table 1. Quantitative comparison on the task of unconditional mesh generation on a subset of categories from the ShapeNet [5] dataset. GET3D\* refers to meshes simplified to 400 faces using QEM [15]. MMD values are multiplied by 103. We outperform the baselines on shape quality, visual and compactness metrics. + +ShapeNet meshes as images from eight different viewpoints using Blender, applying a metallic material to emphasize the geometric structures. Subsequently, we calculate the FID (Frechet Inception Distance) and KID (Kernel Incep-´ tion Distance) scores for these image sets. For both FID and KID, lower scores indicate better performance. We further report compactness as the average number of vertices and faces in the generated meshes. + +## 4.2. Results + +We benchmark our approach against leading mesh generation methods: Polygen [43], which generates polygonal meshes by first generating vertices followed by faces conditioned on the vertices; BSPNet [7], which represents a mesh through convex decompositions; and AtlasNet [18], which represents a 3D mesh as a deformation of multiple 2D planes. We additionally compare with a state-of-the-art neural field-based method, GET3D [14], that creates shapes as 3D signed distance fields (SDFs) from which a mesh is extracted by differentiable marching tetrahedra. For BSP-Net and AtlasNet, which are built on autoencoder backbones, we follow [1] to fit a Gaussian mixture model with 32 components to enable unconditional sampling of shapes. + +As shown in Fig. 6, Fig. 7 and Tab. 1, our method outperforms all baselines in all four categories. Our method can generate sharp and compact meshes with high geometric details. Compared to Polygen, our approach creates shapes with more intricate details. Additionally, Polygen’s separate training for vertex and face models, with the latter only exposed to ground truth vertex distributions, makes it more susceptible to error accumulation during inference. Atlas-Net often suffers from folding artifacts, resulting in lower diversity and shape quality. BSPNet’s use of BSP tree of planes tends to produce blocky shapes with unusual triangulation patterns. GET3D generates good high-level shape structures, but over-triangulated and with imperfect flat surfaces. Simplifying GET3D-generated meshes with algorithms such as QEM [15] results in a loss of fine structures. + +![](images/76068c6dfb1898f16de88ae3f72de3ea3ccab75df28511e16f84b9e6bd9d5116.jpg) + +
+text_image + +GT Samples +AtlasNet BSPNetGET3DGET3D-QEMPolygenOurs +100000000000000000000000000000000000000000000000000000000000000000000000000 +
+ +Figure 6. Qualitative comparison of Chair and Table meshes from ShapeNet [5]. Our approach produces compact meshes with sharp geometric details. In contrast, baselines often either miss these details, produce over-triangulated meshes, or output too simplistic shapes. + +User Study. We further conducted a user study, in Tab. 2, to assess generated mesh quality. 49 participants were shown pairs of four meshes, randomly selected from our method and each baseline method. Additionally, users were presented with ground truth ShapeNet meshes for comparison. Participants were asked their preference between our method and the baseline in terms of both overall shape quality and similarity of triangulation patterns to the ground truth meshes. This resulted in 784 total question responses. Our method was significantly preferred over Atlas-Net, Polygen, and BSPNet in both shape and triangulation quality. Moreover, a majority of users (68%) favored our method over neural field-based GET3D in shape quality, with even higher preference (73%) for triangulation quality. This underscores our ability to generate high-quality meshes that align with human users’ preferences. Further user study details are provided in the supplemental. + +![](images/45b493818f6537a57fadcb2454130c2c50c5a184adc6d1ed712e535a4a05c269.jpg) + +
+text_image + +GT Samples +AtlasNet BSPNet Polygen Ours +
+ +Figure 7. Qualitative comparison of Bench and Lamp meshes from the ShapeNet [5] dataset. Compared to baselines, our method produces valid meshes with high geometric fidelity. + +
PreferenceAtlasNet [18]BSPNet [7]Polygen [43]GET3D [14]
Our Shape82.65%78.57%85.71%68.37%
Our Triangulation84.69%71.43%84.69%73.47%
+ +Table 2. Percentage of users who prefer our method over the baselines in terms of shape quality and the triangulation quality. Our generated meshes are preferred significantly more often. + +
MethodCOV↑MMD↓1-NNAFID↓KID↓
w/o Learned Tokens27.504.5193.1540.200.024
w/o Encoder Features39.243.4384.4830.350.017
w/o Pretraining36.973.7384.6927.540.014
w/o Sequence Compression30.984.1588.9838.760.023
w/o per Vertex Quantization23.575.4998.3574.940.050
MeshGPT43.283.2975.5118.460.010
+ +Table 3. Ablations of our design choices on the Chair category of the ShapeNet [5] dataset. As highlighted by the drop in performance by removing any of them, each of these contribute to the final method. + +Shape Novelty Analysis. We investigate whether our method can generate novel shapes that extend beyond the training dataset, ensuring the model is not merely retrieving existing shapes. Following the methodology in previous studies [13, 24], we generate 500 shapes using our model. For each generated shape, we identify the top three nearest neighbors from the training set based on Chamfer Distance (CD). To ensure a fair distance computation, accounting for potential discrepancies due to scale or shift in the augmented generations, we normalize all generated and train shapes to be centered within [0, 1]3. + +![](images/c529395af6d980051ddecada4916f283df5a930f3e3dfe3b5e19f6ee6a2f96a9.jpg) + +
+bar + +| Chamfer Distance (x10^3) | Proportion of Generated Shapes | +| --- | --- | +| 0 | ~0.5 | +| 1 | ~4.5 | +| 2 | ~6.5 | +| 3 | ~3.5 | +| 4 | ~2.5 | +| 5 | ~1.5 | +| 6 | ~1.5 | +| 7 | ~1.5 | +| 8 | ~1.0 | +| 9 | ~0.5 | +| 10+ | ~4.5 | +
+ +Figure 8. Shape novelty analysis on ShapeNet [5] chair category. We show the 3 nearest neighbors in terms of Chamfer Distance (CD) for a generated shape (top). We also plot the distribution of 500 generated chair samples from our method and their closeness to training distribution. Our method can generate shapes that are similar (low CD) as well as different (high CD) from the training distribution, with shapes at the 50th percentile looking different from closest train shape. +![](images/5b3a33b4221fb57854918e5b77130294ccf40f3adc775ccf038ce130eb125645.jpg) + +
+natural_image + +3D model of wooden furniture with various shapes and layouts, including chairs, tables, and blocks (no text or symbols) +
+ +Figure 9. Given a partial mesh, our method can infer multiple possible shape completions. + +Fig. 8 displays the most similar shapes from the train set corresponding to a sample generated by our model. We conduct a detailed analysis of the shape similarity distribution between the retrieved and generated shapes on the + +Chair category in Fig. 8. The CD distribution reveals that our method not only covers shapes in the training set, indicated by low CD values, but also successfully generates novel and realistic-looking shapes, indicated by high CD values. In the supplemental, we present further analysis of the novelty of all meshes generated by our method, which are featured in the figures of this paper. + +Shape Completion. Our model can infer multiple possible completions for a given partial shape, leveraging its probabilistic nature to generate diverse shape hypotheses. Fig. 9 illustrates examples of chair and table completions. + +## 4.2.1 Ablations + +In Tab. 3, we show a set of ablations on the task of unconditional mesh generation on ShapeNet Chair category. Further ablations are detailed in the supplementary. + +![](images/c106cef48f10754a10c06872decaa8bd01f67062fb929d7f25e9990aa5bda13f.jpg) +w/o Encoder Features +w/o Pretraining + +w/o Learned Tokens +![](images/ad9fafe54b97a2db08791ed1d9d6d5fc1f9740c532fa025b564f6f99b7850f35.jpg) + +
+natural_image + +3D illustration of a wooden chair with vertical supports and a curved top (no text or symbols) +
+ +w/o Sequence Compression + +![](images/7cd31a0f47e47c84d92e08dca904b6c960a3e46e34d19fe04d035df0379c8406.jpg) + +
+natural_image + +3D illustration of a wooden chair with geometric panel design (no text or symbols) +
+ +w/o per Vertex Quantization + +![](images/a1fcd1221add5906336612abb60dd62afe146092c590f7e919b6ddaee9d492a5.jpg) + +
+natural_image + +3D illustration of a wooden chair with yellow cushion and side legs (no text or symbols) +
+ +Ours (Complete) +Figure 10. Ablation over our method’s components. Naive tokenization (w/o Learned Tokens) and naive per face quantization (w/o per-vertex quantization) markedly diminishes shape quality. Longer sequences without sequence compression (w/o Sequence Compression) lead to the model forgetting the context and repeating shape elements in the output. + +Do learned geometric embeddings help? Using our geometric embeddings in vocabulary learning significantly improves over naive coordinate tokenization (w/o Learned Tokens), as shown in Tab. 3 and Fig. 3. + +Does sequence length compression help? As evidenced by Tab. 3 and Fig. 3, a model with a shorter sequence length performs better than without (w/o Sequence Compression), as shorter sequence lengths fit transformer context windows better. Visually, with longer sequences, shapes exhibit repeating structures due to limited context. + +What is the effect of aggregation and quantization across vertex indices instead of faces? As discussed in Section 3, an alternative to having embeddings aggregated and quantized across vertex indices, is to simply have the same number of embeddings directly per face (w/o per Vertex Quantization). In Tab. 3, we observe that this makes sequences much harder to learn with the transformer. + +Do features from graph convolutional encoder help in mesh generation? An alternative to using embeddings from the graph encoder and the codebook is to only use the codebook indices of these tokens as input to the transformer, and let the transformer learn the discrete token embeddings (w/o Encoder Features). While the transformer is able to still learn meaningful embeddings, these are still not as effective as using graph encoder features. + +What is the effect of large-scale shape pretraining? Tab. 3 shows that training only on shapes from individual categories (w/o Pretraining) leads to overfitting and subobtimal performance, in contrast to pre-training our GPT transformer on all ShapeNet train shapes. + +Limitations. MeshGPT significantly advances direct mesh generation but faces several limitations. Its autoregressive nature leads to slower sampling performance, with mesh generation times taking 30 to 90 seconds. Despite our learned tokenization approach reducing sequence lengths, which suffices for single object generation, it may not be as effective for scene-scale generation, suggesting an area for future enhancement. Moreover, our current computational resources limit us to using a GPT2-medium transformer, which is smaller than more sophisticated models like Llama2 [58]. Given that larger language models benefit from increased data and computational power, expanding these resources could significantly boost MeshGPT’s performance and capabilities. + +## 5. Conclusion + +We have introduced MeshGPT, a novel shape generation approach that outputs meshes directly as triangles. We learn a vocabulary of geometric embeddings over a distribution of meshes, over which a transformer is trained to predict meshes autoregressively as a sequence of triangles. In contrast to existing mesh generation approaches, our method generates clean, coherent meshes which are compact and follow the triangulation patterns in real data more closely. We believe that MeshGPT will not only elevate the current landscape of mesh generation but also inspire new research in the area, offering a unique alternative to the more commonly explored representations for 3D content creation. + +## Acknowledgements + +This work was funded by AUDI AG. Matthias Nießner was supported by the ERC Starting Grant Scan2CAD (804724). Angela Dai was supported by the Bavarian State Ministry of Science and the Arts coordinated by the Bavarian Research Institute for Digital Transformation (BIDT). We would like to thank Ziya Erkoc¸, Quyet-Chien Nguyen, Haoxuan Li and Artem Sevastopolsky for the helpful discussions. + +## References + +[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40–49. PMLR, 2018. 2, 5 +[2] Henry Blumberg. Hausdorff’s grundzuge der mengenlehre.¨ 1920. 12 +[3] Andrew Brock, Theodore Lim, James M Ritchie, and Nick Weston. Generative and discriminative voxel modeling with convolutional neural networks. arXiv preprint arXiv:1608.04236, 2016. 1, 2 +[4] Ruojin Cai, Guandao Yang, Hadar Averbuch-Elor, Zekun Hao, Serge Belongie, Noah Snavely, and Bharath Hariharan. Learning gradient fields for shape generation. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5826–5835, 2021. 1, 2, 5 + +## Appendix + +In this supplementary document, we discuss additional details about our method MeshGPT. We provide implementation details of our method, loss functions, and the baselines in Section B. Additional details about the user study are provided in Section C. We also provide further qualitative and quantitative results (Section E), including a shape novelty analysis (Section D) for shapes from the main paper. We further encourage the readers to check out the supplemental video for a summary of the method and an overview of results. + +## A. Data + +Selection. We use the ShapeNetV2 [5] dataset for all our experiments. We first apply planar decimation to each shape using Blender [10], with the angle tolerance parameter α set within [1, 60]. The impact of this decimation is assessed by calculating the Hausdorff distance [2] between the decimated and original shapes. We then choose, for each original shape, the decimated version with the Hausdorff distance closest to, but below, a pre-set threshold $\delta _ { \mathrm { h a u s d o r f f } } .$ Shapes with more than 800 faces are excluded, resulting in a final count of 28980 shapes across all categories. The Chair, Table, Bench, and Lamp categories are further divided into a 9:1 train-test split. All shapes from rest of the categories are used for pretraining phase, while only the training subset from specific categories is used for pretraining and finetuning. All shapes are normalized to be centered at the origin and scaled to ensure the longest side is of unit length. + +Augmentation. During the training of both the encoderdecoder and the transformer, multiple augmentation techniques are applied to all train shapes. Scaling augmentation, ranging from 0.75 to 1.25, is independently applied across each axis. Post-scaling, meshes are resized to keep the longest side at unit length. Additionally, jitter-shift augmentation in the range of [−0.1, 0.1] is used, adjusted to maintain the mesh within the unit bounding box around the origin. We also implement varying levels of planar decimation for training shapes, provided the distortion remains below $\delta _ { \mathrm { h a u s d o r f f } } .$ + +## B. Method Details + +## B.1. Architecture + +The architecture of our encoder-decoder network is elaborated in Fig. 14. The encoder comprises a series of SAGE-Conv [20] graph convolution layers, processing the mesh in the form of a face graph. For each graph node, input features include the positionally encoded 9 coordinates of the face triangle, its area, the angles between its edges, and the normal of the face. The decoder is essentially a 1D + +ResNet-34 [22] network, applied to the face features interpreted as a 1D sequence. It outputs logits corresponding to the 9 discrete coordinates of each face triangle, which are discretized within a $1 2 8 ^ { 3 }$ space. The codebook C has a size of 16384. The architecture of the transformer is simply a GPT-2 medium architecture, i.e. 24 multi-headed self attention layers, 16 heads, 768 as feature width, with context length of 4608. + +## B.2. Residual Vector Quantization + +Fundamentals. For quantization, we employ residual vector quantization (RQ) [29, 38]. RQ discretizes a vector z with a stack of D ordered codes. Starting with the $0 ^ { \mathrm { t h } }$ residual $\mathbf { r } ^ { 0 } = \mathbf { z } ,$ , RQ recursively computes $t ^ { d }$ as the code of the residual $\mathbf { r } ^ { d - 1 }$ , and the next residual $\mathbf { r } ^ { d }$ as + +$$ +t ^ {d} = \mathcal {Q} \left(\mathbf {r} ^ {d - 1}; \mathcal {C}\right) \tag {7} +$$ + +$$ +\mathbf {r} ^ {d} = \mathbf {r} ^ {d - 1} - \mathbf {e} (t ^ {d}) \tag {8} +$$ + +where $\mathcal { Q } ( \mathbf { z } ; \mathcal { C } )$ denotes vector quantization of z with codebook ${ \mathcal { C } } ,$ , and $\mathbf { e } ( t ^ { d } )$ is the embedding in the codebook C. Further, we define + +$$ +\hat {\mathbf {z}} ^ {(d)} = \sum_ {1} ^ {d} \mathbf {e} (t ^ {d}) \tag {9} +$$ + +as the partial sum of up to d code embeddings, and $\hat { \mathbf { z } } = \hat { \mathbf { z } } ^ { D }$ is the quantized vector of z. The recursive quantization of RQ thus approximates the vector z in a coarse-to-fine manner [29]. The commitment loss can now be defined between vector z and its quantization zˆ as + +$$ +\mathcal {L} _ {\text {commit}} (\mathbf {z}, \hat {\mathbf {z}}) = \sum_ {d = 1} ^ {D} \| \mathbf {z} - \mathrm{sg} [ \hat {\mathbf {z}} ^ {(d)} ] \| _ {2} ^ {2} \tag {10} +$$ + +where sg denotes the stop gradient operation. + +Per Vertex Residual Vector Quantization. Instead of directly applying RQ, for a face feature $\mathbf { z _ { i } }$ extracted by the graph encoder, we first split this 576 dimension face feature $\mathbf { z _ { i } }$ into 3 features, $( \mathbf { z } _ { i } ^ { 1 } , \mathbf { z } _ { i } ^ { 2 } , \mathbf { z } _ { i } ^ { 3 } )$ ), each of 192 dimensions representing the features of the face triangle’s 3 vertices. The features the fall on vertices that are shared across faces are averaged. On these per vertex index feature $\mathbf { z } _ { i } ^ { j }$ , RQ quantizes them into a stack of $\textstyle { \frac { D } { 3 } }$ features, + +$$ +\mathrm{RQ} (\mathbf {z _ {i}}; \mathcal {C}, D) = (\mathrm{RQ} (\mathbf {z _ {i} ^ {1}}; \mathcal {C}, \frac {D}{3}), \dots , \mathrm{RQ} (\mathbf {z _ {i} ^ {3}}; \mathcal {C}, \frac {D}{3})) \tag {11} +$$ + +for codebook C, with + +$$ +\mathrm{RQ} (\mathbf {z} _ {\mathbf {i}} ^ {\mathbf {j}}; \mathcal {C}, \frac {D}{3}) = (t _ {i} ^ {2 j - \frac {D}{3} + 1}, t _ {i} ^ {2 j - \frac {D}{3} + 2}, \dots , t _ {i} ^ {2 j}), \tag {12} +$$ + +where $t _ { i } ^ { d }$ is the index to the embedding $\mathbf { e } ( t _ { i } ^ { d } )$ in the codebook C. Taken together for each vertex, these form a stack of D features, + +$$ +\mathrm{RQ} (\mathbf {z _ {i}}; \mathcal {C}, D) = (t _ {i} ^ {1}, t _ {i} ^ {2}, \dots , t _ {i} ^ {D}) = t _ {i}. \tag {13} +$$ + +![](images/22c1035334c0e2d06f3f6dff66da36e08b29b61356c3f3ee05ec77a5c69fdd7e.jpg) + +
+natural_image + +Collection of 3D architectural and furniture models including wooden chairs, tables, benches, and decorative objects (no text or symbols) +
+ +Figure 11. Additional novel shapes on Chairs, Tables, Benches and Lamps generated by our method. + +Thus, the residual quantization for the features extracted for all the N faces of the mesh $\mathbf { Z } = ( z _ { 1 } , z _ { 2 } , \ldots , z _ { N } )$ is given as + +$$ +\mathrm{RQ} (\mathbf {Z}; \mathcal {C}, D) = \mathrm{RQ} (\mathbf {z _ {1}} \dots \mathbf {z _ {N}}; \mathcal {C}, D) \tag {14} +$$ + +$$ +\mathrm{RQ} (\mathbf {z _ {1}} \dots \mathbf {z _ {N}}; \mathcal {C}, D) = (t _ {0}, t _ {1}, \dots , t _ {N}). \tag {15} +$$ + +Fig. 16 gives an intuition on why ‘per vertex’ tokenization is better than ‘per face’ tokenization, with ablations in the main paper confirming it. + +## B.3. Loss Functions + +Vocabulary Learning. Let $\mathcal { P } _ { n i j k }$ be the predicted probability distribution over the discrete coordinates, where n is the face index, i is the vertex index inside the face, $j$ is the coordinate’s axis index $( x , y \ \mathrm { o r } \ z )$ , and k goes over the discretized positions $\in \{ 1 , 2 , 3 , \ldots , 1 2 8 \}$ . If $V _ { n i j }$ is the target discretized position, then the reconstruction loss for the encoder-decoder network is given as + +$$ +\mathcal {L} _ {\text {recon}} = \sum_ {n = 1} ^ {N} \sum_ {i = 1} ^ {3} \sum_ {j = 1} ^ {3} \sum_ {k = 1} ^ {1 2 8} \mathrm{w} _ {n i j k} \log \mathcal {P} _ {n i j k} \tag {16} +$$ + +with + +$$ +\mathrm{w} _ {n i j k} = \text {smooth} \left(\text {one - hot} _ {1 2 8} \left(V _ {n i j}\right)\right) \tag {17} +$$ + +is a smoothening kernel applied across the one-hot probability distribution over the targets, encouraging physically close coordinates to be penalized less. The loss over the encoder-decoder network is the sum of ${ \mathcal { L } } _ { \mathrm { r e c o n } }$ and $\mathcal { L } _ { \mathrm { c o m m i t } }$ previously described. + +Transformer. Given a target sequence $\begin{array} { r l } { \mathbf T } & { { } = } \end{array}$ $( t _ { 0 } , t _ { 1 } , \ldots , t _ { N } )$ with $\begin{array} { c c l } { t _ { i } } & { = } & { ( t _ { i } ^ { 1 } , \bar { t } _ { i } ^ { 2 } , \dots , \bar { t } _ { i } ^ { D } ) } \end{array}$ , and $s _ { i } ^ { j } \mathrm { i s }$ the corresponding predicted sequence element, then the transformer is trained with the loss + +![](images/af8b3cd584542eb6776b8e675298e42cc5c1a00283f7ad4d41092a1e2cc3a20a.jpg) + +
+natural_image + +Grid of 3D-rendered wooden chairs with varying colors and line textures, no text or symbols present. +
+ +Generated Shape +Most similar shapes retrieved from training set + +![](images/d00aabe098c8a3f3b7dac3186467ea197ed472f32e2fee65cd05d4e034e6f1e2.jpg) + +
+natural_image + +Collection of 3D-rendered wooden table and chair models in various colors, showing different shapes and sizes (no text or symbols) +
+ +Generated Shape +Most similar shapes retrieved from training set +Figure 12. Shape novelty analysis on ShapeNet [5] chair and table category for shapes generated by our method shown in main paper. We show the 3 nearest neighbors in terms of Chamfer Distance (CD) for a generated shape. Shapes are scaled to a unit length along all axes to account for augmented generations before computing CD. + +$$ +\mathcal {L} _ {\mathrm{recon}} = \sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {D} \sum_ {k = 1} ^ {| \mathcal {C} |} \log p (s _ {i} ^ {k} = t _ {i} ^ {j}). \tag {18} +$$ + +## B.4. Baselines + +We utilize the official implementations for BSPNet [7], AtlasNet [18], and GET3D [14]. For Polygen [43], we reimplement it following the details in their paper. To align its architecture with our method, we employ the same GPT2- medium architecture for the vertex model in Polygen. Additionally, mirroring our approach, Polygen undergoes pretraining on all categories and is finetuned for each evaluated category, applying the same train-time augmentations as used in our method. + +## C. User Study Details + +We develop a Django-based web application for the user study. In Fig. 15, we show the interface for the questionnaire. We randomly select 16 pairs of meshes from each baseline and our method across the Chair and Table categories, half of which are used for a question on preference based on shape quality, and the other half for preference based on triangulation quality. After the samples are prepared, we ask the users to pick the sample which they prefer more based on the question. To avoid biases in this user study, we shuffle the pairs so that there is no positional hint to our method. We also show a collection of ground-truth meshes to the user for them to get an idea of the real distribution. In the end, we gather 784 responses from 49 participants to calculate the preferences. + +![](images/95d2fd7dc948e6e373c37d2368438952d9cd7875e959f9b4d76310b4db266b77.jpg) + +
+text_image + +Generated Shape +Most similar shapes retrieved from training set +
+ +![](images/7e8ea87daf63578d77b643fe27855345f3b330fc8382177835e2da7c30cd4d4c.jpg) + +
+text_image + +Generated Shape +Most similar shapes retrieved from training set +
+ +Figure 13. Shape novelty analysis on ShapeNet [5] bench and lamp category for shapes generated by our method shown in main paper. We show the 3 nearest neighbors in terms of Chamfer Distance (CD) for a generated shape. Shapes are scaled to a unit length along all axes to account for augmented generations before computing CD. + +![](images/4ec5ee7755bd6f8b5c1ddbe9d84366f8031e24b91ec1d239bef0eaaa83da18f7.jpg) + +
+flowchart + +```mermaid +graph LR + InputMesh["Input Mesh"] -->|"F| x196"| GraphConvEncoder["Graph Conv Encoder"] + GraphConvEncoder -->|"F| x576"| ResidualQuantizationModule["Residual Face Quantization Module"] + SequenceOfFaces["Sequence Of Faces"] -->|"F| x576"| ResNet34Decoder["ResNet34 Decoder"] + ResNet34Decoder --> ReconstructedMesh["Reconstructed Mesh"] +``` +
+ +Figure 14. Our encoder-decoder network features an encoder with SAGEConv [20] layers processing mesh faces as a graph. Each node inputs positionally encoded face triangle coordinates, area, edge angles, and normal. The decoder, a 1D ResNet-34 [22], interprets face features as a sequence, outputting logits for the discretized face triangle coordinates in a 1283 space. + +## D. Shape Novelty Analysis + +Fig. 12 and 13 displays the top-3 most similar shapes from the train set corresponding to all samples used in the main paper that were generated by our model. These nearest neighbor shapes are identified based on Chamfer Distance (CD). To ensure a fair distance computation, accounting for potential discrepancies due to scale or shift in the augmented generations, we normalize all generated and train shapes to be centered within [0, 1]3 and scaled to the extremes of this cube. + +## E. Additional Results + +Metrics. Following recent works for unconditional shape generation [13, 66, 67] for calculating the shape metrics we define + +$$ +\begin{array}{l} \mathrm{MMD} (S _ {g}, S _ {r}) = \frac {1}{| S _ {r} |} \sum_ {Y \in S _ {r}} \min _ {X \in S _ {g}} D (X, Y), \\ \operatorname{COV} (S _ {g}, S _ {r}) = \frac {| \{\operatorname{argmin} _ {Y \in S _ {r}} D (X , Y) | X \in S _ {g} \} |}{| S _ {r} |}, \\ 1 \text {-NNA} (S _ {g}, S _ {r}) = \frac {\sum_ {X \in S _ {g}} \mathbb {1} _ {X} + \sum_ {Y \in S _ {r}} \mathbb {1} _ {Y}}{| S _ {g} | + | S _ {r} |}, \\ \mathbb {1} _ {X} = \mathbb {1} [ N _ {X} \in S _ {g} ], \\ \mathbb {1} _ {Y} = \mathbb {1} [ N _ {Y} \in S _ {r} ], \\ \end{array} +$$ + +where in the 1-NNA metric N is a point cloud that is closest to X in both generated and reference dataset, i.e., + +$$ +N _ {X} = \underset {K \in S _ {r} \cup S _ {g}} {\operatorname{argmin}} D (X, K) +$$ + +![](images/9c8f17f2ed164e56329aa2345718e115db7f4d94e1cb5a94b39d1e155c6a929e.jpg) + +
+text_image + +I filter your name +were are some artist designed mesh of the category chair: +Please answer the following questions keeping these in mind. +• which of the objects is a better quality mesh for this category? +• which of the objects better matches the quality of artist meshes in this category! +
+ +Figure 15. User study interface. We show users a set of random ground-truth shapes for a category and then ask users for shape quality and triangulation preference among meshed generated by two methods. + +
VariantTriangle Accuracy (%) ↑Cross-Entropy ↓
w/o Positional Encoding79.330.2484
w/o Output Discretization22.030.5705
w/o Residual Quantization1.294.6679
w/o per Vertex Quantization98.640.1413
w/ PointNet Encoder88.730.1896
w/ GAT [60] Encoder86.140.2015
w/ EdgeConv [61] Encoder91.230.1702
w/ ResNet19 Decoder96.290.1492
w/ PointNet Decoder95.470.1528
MeshGPT98.490.1473
+ +Table 4. Ablations of our design choices for the encoder-decoder network on the Chair category of the ShapeNet [5] dataset. + +We use a Chamfer Distance (CD) distance measure $D ( X , Y )$ for computing these metrics in 3D. To evaluate these point-based measures, we sample 2048 points randomly from all baseline outputs; and use 6000, 1200, 1000, 8000 generated shapes from chair, bench, lamp and table categories. + +Qualitative Results. Fig. 11 shows more unconditional generations from our model across different ShapeNet categories. + +Encoder-Decoder Ablations. In Tab. 4, we show a set of ablations on the design choice for our encoder-decoder network used for learning the triangle embeddings. We measure the performance in terms of triangle accuracy, which measures average accuracy with which all 9 coordinates of faces are correctly predicted, and the cross-entropy loss on the test set. + +![](images/93ed53b8c4f1a77bc0a632004090c5a0533351b6ab70863f6b98e63b4c7c521a.jpg) + +
+text_image + +Sequence of Faces = (F₁, F₂) = ((V₁, V₂, V₃), (V₂, V₄, V₃)) +If 6 tokens are assigned per face: +Sequence: (t₁¹, t₁², t₁³, t₁⁴, t₁⁵, t₁⁶, t₂¹, t₂², t₂³, t₂⁴, t₂⁵, t₂⁶) +If 2 tokens are assigned per vertex: +Sequence: (t₁¹, t₁², t₁³, t₁⁴, t₁⁵, t₁⁶, t₂¹, t₂², t₂³, t₂⁴, t₂⁵, t₂⁶) +Repetition of tokens +
+ +Figure 16. The effectiveness of per-vertex quantization over perface quantization can be understood through an example where two faces share an edge as shown above. With per-face tokenization assigning 6 tokens per face, the sequence yields 12 unique tokens. In contrast, per-vertex tokenization leads to repeated tokens in the sequence due to shared vertices between faces. This repetition makes the sequence easier for the transformer to learn compared to a wholly unique sequence per face, especially when both sequences are of equal length. + +We evaluate the effect of various choices – how much does the positional encoding at input help, effect of using continuous predictions instead of discrete as outputs, using vector quantization (1 token per face) instead of residual quantization (D tokens per face), encoder architecture as a point encoder, or different graph convolution operators, and decoder architecture as either ResNet19 or Point-Net decoder. Note that even though for encoder-decoder reconstruction, ‘w/o per Vertex Quantization’ performs best, this variant works significantly worse than with per Vertex Quantization, as shown in the main paper. Fig. 16 describes an intuition of why the embeddings from this variant are more transformer friendly. \ No newline at end of file diff --git a/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_content_list.json b/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7da5a5812d8675115c456a2789fc12c756799925 --- /dev/null +++ b/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_content_list.json @@ -0,0 +1,2364 @@ +[ + { + "type": "text", + "text": "MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers", + "text_level": 1, + "bbox": [ + 112, + 92, + 854, + 113 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yawar Siddiqui1 Antonio Alliegro2 Alexey Artemov1", + "bbox": [ + 254, + 142, + 702, + 160 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tatiana Tommasi2 Daniele Sirigatti3 Vladislav Rosov3 Angela Dai1 Matthias Nießner1", + "bbox": [ + 106, + 160, + 841, + 179 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Technical University of Munich1 Politecnico di Torino2 AUDI AG3", + "bbox": [ + 209, + 185, + 754, + 203 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3545e4e678461da72e464d2647815436fc502f261b64157952c11a9676ecbf7e.jpg", + "image_caption": [ + "Figure 1. Our method creates triangle meshes by autoregressively sampling from a transformer model that has been trained to produce tokens from a learned geometric vocabulary. These tokens can then be decoded into the faces of a triangle mesh. Our method generates clean, coherent, and compact meshes, characterized by sharp edges and high fidelity." + ], + "image_footnote": [], + "content": "```mermaid\ngraph LR\n A[\"Shape Dataset\"] --> B[\"Face Encoder\"]\n B --> C[\"Embedding Codebook\"]\n C --> D[\"Token Decoder\"]\n D --> E[\"GPT-Style Transformer\"]\n E --> F[\"MeshGPT: Autoregressive Mesh Generation\"]\n```", + "sub_type": "flowchart", + "bbox": [ + 81, + 220, + 883, + 385 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 2, + "bbox": [ + 233, + 449, + 313, + 465 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We introduce MeshGPT, a new approach for generating triangle meshes that reflects the compactness typical of artist-created meshes, in contrast to dense triangle meshes extracted by iso-surfacing methods from neural fields. Inspired by recent advances in powerful large language models, we adopt a sequence-based approach to autoregressively generate triangle meshes as sequences of triangles. Wefirst learn a vocabulary oflatent quantized embeddings, using graph convolutions, which inform these embeddings ofthe local mesh geometry and topology. These embeddings are sequenced and decoded into triangles by a decoder, ensuring that they can effectively reconstruct the mesh. A transformer is then trained on this learned vocabulary to predict the index of the next embedding given previous embeddings. Once trained, our model can be autoregressively sampled to generate new triangle meshes, directly generating compact meshes with sharp edges, more closely imitating the efficient triangulation patterns of human-crafted meshes. MeshGPT demonstrates a notable improvement over state of the art mesh generation methods, with a 9% increase in shape coverage and a 30-point enhancement in FID scores across various categories.", + "bbox": [ + 75, + 481, + 473, + 815 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 2, + "bbox": [ + 76, + 829, + 209, + 845 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Triangle meshes are the main representation for 3D geometry in computer graphics. They are the predominant representation for 3D assets used in video games, movies, and virtual reality interfaces. Compared to alternative 3D shape representations such as point clouds or voxels, meshes provide a more coherent surface representation; they are more controllable, easier to manipulate, more compact, and fit directly into modern rendering pipelines, attaining high visual quality with far fewer primitives. In this paper, we tackle the task of automated generation of triangle meshes, streamlining the process of crafting 3D assets.", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 496, + 450, + 890, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, 3D vision research has seen great interest in generative 3D models using representations such as voxels [3, 62], point clouds [37, 67, 68], and neural fields [14, 19, 31, 35, 41]. However, these representations must then be converted into meshes through a post-process for use in downstream applications, for instance by iso-surfacing with Marching Cubes [36]. Unfortunately, this results in dense, over-tessellated meshes that often exhibit oversmoothing and bumpy artifacts from the iso-surfacing, as shown in Figure 2. In contrast, artist-modeled 3D meshes are compact in representation, while maintaining sharp details with much fewer triangles.", + "bbox": [ + 496, + 571, + 892, + 753 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Thus, we propose MeshGPT1 to generate a mesh representation directly, as a set of triangles. Inspired by powerful recent advances in generative models for language, we adopt a direct sequence generation approach to synthesize triangle meshes as sequences of triangles. Following text generation paradigms, we first learn a vocabulary of triangles. Triangles are encoded into latent quantized embeddings through an encoder. To encourage learned triangle embeddings to maintain local geometric and topological features, we employ a graph convolutional encoder. These triangle embeddings are then decoded by a ResNet [22] decoder that processes the sequence of tokens representing a triangle to produce its vertex coordinates. We can then train a GPT-based architecture on this learned vocabulary to autoregressively produce sequences of triangles representing a mesh. Experiments across multiple categories of the ShapeNet dataset demonstrate that our method significantly improves 3D mesh generation quality in comparison with state of the art, with an average 9% increase in shape coverage and a 30-point improvement in FID scores.", + "bbox": [ + 496, + 753, + 893, + 875 + ], + "page_idx": 0 + }, + { + "type": "aside_text", + "text": "arXiv:2311.15475v1 [cs.CV] 27 Nov 2023", + "bbox": [ + 22, + 258, + 57, + 707 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1nihalsid.github.io/mesh-gpt", + "bbox": [ + 517, + 887, + 671, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1", + "bbox": [ + 480, + 924, + 488, + 936 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9c49a05ead13fc277ddba7a5d49bbf787caf1c0d5ba8613e0e8d8d464e85ac30.jpg", + "image_caption": [ + "Figure 2. Meshes generated by our method (top) for chairs, tables, benches, and lamps when trained on ShapeNet [5]. MeshGPT meshes tend to be compact, with the ability to represent both sharp details and curved boundaries. This contrasts with neural fieldbased approaches that yield dense triangulations not easily simplified through decimation (bottom)." + ], + "image_footnote": [], + "content": "", + "bbox": [ + 86, + 87, + 465, + 327 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 75, + 435, + 468, + 616 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are:", + "bbox": [ + 76, + 617, + 307, + 630 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "• A new generative formulation for meshes as a sequence of triangles, tailoring a GPT-inspired decoder-only transformer, to produce compact meshes with sharp edges.", + "• Triangles are represented as a vocabulary of latent geometric tokens to enable coherent mesh generation in an autoregressive fashion." + ], + "bbox": [ + 76, + 631, + 468, + 720 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 2, + "bbox": [ + 76, + 734, + 218, + 750 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Voxel-based 3D Shape Generation. Early shape generation approaches generated shapes as a grid of low-resolution voxels [3, 9, 26, 62] or, more recently, as high-resolution grids using efficient representations such as Octrees [57] and sparse voxels [50], with generative models such as GANs [17]. These methods pioneered the extension of 2D generative techniques into the 3D domain. However, the voxel representation inherently constrains them with gridlike artifacts and high memory requirements, limiting their practical utility in capturing fine details and complex geometries.", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Point Cloud Generation. Methods in this category represent 3D shapes by point samples on their surfaces, aiming to learn point distributions across shape datasets. Early works involved GANs for synthesizing point locations [30, 54, 59] and latent shape codes [1]. Flow-based [64] and gradient field-based models [4] also yield impressive results. Recently, diffusion-based techniques have been adapted for point cloud generation [44, 67, 68], showing competitive performance in shape generation. However, point clouds, while useful, are not the ideal format for downstream applications requiring 3D content, as converting them to meshes, which apart from being non-trivial [42, 47, 51, 65], can often fail to accurately reflect the characteristics of the underlying mesh datasets.", + "bbox": [ + 498, + 128, + 892, + 339 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Implicit Fields. Implicit representation of shapes as volumetric functions (e.g., signed distance functions) has become popular for encoding arbitrary topologies at any resolution [39, 45]. Various implicit generative methods have shown impressive performance using adversarial [6, 53] and diffusion-based [8, 14, 41] models. Diffusion-based neural field synthesis in MLP weight spaces [13] and triplanes [55] have also been explored, alongside leveraging image-based models for optimizing NeRFs [25, 34, 48, 63]. However, like point clouds, these methods require mesh conversion [12, 32, 36, 49, 53] for downstream applications, often leading to dense meshes that don’t capture the properties of the underlying datasets (e.g., edge lengths, dihedral angles). In contrast, we directly fit a generative model to triangulated meshes, explicitly modeling the training data, resulting in clean, compact and coherent meshes as outputs.", + "bbox": [ + 498, + 345, + 892, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Mesh Generation. While several discriminative approaches capable of learning signals directly on mesh structure were proposed over the recent years [16, 21, 23, 33, 40, 52, 56], direct mesh generation remains underexplored. Mesh generation has been approached with various learning-based methods [7, 11, 18, 43]. AtlasNet [18] and BSPNet [7], for example, produce mesh patches and compact meshes through binary space partitioning, respectively. However, as we demonstrate in Sec. 4, these struggle with accurately capturing shape detail.", + "bbox": [ + 498, + 595, + 890, + 746 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Closely related to our work, PolyGen [43] employs two autoregressively trained networks to create explicit mesh structures. In contrast, our method utilizes a single decoderonly network, representing triangles through learned tokens for a more streamlined generation process compared to PolyGen’s separate vertex-and-face sequence approach. Additionally, we observe that PolyGen’s vertex generator, oblivious to face generation, and the face generator, not exposed to the generated vertex distribution during training, exhibit limited robustness during inference.", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2", + "bbox": [ + 478, + 924, + 491, + 936 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 2, + "bbox": [ + 76, + 89, + 168, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by advancements in large language models, we develop a sequence-based approach to autoregressively generate triangle meshes as sequences of triangles. We first learn a vocabulary of geometric embeddings from a large collection of 3D object meshes, enabling triangles to be encoded to and decoded from this embedding. We then train a transformer for mesh generation as autoregressive nextindex prediction over the learned vocabulary embeddings.", + "bbox": [ + 75, + 114, + 468, + 234 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To learn the triangle vocabulary, we employ a graph convolution encoder operating on triangles of a mesh and their neighborhood to extract geometrically rich features that capture the intricate details of 3D shapes. These features are quantized as embeddings of a codebook using residual quantization [27, 38], effectively reducing sequence lengths of the mesh representation. These embeddings are sequenced and then decoded by a 1D ResNet [22] guided by a reconstruction loss. This phase lays the groundwork for the subsequent training of the transformer.", + "bbox": [ + 75, + 236, + 470, + 385 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We then train a GPT-style decoder-only transformer, which leverages these quantized geometric embeddings. Given a sequence of geometric embeddings extracted from the triangles of a mesh, the transformer is trained to predict the codebook index of the next embedding in the sequence. Once trained, the transformer can be auto-regressively sampled to predict sequences of embeddings. These embeddings can then be decoded to generate novel and diverse mesh structures that display efficient, irregular triangulations similar to human-crafted meshes.", + "bbox": [ + 75, + 386, + 468, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Learning Quantized Triangle Embeddings", + "text_level": 2, + "bbox": [ + 76, + 545, + 437, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Autoregressive generative models, such as transformers, synthesize sequences of tokens where each new token is conditioned on previously generated tokens. For generating meshes using transformers, we must then define the ordering convention of generation, along with the tokens.", + "bbox": [ + 75, + 569, + 468, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For sequence ordering, Polygen [43] suggests a convention where faces are ordered based on their lowest vertex index, followed by the next lowest, and so forth. Vertices are sorted in $z - y - x$ order (z representing the vertical axis), progressing from lowest to highest. Within each face, indices are cyclically permuted to place the lowest index first. In our method, we also adopt this sequencing approach.", + "bbox": [ + 75, + 643, + 468, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To define the tokens to generate, we consider a practical approach to represent a mesh M for autoregressive generation: a sequence of triangles,", + "bbox": [ + 75, + 750, + 468, + 795 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {M} := (f _ {1}, f _ {2}, f _ {3}, \\dots , f _ {N}), \\tag {1}\n$$", + "text_format": "latex", + "bbox": [ + 179, + 801, + 468, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with N faces (triangles), $f _ { i } \\in \\mathbb { R } ^ { n _ { \\mathrm { i n } } }$ having $n _ { \\mathrm { i n } }$ features. A simple approach to describe each triangle is as its three vertices, comprising nine total coordinates. Upon discretization, these coordinates can be treated as tokens. The sequence length in this case would be 9N.", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/68bf00eef4f292ec6f6d2b982ffb3ea487e15df8e5bbe5ed3e13d7f0d3653820.jpg", + "image_caption": [ + "Figure 3. We employ a graph convolutional encoder to process mesh faces, leveraging geometric neighborhood information to capture strong features representing intricate details of 3D shapes. These features are then quantized into codebook embeddings using residual quantization [27, 38]. In contrast to naive vector quantization, this ensures better reconstruction quality. The quantized embeddings are subsequently sequenced and decoded through a 1D ResNet [22], guided by a reconstruction loss." + ], + "image_footnote": [], + "content": "```mermaid\ngraph LR\n InputMesh[\"Input Mesh\"] -->|\"| F| × C_in\"| GraphConv[\"Graph Convolutional Encoder\"]\n ReconstructedMesh[\"Reconstructed Mesh\"] -->|\"| F| × 9\"| ResNetDecoder[\"ResNet Decoder\"]\n GraphConv -->|\"| F| × C_e\"| ResidualFaceQuant[\"Residual Face Quantization Module\"]\n ResNetDecoder --> SequenceOfFaces[\"Sequence Of Faces\"]\n SequenceOfFaces -->|\"| F| × C_e\"| ResidualFaceQuant\n ResidualFaceQuant -->|\"| F| ×\"| ResidualFaceQuantModule[\"Residual Face Quantization Module\"]\n ResidualFaceQuantModule -->|\"C_e\"| SumResidualFeatures[\"Sum Residual Features\"]\n ResidualFaceQuantModule -->|\"D × C_e\"| Reshape[\"Reshape\"]\n Reshape --> FeatureCodebook[\"Feature Codebook\"]\n FeatureCodebook --> MeanAcrossSharedVertices[\"Mean across Shared Vertices\"]\n MeanAcrossSharedVertices --> SplitFeature[\"Split Feature\"]\n SplitFeature -->|\"C_e\"| SumResidualFeatures\n```", + "sub_type": "flowchart", + "bbox": [ + 498, + 88, + 893, + 289 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, we observe two major challenges when using coordinates directly as tokens. First, the sequence lengths become excessively long, as each face is represented by nine values. This length does not scale well with transformer architectures, which often have limited context windows. Second, representing discrete positions of a triangle as tokens fails to capture geometric patterns effectively. This is because such a representation lacks information about neighboring triangles and does not incorporate any priors from mesh distributions.", + "bbox": [ + 496, + 436, + 890, + 587 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address the aforementioned challenges, we propose to learn geometric embeddings from a collection of triangular meshes, utilizing an encoder-decoder architecture with residual vector quantization at its bottleneck (Fig. 3).", + "bbox": [ + 496, + 588, + 890, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The network’s encoder E employs graph convolutions on mesh faces, where each face forms a node and neighboring faces are connected by undirected edges. The input face node features are comprised of the nine positionally encoded coordinates of its vertices, face normal, angles between its edges, and area. These features undergo processing through a stack of SAGEConv [20] layers, extracting a feature vector for each face. This graph convolutional approach enables the extraction of geometrically enriched features $z _ { i } \\in \\mathbb { R } ^ { n _ { \\mathrm { z } } }$ for each face,", + "bbox": [ + 496, + 648, + 892, + 799 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "$$\n\\mathbf {Z} = (z _ {1}, z _ {2}, \\dots , z _ {N}) = E (\\mathcal {M}), \\tag {2}\n$$", + "text_format": "latex", + "bbox": [ + 586, + 811, + 890, + 828 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "fusing neighborhood information into the learned embeddings.", + "bbox": [ + 496, + 839, + 890, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For quantization, we employ residual vector quantization (RQ) [38]. We found that using a single code per face is insufficient for accurate reconstruction. Instead, we use a stack of D codes per face. Further, we find that instead of directly using D codes per face, it is more effective to first divide the feature channels among the vertices, aggregate the features by shared vertex indices, and then quantize these vertex-based features, giving $\\frac { \\mathrm { D } } { 3 }$ codes per vertex, and therefore effectively D codes per face. This leads to sequences that are easier to learn for the transformer trained subsequently (see Tab. 3 and Fig. 10 for comparison). Formally, given a codebook C, RQ with depth D represents features Z as", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3", + "bbox": [ + 478, + 924, + 490, + 936 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "", + "bbox": [ + 75, + 90, + 472, + 256 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "$$\n\\mathbf {T} = (t _ {1}, t _ {2}, \\dots , t _ {N}) = \\mathrm{RQ} (\\mathbf {Z}; \\mathcal {C}, D), \\tag {3}\n$$", + "text_format": "latex", + "bbox": [ + 145, + 258, + 468, + 276 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "$$\nt _ {i} = (t _ {i} ^ {1}, t _ {i} ^ {2}, \\dots , t _ {i} ^ {D}), \\tag {4}\n$$", + "text_format": "latex", + "bbox": [ + 200, + 286, + 468, + 305 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $t _ { i }$ is a stack of tokens, each token $t _ { i } ^ { d }$ being an index to an embedding $\\mathbf { e } ( t _ { i } ^ { d } )$ in the codebook C.", + "bbox": [ + 76, + 313, + 468, + 344 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The decoder then decodes the quantized face embeddings to triangles. First, the stack of D features is reduced to a single feature per face through summation across embeddings and concatenation across vertices,", + "bbox": [ + 76, + 345, + 468, + 405 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "$$\n\\hat {\\mathbf {Z}} = (\\hat {z} _ {1}, \\dots , \\hat {z} _ {N}), \\text {with} \\hat {z} _ {i} = \\oplus_ {v = 0} ^ {2} \\sum_ {d = 1} ^ {\\frac {D}{3}} \\mathbf {e} (t _ {i} ^ {3. v + d}). \\tag {5}\n$$", + "text_format": "latex", + "bbox": [ + 94, + 419, + 468, + 464 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The face embeddings are arranged in the previously described order, and a 1D ResNet34 decoding head G processes the resulting sequence to output the reconstructed mesh ${ \\hat { \\mathcal { M } } } = G ( { \\hat { \\mathbf { Z } } } )$ with 9 coordinates representing each face. We observe that predicting these coordinates as discrete variables, i.e. as a probability distribution over a set of discrete values, leads to a more accurate reconstruction compared to regressing them as real values (Fig. 4). A cross-entropy loss on the discrete mesh coordinates and a commitment loss for the embeddings guides the reconstruction process. More details can be found in supplementary.", + "bbox": [ + 75, + 476, + 472, + 643 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ee8d3956b2fa1fe0a598529c608460da65258fd9b5188ac3e5354bbc23759131.jpg", + "image_caption": [ + "Figure 4. Our method utilizes a ResNet [22] decoder that outputs mesh faces as a distribution over discretized coordinate values (center), as opposed to regression of continuous values (left). This significantly reduces floating face artifacts, leading to reconstructions that more closely resemble the ground truth (right)." + ], + "image_footnote": [], + "content": "Three 3D wireframe models of a chair: one with real-valued outputs, one with discrete outputs, and the ground truth (no text or symbols on the models themselves)", + "sub_type": "natural_image", + "bbox": [ + 98, + 657, + 450, + 818 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After training, the graph encoder E and codebook C are incorporated into the transformer training, using T from Eq. 3 as the token sequence. With $| \\mathbf { T } | = D N$ , this sequence is more concise than the naive 9N-length tokenization when $D \\ < \\ 9 .$ Thus, we obtain geometrically rich embeddings with shorter sequence lengths, overcoming our initial challenges and paving the way for efficient mesh generation.", + "bbox": [ + 498, + 90, + 893, + 198 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Mesh Generation with Transformers", + "text_level": 2, + "bbox": [ + 500, + 205, + 818, + 220 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/72cb966cd94dd8b5076080c802a06cda11de1a0168b09a46a1aa9944576b1ec9.jpg", + "image_caption": [ + "Figure 5. We employ a transformer to generate mesh sequences as token indices from a pre-learned codebook vocabulary. During training, a graph encoder extracts features from mesh faces, which are quantized into a set of face embeddings. These embeddings are flattened, bookended with start and end tokens, and fed into a GPTstyle transformer. This decoder predicts the subsequent codebook index for each embedding, optimized via cross-entropy loss." + ], + "image_footnote": [], + "content": "```mermaid\ngraph LR\n A[\"Face Graph + Input Features\"] --> B[\"Graph Convolutional Encoder\"]\n B --> C[\"Residual Face Quantization Module\"]\n C --> D[\"Sequence & Flatten\"]\n D --> E[\"GPT-Style Transformer\"]\n E --> F[\"Predicted Codebook Indices\"]\n F --> G[\"GT Codebook Indices\"]\n G --> H[\"CE Loss\"]\n```", + "sub_type": "flowchart", + "bbox": [ + 501, + 237, + 893, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We employ a decoder-only transformer architecture from the GPT family of models to predict meshes as sequences of indices from the learned codebook in Sec. 3.1. The input to this transformer consists of embeddings $\\mathbf { e } ( t _ { i } ^ { d } )$ extracted from the mesh M using the GraphConv encoder E and quantized using RQ (Eq. 3). The embeddings are prefixed and suffixed with a learned start and end embedding. Additionally, learned discrete positional encodings are added, indicating the position of each face in the sequence and the index of each embedding within the face. The features then pass through a stack of multiheaded self-attention layers, where the transformer is trained to predict the codebook index of the next embedding in the sequence (Fig. 5). Essentially, we maximize the log probability of the training sequences with respect to the transformer parameters θ,", + "bbox": [ + 496, + 479, + 893, + 705 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "$$\n\\prod_ {i = 1} ^ {N} \\prod_ {d = 1} ^ {D} p (t _ {i} ^ {d} \\mid \\mathbf {e} (t _ {< i} ^ {d}), \\mathbf {e} (t _ {i} ^ {< d}); \\theta). \\tag {6}\n$$", + "text_format": "latex", + "bbox": [ + 584, + 714, + 890, + 757 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Once the transformer is trained, it can autoregressively generate a sequence of tokens, starting with a start token and continuing until a stop token is encountered using beam sampling. The codebook embeddings indexed by this sequence of tokens is then decoded by decoder G to produce the generated mesh. As this output initially forms a ‘triangle soup’ with duplicate vertices for neighboring faces, we apply a simple post-processing operation to merge close vertices (e.g., with MeshLab), to yield the final mesh.", + "bbox": [ + 496, + 763, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4", + "bbox": [ + 478, + 924, + 491, + 936 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Implementation Details", + "text_level": 2, + "bbox": [ + 76, + 90, + 294, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In learning the triangle vocabulary, our residual quantization layer features a depth of 2, yielding D = 6 embeddings per face, each with dimension 192. The codebook is dynamically updated using an exponential moving average of the clustered features. Following [29], we incorporate stochastic sampling of codes and employ a shared codebook across all levels. The decoder predicts the coordinates of the faces across 128 classes, resulting in a discretization of space to 1283 possible values. This encoder-decoder network is trained using 2 A100 GPUs for ≈ 2 days.", + "bbox": [ + 75, + 114, + 468, + 265 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For our transformer, we use a GPT2-medium model, equipped with a context window of up to 4608 embeddings. The model is trained on 4 A100 GPUs, for ≈ 5 days.", + "bbox": [ + 76, + 266, + 468, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Both the encoder-decoder network and the transformer are written using the Pytorch [46] and are trained utilizing the ADAM optimizer [28]. We set the learning rate at 1 × $1 0 ^ { - 4 }$ and use an effective batch size of 64.", + "bbox": [ + 76, + 311, + 468, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 2, + "bbox": [ + 76, + 388, + 209, + 406 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset and Metrics", + "text_level": 2, + "bbox": [ + 76, + 414, + 267, + 429 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data. We present our results on the ShapeNetV2 dataset. Both the encoder-decoder network and the GPT model are trained across all 55 categories of this dataset. Additionally, we fine-tune the GPT model specifically on four categories: Chair, Table, Bench, and Lamp. The results are reported on these categories. During training, we employ augmentation techniques including random shifts and random scaling to enhance the diversity of the training meshes. Similar to Polygen [43], we also apply planar decimation to further augment the shapes. To ensure that the entire mesh fits into the transformer’s context window, we select only those meshes for training that have fewer than 800 faces post-decimation. Detailed information regarding the augmentation processes, decimation techniques, and data splits are provided in the supplementary material.", + "bbox": [ + 75, + 441, + 468, + 669 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Metrics. Evaluating the unconditional synthesis of 3D shapes presents challenges due to the absence of direct ground truth correspondence. Hence, we utilize established metrics for assessment, consistent with previous works [37, 67, 68]. These include Minimum Matching Distance (MMD), Coverage (COV), and 1-Nearest-Neighbor Accuracy (1-NNA). For MMD, lower is better; for COV, higher is better; for 1-NNA, 50% is the optimal. We use a Chamfer Distance (CD) distance measure for computing these metrics in 3D. More details about these metrics can be found in the supplementary.", + "bbox": [ + 75, + 672, + 468, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The aforementioned metrics effectively measure the quality of shapes but do not address the visual similarity of the generated meshes to the real distribution. To assess this aspect, we render both the generated meshes and the", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8b871bacf5cfff1883e75b5abcb4c81fe4a612a1d79d755738c7bec1d17f5365.jpg", + "table_caption": [ + "Table 1. Quantitative comparison on the task of unconditional mesh generation on a subset of categories from the ShapeNet [5] dataset. GET3D\\* refers to meshes simplified to 400 faces using QEM [15]. MMD values are multiplied by 103. We outperform the baselines on shape quality, visual and compactness metrics." + ], + "table_footnote": [], + "table_body": "
ClassMethodCOV↑MMD↓1-NNAFID↓KID↓|V||F|
ChairAtlasNet [18]9.034.0595.13170.710.16925004050
BSPNet [7]16.483.6291.7546.730.0306731165
Polygen [43]31.224.4193.5661.100.043248603
GET3D [14]40.853.5683.0481.450.0541372527457
GET3D*38.753.5784.0778.290.065199399
MeshGPT43.283.2975.5118.460.010125228
TableAtlasNet [18]7.163.8596.30161.380.15025004050
BSPNet [7]16.833.1493.5830.780.017420699
Polygen [43]32.993.0088.6538.530.029147454
GET3D [14]41.702.7885.5493.930.0761376727537
GET3D*37.952.8581.9350.460.037199399
MeshGPT45.682.3672.886.240.00299187
BenchAtlasNet [18]20.532.4790.58189.390.16325004050
BSPNet [7]28.742.0588.4459.110.030457756
Polygen [43]51.921.9776.9849.340.031172430
MeshGPT55.231.4468.248.720.001159291
LampAtlasNet [18]19.974.6891.85177.910.13925004050
BSPNet [7]18.385.3293.13112.650.0775871011
Polygen [43]47.864.1881.4252.480.025185558
MeshGPT53.883.9465.7319.910.004150288
", + "bbox": [ + 504, + 90, + 890, + 323 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ShapeNet meshes as images from eight different viewpoints using Blender, applying a metallic material to emphasize the geometric structures. Subsequently, we calculate the FID (Frechet Inception Distance) and KID (Kernel Incep-´ tion Distance) scores for these image sets. For both FID and KID, lower scores indicate better performance. We further report compactness as the average number of vertices and faces in the generated meshes.", + "bbox": [ + 498, + 414, + 890, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Results", + "text_level": 2, + "bbox": [ + 500, + 545, + 591, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We benchmark our approach against leading mesh generation methods: Polygen [43], which generates polygonal meshes by first generating vertices followed by faces conditioned on the vertices; BSPNet [7], which represents a mesh through convex decompositions; and AtlasNet [18], which represents a 3D mesh as a deformation of multiple 2D planes. We additionally compare with a state-of-the-art neural field-based method, GET3D [14], that creates shapes as 3D signed distance fields (SDFs) from which a mesh is extracted by differentiable marching tetrahedra. For BSP-Net and AtlasNet, which are built on autoencoder backbones, we follow [1] to fit a Gaussian mixture model with 32 components to enable unconditional sampling of shapes.", + "bbox": [ + 498, + 568, + 890, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 6, Fig. 7 and Tab. 1, our method outperforms all baselines in all four categories. Our method can generate sharp and compact meshes with high geometric details. Compared to Polygen, our approach creates shapes with more intricate details. Additionally, Polygen’s separate training for vertex and face models, with the latter only exposed to ground truth vertex distributions, makes it more susceptible to error accumulation during inference. Atlas-Net often suffers from folding artifacts, resulting in lower diversity and shape quality. BSPNet’s use of BSP tree of planes tends to produce blocky shapes with unusual triangulation patterns. GET3D generates good high-level shape structures, but over-triangulated and with imperfect flat surfaces. Simplifying GET3D-generated meshes with algorithms such as QEM [15] results in a loss of fine structures.", + "bbox": [ + 498, + 765, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5", + "bbox": [ + 478, + 924, + 490, + 936 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/76068c6dfb1898f16de88ae3f72de3ea3ccab75df28511e16f84b9e6bd9d5116.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison of Chair and Table meshes from ShapeNet [5]. Our approach produces compact meshes with sharp geometric details. In contrast, baselines often either miss these details, produce over-triangulated meshes, or output too simplistic shapes." + ], + "image_footnote": [], + "content": "GT Samples\nAtlasNet\tBSPNetGET3DGET3D-QEMPolygenOurs\n100000000000000000000000000000000000000000000000000000000000000000000000000", + "sub_type": "text_image", + "bbox": [ + 81, + 89, + 890, + 688 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "", + "bbox": [ + 75, + 736, + 470, + 828 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "User Study. We further conducted a user study, in Tab. 2, to assess generated mesh quality. 49 participants were shown pairs of four meshes, randomly selected from our method and each baseline method. Additionally, users were presented with ground truth ShapeNet meshes for comparison. Participants were asked their preference between our method and the baseline in terms of both overall shape quality and similarity of triangulation patterns to the ground truth meshes. This resulted in 784 total question responses. Our method was significantly preferred over Atlas-Net, Polygen, and BSPNet in both shape and triangulation quality. Moreover, a majority of users (68%) favored our method over neural field-based GET3D in shape quality, with even higher preference (73%) for triangulation quality. This underscores our ability to generate high-quality meshes that align with human users’ preferences. Further user study details are provided in the supplemental.", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "", + "bbox": [ + 496, + 736, + 893, + 888 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6", + "bbox": [ + 478, + 924, + 491, + 936 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/45b493818f6537a57fadcb2454130c2c50c5a184adc6d1ed712e535a4a05c269.jpg", + "image_caption": [], + "image_footnote": [], + "content": "GT Samples\nAtlasNet\tBSPNet\tPolygen\tOurs", + "sub_type": "text_image", + "bbox": [ + 80, + 89, + 460, + 415 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/469b0707a1d0c24a76a461e6a0fbb95c58ce28348c8e9ee5a08dff8e39ee4713.jpg", + "table_caption": [ + "Figure 7. Qualitative comparison of Bench and Lamp meshes from the ShapeNet [5] dataset. Compared to baselines, our method produces valid meshes with high geometric fidelity." + ], + "table_footnote": [], + "table_body": "
PreferenceAtlasNet [18]BSPNet [7]Polygen [43]GET3D [14]
Our Shape82.65%78.57%85.71%68.37%
Our Triangulation84.69%71.43%84.69%73.47%
", + "bbox": [ + 80, + 472, + 468, + 518 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0500b44c57dd1a58136123af0b3f1b93b7cfad5e8dead5b38ee8706f0c22e0c7.jpg", + "table_caption": [ + "Table 2. Percentage of users who prefer our method over the baselines in terms of shape quality and the triangulation quality. Our generated meshes are preferred significantly more often.", + "Table 3. Ablations of our design choices on the Chair category of the ShapeNet [5] dataset. As highlighted by the drop in performance by removing any of them, each of these contribute to the final method." + ], + "table_footnote": [], + "table_body": "
MethodCOV↑MMD↓1-NNAFID↓KID↓
w/o Learned Tokens27.504.5193.1540.200.024
w/o Encoder Features39.243.4384.4830.350.017
w/o Pretraining36.973.7384.6927.540.014
w/o Sequence Compression30.984.1588.9838.760.023
w/o per Vertex Quantization23.575.4998.3574.940.050
MeshGPT43.283.2975.5118.460.010
", + "bbox": [ + 80, + 580, + 468, + 679 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 76, + 760, + 468, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Shape Novelty Analysis. We investigate whether our method can generate novel shapes that extend beyond the training dataset, ensuring the model is not merely retrieving existing shapes. Following the methodology in previous studies [13, 24], we generate 500 shapes using our model. For each generated shape, we identify the top three nearest neighbors from the training set based on Chamfer Distance (CD). To ensure a fair distance computation, accounting for potential discrepancies due to scale or shift in the augmented generations, we normalize all generated and train shapes to be centered within [0, 1]3.", + "bbox": [ + 76, + 810, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "chart", + "img_path": "images/c529395af6d980051ddecada4916f283df5a930f3e3dfe3b5e19f6ee6a2f96a9.jpg", + "content": "| Chamfer Distance (x10^3) | Proportion of Generated Shapes |\n| --- | --- |\n| 0 | ~0.5 |\n| 1 | ~4.5 |\n| 2 | ~6.5 |\n| 3 | ~3.5 |\n| 4 | ~2.5 |\n| 5 | ~1.5 |\n| 6 | ~1.5 |\n| 7 | ~1.5 |\n| 8 | ~1.0 |\n| 9 | ~0.5 |\n| 10+ | ~4.5 |", + "chart_caption": [], + "chart_footnote": [], + "sub_type": "bar", + "bbox": [ + 498, + 85, + 890, + 402 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5b3a33b4221fb57854918e5b77130294ccf40f3adc775ccf038ce130eb125645.jpg", + "image_caption": [ + "Figure 8. Shape novelty analysis on ShapeNet [5] chair category. We show the 3 nearest neighbors in terms of Chamfer Distance (CD) for a generated shape (top). We also plot the distribution of 500 generated chair samples from our method and their closeness to training distribution. Our method can generate shapes that are similar (low CD) as well as different (high CD) from the training distribution, with shapes at the 50th percentile looking different from closest train shape.", + "Figure 9. Given a partial mesh, our method can infer multiple possible shape completions." + ], + "image_footnote": [], + "content": "3D model of wooden furniture with various shapes and layouts, including chairs, tables, and blocks (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 500, + 527, + 885, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 498, + 763, + 893, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 8 displays the most similar shapes from the train set corresponding to a sample generated by our model. We conduct a detailed analysis of the shape similarity distribution between the retrieved and generated shapes on the", + "bbox": [ + 498, + 840, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7", + "bbox": [ + 480, + 924, + 490, + 936 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Chair category in Fig. 8. The CD distribution reveals that our method not only covers shapes in the training set, indicated by low CD values, but also successfully generates novel and realistic-looking shapes, indicated by high CD values. In the supplemental, we present further analysis of the novelty of all meshes generated by our method, which are featured in the figures of this paper.", + "bbox": [ + 75, + 90, + 472, + 196 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Shape Completion. Our model can infer multiple possible completions for a given partial shape, leveraging its probabilistic nature to generate diverse shape hypotheses. Fig. 9 illustrates examples of chair and table completions.", + "bbox": [ + 75, + 200, + 470, + 262 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2.1 Ablations", + "text_level": 2, + "bbox": [ + 76, + 281, + 199, + 294 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Tab. 3, we show a set of ablations on the task of unconditional mesh generation on ShapeNet Chair category. Further ablations are detailed in the supplementary.", + "bbox": [ + 75, + 305, + 470, + 351 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c106cef48f10754a10c06872decaa8bd01f67062fb929d7f25e9990aa5bda13f.jpg", + "image_caption": [ + "w/o Encoder Features", + "w/o Pretraining" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 78, + 362, + 460, + 508 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ad9fafe54b97a2db08791ed1d9d6d5fc1f9740c532fa025b564f6f99b7850f35.jpg", + "image_caption": [ + "w/o Learned Tokens", + "w/o Sequence Compression" + ], + "image_footnote": [], + "content": "3D illustration of a wooden chair with vertical supports and a curved top (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 86, + 531, + 189, + 671 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7cd31a0f47e47c84d92e08dca904b6c960a3e46e34d19fe04d035df0379c8406.jpg", + "image_caption": [ + "w/o per Vertex Quantization" + ], + "image_footnote": [], + "content": "3D illustration of a wooden chair with geometric panel design (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 207, + 532, + 318, + 671 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a1fcd1221add5906336612abb60dd62afe146092c590f7e919b6ddaee9d492a5.jpg", + "image_caption": [ + "Ours (Complete)", + "Figure 10. Ablation over our method’s components. Naive tokenization (w/o Learned Tokens) and naive per face quantization (w/o per-vertex quantization) markedly diminishes shape quality. Longer sequences without sequence compression (w/o Sequence Compression) lead to the model forgetting the context and repeating shape elements in the output." + ], + "image_footnote": [], + "content": "3D illustration of a wooden chair with yellow cushion and side legs (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 336, + 531, + 439, + 671 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Do learned geometric embeddings help? Using our geometric embeddings in vocabulary learning significantly improves over naive coordinate tokenization (w/o Learned Tokens), as shown in Tab. 3 and Fig. 3.", + "bbox": [ + 75, + 806, + 468, + 867 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Does sequence length compression help? As evidenced by Tab. 3 and Fig. 3, a model with a shorter sequence length performs better than without (w/o Sequence Compression), as shorter sequence lengths fit transformer context windows better. Visually, with longer sequences, shapes exhibit repeating structures due to limited context.", + "bbox": [ + 75, + 869, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "What is the effect of aggregation and quantization across vertex indices instead of faces? As discussed in Section 3, an alternative to having embeddings aggregated and quantized across vertex indices, is to simply have the same number of embeddings directly per face (w/o per Vertex Quantization). In Tab. 3, we observe that this makes sequences much harder to learn with the transformer.", + "bbox": [ + 496, + 155, + 893, + 261 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Do features from graph convolutional encoder help in mesh generation? An alternative to using embeddings from the graph encoder and the codebook is to only use the codebook indices of these tokens as input to the transformer, and let the transformer learn the discrete token embeddings (w/o Encoder Features). While the transformer is able to still learn meaningful embeddings, these are still not as effective as using graph encoder features.", + "bbox": [ + 496, + 265, + 892, + 385 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "What is the effect of large-scale shape pretraining? Tab. 3 shows that training only on shapes from individual categories (w/o Pretraining) leads to overfitting and subobtimal performance, in contrast to pre-training our GPT transformer on all ShapeNet train shapes.", + "bbox": [ + 496, + 388, + 890, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. MeshGPT significantly advances direct mesh generation but faces several limitations. Its autoregressive nature leads to slower sampling performance, with mesh generation times taking 30 to 90 seconds. Despite our learned tokenization approach reducing sequence lengths, which suffices for single object generation, it may not be as effective for scene-scale generation, suggesting an area for future enhancement. Moreover, our current computational resources limit us to using a GPT2-medium transformer, which is smaller than more sophisticated models like Llama2 [58]. Given that larger language models benefit from increased data and computational power, expanding these resources could significantly boost MeshGPT’s performance and capabilities.", + "bbox": [ + 496, + 468, + 892, + 680 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 2, + "bbox": [ + 500, + 694, + 617, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have introduced MeshGPT, a novel shape generation approach that outputs meshes directly as triangles. We learn a vocabulary of geometric embeddings over a distribution of meshes, over which a transformer is trained to predict meshes autoregressively as a sequence of triangles. In contrast to existing mesh generation approaches, our method generates clean, coherent meshes which are compact and follow the triangulation patterns in real data more closely. We believe that MeshGPT will not only elevate the current landscape of mesh generation but also inspire new research in the area, offering a unique alternative to the more commonly explored representations for 3D content creation.", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8", + "bbox": [ + 480, + 924, + 488, + 936 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 2, + "bbox": [ + 78, + 90, + 243, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was funded by AUDI AG. Matthias Nießner was supported by the ERC Starting Grant Scan2CAD (804724). Angela Dai was supported by the Bavarian State Ministry of Science and the Arts coordinated by the Bavarian Research Institute for Digital Transformation (BIDT). We would like to thank Ziya Erkoc¸, Quyet-Chien Nguyen, Haoxuan Li and Artem Sevastopolsky for the helpful discussions.", + "bbox": [ + 76, + 114, + 468, + 213 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 2, + "bbox": [ + 78, + 244, + 173, + 258 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40–49. PMLR, 2018. 2, 5", + "[2] Henry Blumberg. Hausdorff’s grundzuge der mengenlehre.¨ 1920. 12", + "[3] Andrew Brock, Theodore Lim, James M Ritchie, and Nick Weston. Generative and discriminative voxel modeling with convolutional neural networks. arXiv preprint arXiv:1608.04236, 2016. 1, 2", + "[4] Ruojin Cai, Guandao Yang, Hadar Averbuch-Elor, Zekun Hao, Serge Belongie, Noah Snavely, and Bharath Hariharan. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5826–5835, 2021. 1, 2, 5" + ], + "bbox": [ + 80, + 266, + 473, + 902 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [], + "bbox": [ + 500, + 90, + 893, + 901 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "9", + "bbox": [ + 478, + 924, + 491, + 936 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [], + "bbox": [ + 73, + 88, + 473, + 902 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [], + "bbox": [ + 500, + 88, + 893, + 902 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10", + "bbox": [ + 477, + 924, + 493, + 936 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [], + "bbox": [ + 76, + 90, + 472, + 901 + ], + "page_idx": 10 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [], + "bbox": [ + 500, + 90, + 893, + 459 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11", + "bbox": [ + 477, + 924, + 491, + 936 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Appendix", + "text_level": 2, + "bbox": [ + 76, + 90, + 163, + 107 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "In this supplementary document, we discuss additional details about our method MeshGPT. We provide implementation details of our method, loss functions, and the baselines in Section B. Additional details about the user study are provided in Section C. We also provide further qualitative and quantitative results (Section E), including a shape novelty analysis (Section D) for shapes from the main paper. We further encourage the readers to check out the supplemental video for a summary of the method and an overview of results.", + "bbox": [ + 75, + 114, + 472, + 267 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "A. Data", + "text_level": 2, + "bbox": [ + 76, + 284, + 147, + 300 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Selection. We use the ShapeNetV2 [5] dataset for all our experiments. We first apply planar decimation to each shape using Blender [10], with the angle tolerance parameter α set within [1, 60]. The impact of this decimation is assessed by calculating the Hausdorff distance [2] between the decimated and original shapes. We then choose, for each original shape, the decimated version with the Hausdorff distance closest to, but below, a pre-set threshold $\\delta _ { \\mathrm { h a u s d o r f f } } .$ Shapes with more than 800 faces are excluded, resulting in a final count of 28980 shapes across all categories. The Chair, Table, Bench, and Lamp categories are further divided into a 9:1 train-test split. All shapes from rest of the categories are used for pretraining phase, while only the training subset from specific categories is used for pretraining and finetuning. All shapes are normalized to be centered at the origin and scaled to ensure the longest side is of unit length.", + "bbox": [ + 75, + 314, + 472, + 556 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Augmentation. During the training of both the encoderdecoder and the transformer, multiple augmentation techniques are applied to all train shapes. Scaling augmentation, ranging from 0.75 to 1.25, is independently applied across each axis. Post-scaling, meshes are resized to keep the longest side at unit length. Additionally, jitter-shift augmentation in the range of [−0.1, 0.1] is used, adjusted to maintain the mesh within the unit bounding box around the origin. We also implement varying levels of planar decimation for training shapes, provided the distortion remains below $\\delta _ { \\mathrm { h a u s d o r f f } } .$", + "bbox": [ + 75, + 561, + 472, + 729 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "B. Method Details", + "text_level": 2, + "bbox": [ + 76, + 744, + 233, + 758 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "B.1. Architecture", + "text_level": 2, + "bbox": [ + 76, + 770, + 215, + 785 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "The architecture of our encoder-decoder network is elaborated in Fig. 14. The encoder comprises a series of SAGE-Conv [20] graph convolution layers, processing the mesh in the form of a face graph. For each graph node, input features include the positionally encoded 9 coordinates of the face triangle, its area, the angles between its edges, and the normal of the face. The decoder is essentially a 1D", + "bbox": [ + 75, + 794, + 470, + 901 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "ResNet-34 [22] network, applied to the face features interpreted as a 1D sequence. It outputs logits corresponding to the 9 discrete coordinates of each face triangle, which are discretized within a $1 2 8 ^ { 3 }$ space. The codebook C has a size of 16384. The architecture of the transformer is simply a GPT-2 medium architecture, i.e. 24 multi-headed self attention layers, 16 heads, 768 as feature width, with context length of 4608.", + "bbox": [ + 496, + 90, + 893, + 212 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "B.2. Residual Vector Quantization", + "text_level": 2, + "bbox": [ + 500, + 219, + 767, + 234 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Fundamentals. For quantization, we employ residual vector quantization (RQ) [29, 38]. RQ discretizes a vector z with a stack of D ordered codes. Starting with the $0 ^ { \\mathrm { t h } }$ residual $\\mathbf { r } ^ { 0 } = \\mathbf { z } ,$ , RQ recursively computes $t ^ { d }$ as the code of the residual $\\mathbf { r } ^ { d - 1 }$ , and the next residual $\\mathbf { r } ^ { d }$ as", + "bbox": [ + 498, + 246, + 893, + 321 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "$$\nt ^ {d} = \\mathcal {Q} \\left(\\mathbf {r} ^ {d - 1}; \\mathcal {C}\\right) \\tag {7}\n$$", + "text_format": "latex", + "bbox": [ + 632, + 328, + 890, + 345 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "$$\n\\mathbf {r} ^ {d} = \\mathbf {r} ^ {d - 1} - \\mathbf {e} (t ^ {d}) \\tag {8}\n$$", + "text_format": "latex", + "bbox": [ + 630, + 349, + 890, + 367 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "where $\\mathcal { Q } ( \\mathbf { z } ; \\mathcal { C } )$ denotes vector quantization of z with codebook ${ \\mathcal { C } } ,$ , and $\\mathbf { e } ( t ^ { d } )$ is the embedding in the codebook C. Further, we define", + "bbox": [ + 498, + 375, + 890, + 417 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "$$\n\\hat {\\mathbf {z}} ^ {(d)} = \\sum_ {1} ^ {d} \\mathbf {e} (t ^ {d}) \\tag {9}\n$$", + "text_format": "latex", + "bbox": [ + 637, + 419, + 890, + 458 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "as the partial sum of up to d code embeddings, and $\\hat { \\mathbf { z } } = \\hat { \\mathbf { z } } ^ { D }$ is the quantized vector of z. The recursive quantization of RQ thus approximates the vector z in a coarse-to-fine manner [29]. The commitment loss can now be defined between vector z and its quantization zˆ as", + "bbox": [ + 498, + 462, + 893, + 539 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {L} _ {\\text {commit}} (\\mathbf {z}, \\hat {\\mathbf {z}}) = \\sum_ {d = 1} ^ {D} \\| \\mathbf {z} - \\mathrm{sg} [ \\hat {\\mathbf {z}} ^ {(d)} ] \\| _ {2} ^ {2} \\tag {10}\n$$", + "text_format": "latex", + "bbox": [ + 576, + 546, + 890, + 587 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "where sg denotes the stop gradient operation.", + "bbox": [ + 500, + 593, + 799, + 608 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Per Vertex Residual Vector Quantization. Instead of directly applying RQ, for a face feature $\\mathbf { z _ { i } }$ extracted by the graph encoder, we first split this 576 dimension face feature $\\mathbf { z _ { i } }$ into 3 features, $( \\mathbf { z } _ { i } ^ { 1 } , \\mathbf { z } _ { i } ^ { 2 } , \\mathbf { z } _ { i } ^ { 3 } )$ ), each of 192 dimensions representing the features of the face triangle’s 3 vertices. The features the fall on vertices that are shared across faces are averaged. On these per vertex index feature $\\mathbf { z } _ { i } ^ { j }$ , RQ quantizes them into a stack of $\\textstyle { \\frac { D } { 3 } }$ features,", + "bbox": [ + 498, + 611, + 890, + 733 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "$$\n\\mathrm{RQ} (\\mathbf {z _ {i}}; \\mathcal {C}, D) = (\\mathrm{RQ} (\\mathbf {z _ {i} ^ {1}}; \\mathcal {C}, \\frac {D}{3}), \\dots , \\mathrm{RQ} (\\mathbf {z _ {i} ^ {3}}; \\mathcal {C}, \\frac {D}{3})) \\tag {11}\n$$", + "text_format": "latex", + "bbox": [ + 506, + 739, + 890, + 771 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "for codebook C, with", + "bbox": [ + 500, + 775, + 643, + 789 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "$$\n\\mathrm{RQ} (\\mathbf {z} _ {\\mathbf {i}} ^ {\\mathbf {j}}; \\mathcal {C}, \\frac {D}{3}) = (t _ {i} ^ {2 j - \\frac {D}{3} + 1}, t _ {i} ^ {2 j - \\frac {D}{3} + 2}, \\dots , t _ {i} ^ {2 j}), \\tag {12}\n$$", + "text_format": "latex", + "bbox": [ + 522, + 795, + 890, + 825 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "where $t _ { i } ^ { d }$ is the index to the embedding $\\mathbf { e } ( t _ { i } ^ { d } )$ in the codebook C. Taken together for each vertex, these form a stack of D features,", + "bbox": [ + 498, + 830, + 890, + 876 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "$$\n\\mathrm{RQ} (\\mathbf {z _ {i}}; \\mathcal {C}, D) = (t _ {i} ^ {1}, t _ {i} ^ {2}, \\dots , t _ {i} ^ {D}) = t _ {i}. \\tag {13}\n$$", + "text_format": "latex", + "bbox": [ + 568, + 883, + 890, + 902 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "12", + "bbox": [ + 475, + 924, + 495, + 936 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/22c1035334c0e2d06f3f6dff66da36e08b29b61356c3f3ee05ec77a5c69fdd7e.jpg", + "image_caption": [ + "Figure 11. Additional novel shapes on Chairs, Tables, Benches and Lamps generated by our method." + ], + "image_footnote": [], + "content": "Collection of 3D architectural and furniture models including wooden chairs, tables, benches, and decorative objects (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 138, + 85, + 836, + 583 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Thus, the residual quantization for the features extracted for all the N faces of the mesh $\\mathbf { Z } = ( z _ { 1 } , z _ { 2 } , \\ldots , z _ { N } )$ is given as", + "bbox": [ + 75, + 632, + 470, + 676 + ], + "page_idx": 12 + }, + { + "type": "equation", + "text": "$$\n\\mathrm{RQ} (\\mathbf {Z}; \\mathcal {C}, D) = \\mathrm{RQ} (\\mathbf {z _ {1}} \\dots \\mathbf {z _ {N}}; \\mathcal {C}, D) \\tag {14}\n$$", + "text_format": "latex", + "bbox": [ + 158, + 686, + 468, + 703 + ], + "page_idx": 12 + }, + { + "type": "equation", + "text": "$$\n\\mathrm{RQ} (\\mathbf {z _ {1}} \\dots \\mathbf {z _ {N}}; \\mathcal {C}, D) = (t _ {0}, t _ {1}, \\dots , t _ {N}). \\tag {15}\n$$", + "text_format": "latex", + "bbox": [ + 138, + 705, + 468, + 722 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Fig. 16 gives an intuition on why ‘per vertex’ tokenization is better than ‘per face’ tokenization, with ablations in the main paper confirming it.", + "bbox": [ + 75, + 729, + 468, + 775 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "B.3. Loss Functions", + "text_level": 2, + "bbox": [ + 76, + 782, + 233, + 797 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Vocabulary Learning. Let $\\mathcal { P } _ { n i j k }$ be the predicted probability distribution over the discrete coordinates, where n is the face index, i is the vertex index inside the face, $j$ is the coordinate’s axis index $( x , y \\ \\mathrm { o r } \\ z )$ , and k goes over the discretized positions $\\in \\{ 1 , 2 , 3 , \\ldots , 1 2 8 \\}$ . If $V _ { n i j }$ is the target discretized position, then the reconstruction loss for the encoder-decoder network is given as", + "bbox": [ + 75, + 809, + 470, + 901 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "", + "bbox": [ + 500, + 633, + 743, + 648 + ], + "page_idx": 12 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {L} _ {\\text {recon}} = \\sum_ {n = 1} ^ {N} \\sum_ {i = 1} ^ {3} \\sum_ {j = 1} ^ {3} \\sum_ {k = 1} ^ {1 2 8} \\mathrm{w} _ {n i j k} \\log \\mathcal {P} _ {n i j k} \\tag {16}\n$$", + "text_format": "latex", + "bbox": [ + 557, + 660, + 890, + 704 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "with", + "bbox": [ + 500, + 715, + 535, + 729 + ], + "page_idx": 12 + }, + { + "type": "equation", + "text": "$$\n\\mathrm{w} _ {n i j k} = \\text {smooth} \\left(\\text {one - hot} _ {1 2 8} \\left(V _ {n i j}\\right)\\right) \\tag {17}\n$$", + "text_format": "latex", + "bbox": [ + 573, + 744, + 890, + 762 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "is a smoothening kernel applied across the one-hot probability distribution over the targets, encouraging physically close coordinates to be penalized less. The loss over the encoder-decoder network is the sum of ${ \\mathcal { L } } _ { \\mathrm { r e c o n } }$ and $\\mathcal { L } _ { \\mathrm { c o m m i t } }$ previously described.", + "bbox": [ + 496, + 775, + 890, + 851 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Transformer. Given a target sequence $\\begin{array} { r l } { \\mathbf T } & { { } = } \\end{array}$ $( t _ { 0 } , t _ { 1 } , \\ldots , t _ { N } )$ with $\\begin{array} { c c l } { t _ { i } } & { = } & { ( t _ { i } ^ { 1 } , \\bar { t } _ { i } ^ { 2 } , \\dots , \\bar { t } _ { i } ^ { D } ) } \\end{array}$ , and $s _ { i } ^ { j } \\mathrm { i s }$ the corresponding predicted sequence element, then the transformer is trained with the loss", + "bbox": [ + 500, + 854, + 893, + 901 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "13", + "bbox": [ + 475, + 924, + 493, + 936 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/af8b3cd584542eb6776b8e675298e42cc5c1a00283f7ad4d41092a1e2cc3a20a.jpg", + "image_caption": [ + "Generated Shape", + "Most similar shapes retrieved from training set" + ], + "image_footnote": [], + "content": "Grid of 3D-rendered wooden chairs with varying colors and line textures, no text or symbols present.", + "sub_type": "natural_image", + "bbox": [ + 80, + 89, + 428, + 532 + ], + "page_idx": 13 + }, + { + "type": "image", + "img_path": "images/d00aabe098c8a3f3b7dac3186467ea197ed472f32e2fee65cd05d4e034e6f1e2.jpg", + "image_caption": [ + "Generated Shape", + "Most similar shapes retrieved from training set", + "Figure 12. Shape novelty analysis on ShapeNet [5] chair and table category for shapes generated by our method shown in main paper. We show the 3 nearest neighbors in terms of Chamfer Distance (CD) for a generated shape. Shapes are scaled to a unit length along all axes to account for augmented generations before computing CD." + ], + "image_footnote": [], + "content": "Collection of 3D-rendered wooden table and chair models in various colors, showing different shapes and sizes (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 450, + 90, + 890, + 532 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "", + "bbox": [ + 76, + 633, + 308, + 646 + ], + "page_idx": 13 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {L} _ {\\mathrm{recon}} = \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {D} \\sum_ {k = 1} ^ {| \\mathcal {C} |} \\log p (s _ {i} ^ {k} = t _ {i} ^ {j}). \\tag {18}\n$$", + "text_format": "latex", + "bbox": [ + 151, + 666, + 468, + 710 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "B.4. Baselines", + "text_level": 2, + "bbox": [ + 76, + 736, + 187, + 750 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "We utilize the official implementations for BSPNet [7], AtlasNet [18], and GET3D [14]. For Polygen [43], we reimplement it following the details in their paper. To align its architecture with our method, we employ the same GPT2- medium architecture for the vertex model in Polygen. Additionally, mirroring our approach, Polygen undergoes pretraining on all categories and is finetuned for each evaluated category, applying the same train-time augmentations as used in our method.", + "bbox": [ + 75, + 763, + 470, + 900 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "C. User Study Details", + "text_level": 2, + "bbox": [ + 500, + 630, + 684, + 648 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "We develop a Django-based web application for the user study. In Fig. 15, we show the interface for the questionnaire. We randomly select 16 pairs of meshes from each baseline and our method across the Chair and Table categories, half of which are used for a question on preference based on shape quality, and the other half for preference based on triangulation quality. After the samples are prepared, we ask the users to pick the sample which they prefer more based on the question. To avoid biases in this user study, we shuffle the pairs so that there is no positional hint to our method. We also show a collection of ground-truth meshes to the user for them to get an idea of the real distribution. In the end, we gather 784 responses from 49 participants to calculate the preferences.", + "bbox": [ + 496, + 689, + 893, + 900 + ], + "page_idx": 13 + }, + { + "type": "page_number", + "text": "14", + "bbox": [ + 475, + 924, + 493, + 936 + ], + "page_idx": 13 + }, + { + "type": "image", + "img_path": "images/95d2fd7dc948e6e373c37d2368438952d9cd7875e959f9b4d76310b4db266b77.jpg", + "image_caption": [], + "image_footnote": [], + "content": "Generated Shape\nMost similar shapes retrieved from training set", + "sub_type": "text_image", + "bbox": [ + 76, + 89, + 500, + 420 + ], + "page_idx": 14 + }, + { + "type": "image", + "img_path": "images/7e8ea87daf63578d77b643fe27855345f3b330fc8382177835e2da7c30cd4d4c.jpg", + "image_caption": [ + "Figure 13. Shape novelty analysis on ShapeNet [5] bench and lamp category for shapes generated by our method shown in main paper. We show the 3 nearest neighbors in terms of Chamfer Distance (CD) for a generated shape. Shapes are scaled to a unit length along all axes to account for augmented generations before computing CD." + ], + "image_footnote": [], + "content": "Generated Shape\nMost similar shapes retrieved from training set", + "sub_type": "text_image", + "bbox": [ + 540, + 103, + 893, + 420 + ], + "page_idx": 14 + }, + { + "type": "image", + "img_path": "images/4ec5ee7755bd6f8b5c1ddbe9d84366f8031e24b91ec1d239bef0eaaa83da18f7.jpg", + "image_caption": [ + "Figure 14. Our encoder-decoder network features an encoder with SAGEConv [20] layers processing mesh faces as a graph. Each node inputs positionally encoded face triangle coordinates, area, edge angles, and normal. The decoder, a 1D ResNet-34 [22], interprets face features as a sequence, outputting logits for the discretized face triangle coordinates in a 1283 space." + ], + "image_footnote": [], + "content": "```mermaid\ngraph LR\n InputMesh[\"Input Mesh\"] -->|\"F| x196\"| GraphConvEncoder[\"Graph Conv Encoder\"]\n GraphConvEncoder -->|\"F| x576\"| ResidualQuantizationModule[\"Residual Face Quantization Module\"]\n SequenceOfFaces[\"Sequence Of Faces\"] -->|\"F| x576\"| ResNet34Decoder[\"ResNet34 Decoder\"]\n ResNet34Decoder --> ReconstructedMesh[\"Reconstructed Mesh\"]\n```", + "sub_type": "flowchart", + "bbox": [ + 78, + 502, + 467, + 661 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "D. Shape Novelty Analysis", + "text_level": 2, + "bbox": [ + 76, + 780, + 302, + 797 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Fig. 12 and 13 displays the top-3 most similar shapes from the train set corresponding to all samples used in the main paper that were generated by our model. These nearest neighbor shapes are identified based on Chamfer Distance (CD). To ensure a fair distance computation, accounting for potential discrepancies due to scale or shift in the augmented generations, we normalize all generated and train shapes to be centered within [0, 1]3 and scaled to the extremes of this cube.", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "", + "bbox": [ + 498, + 503, + 890, + 549 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "E. Additional Results", + "text_level": 2, + "bbox": [ + 500, + 566, + 684, + 582 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Metrics. Following recent works for unconditional shape generation [13, 66, 67] for calculating the shape metrics we define", + "bbox": [ + 500, + 597, + 890, + 641 + ], + "page_idx": 14 + }, + { + "type": "equation", + "text": "$$\n\\begin{array}{l} \\mathrm{MMD} (S _ {g}, S _ {r}) = \\frac {1}{| S _ {r} |} \\sum_ {Y \\in S _ {r}} \\min _ {X \\in S _ {g}} D (X, Y), \\\\ \\operatorname{COV} (S _ {g}, S _ {r}) = \\frac {| \\{\\operatorname{argmin} _ {Y \\in S _ {r}} D (X , Y) | X \\in S _ {g} \\} |}{| S _ {r} |}, \\\\ 1 \\text {-NNA} (S _ {g}, S _ {r}) = \\frac {\\sum_ {X \\in S _ {g}} \\mathbb {1} _ {X} + \\sum_ {Y \\in S _ {r}} \\mathbb {1} _ {Y}}{| S _ {g} | + | S _ {r} |}, \\\\ \\mathbb {1} _ {X} = \\mathbb {1} [ N _ {X} \\in S _ {g} ], \\\\ \\mathbb {1} _ {Y} = \\mathbb {1} [ N _ {Y} \\in S _ {r} ], \\\\ \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 516, + 667, + 879, + 819 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "where in the 1-NNA metric N is a point cloud that is closest to X in both generated and reference dataset, i.e.,", + "bbox": [ + 498, + 832, + 890, + 862 + ], + "page_idx": 14 + }, + { + "type": "equation", + "text": "$$\nN _ {X} = \\underset {K \\in S _ {r} \\cup S _ {g}} {\\operatorname{argmin}} D (X, K)\n$$", + "text_format": "latex", + "bbox": [ + 607, + 876, + 784, + 902 + ], + "page_idx": 14 + }, + { + "type": "page_number", + "text": "15", + "bbox": [ + 475, + 924, + 493, + 936 + ], + "page_idx": 14 + }, + { + "type": "image", + "img_path": "images/9c8f17f2ed164e56329aa2345718e115db7f4d94e1cb5a94b39d1e155c6a929e.jpg", + "image_caption": [ + "Figure 15. User study interface. We show users a set of random ground-truth shapes for a category and then ask users for shape quality and triangulation preference among meshed generated by two methods." + ], + "image_footnote": [], + "content": "I filter your name\nwere are some artist designed mesh of the category chair:\nPlease answer the following questions keeping these in mind.\n• which of the objects is a better quality mesh for this category?\n• which of the objects better matches the quality of artist meshes in this category!", + "sub_type": "text_image", + "bbox": [ + 81, + 99, + 467, + 396 + ], + "page_idx": 15 + }, + { + "type": "table", + "img_path": "images/49f0a0b67bf0922c8a8f7cf55a35efdf69ee6af7dd796a2f5d42c77189f570d4.jpg", + "table_caption": [ + "Table 4. Ablations of our design choices for the encoder-decoder network on the Chair category of the ShapeNet [5] dataset." + ], + "table_footnote": [], + "table_body": "
VariantTriangle Accuracy (%) ↑Cross-Entropy ↓
w/o Positional Encoding79.330.2484
w/o Output Discretization22.030.5705
w/o Residual Quantization1.294.6679
w/o per Vertex Quantization98.640.1413
w/ PointNet Encoder88.730.1896
w/ GAT [60] Encoder86.140.2015
w/ EdgeConv [61] Encoder91.230.1702
w/ ResNet19 Decoder96.290.1492
w/ PointNet Decoder95.470.1528
MeshGPT98.490.1473
", + "bbox": [ + 81, + 479, + 468, + 625 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "We use a Chamfer Distance (CD) distance measure $D ( X , Y )$ for computing these metrics in 3D. To evaluate these point-based measures, we sample 2048 points randomly from all baseline outputs; and use 6000, 1200, 1000, 8000 generated shapes from chair, bench, lamp and table categories.", + "bbox": [ + 76, + 680, + 468, + 770 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Qualitative Results. Fig. 11 shows more unconditional generations from our model across different ShapeNet categories.", + "bbox": [ + 76, + 775, + 468, + 821 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Encoder-Decoder Ablations. In Tab. 4, we show a set of ablations on the design choice for our encoder-decoder network used for learning the triangle embeddings. We measure the performance in terms of triangle accuracy, which measures average accuracy with which all 9 coordinates of faces are correctly predicted, and the cross-entropy loss on the test set.", + "bbox": [ + 76, + 825, + 468, + 900 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 15 + }, + { + "type": "image", + "img_path": "images/93ed53b8c4f1a77bc0a632004090c5a0533351b6ab70863f6b98e63b4c7c521a.jpg", + "image_caption": [ + "Figure 16. The effectiveness of per-vertex quantization over perface quantization can be understood through an example where two faces share an edge as shown above. With per-face tokenization assigning 6 tokens per face, the sequence yields 12 unique tokens. In contrast, per-vertex tokenization leads to repeated tokens in the sequence due to shared vertices between faces. This repetition makes the sequence easier for the transformer to learn compared to a wholly unique sequence per face, especially when both sequences are of equal length." + ], + "image_footnote": [], + "content": "Sequence of Faces = (F₁, F₂) = ((V₁, V₂, V₃), (V₂, V₄, V₃))\nIf 6 tokens are assigned per face:\nSequence: (t₁¹, t₁², t₁³, t₁⁴, t₁⁵, t₁⁶, t₂¹, t₂², t₂³, t₂⁴, t₂⁵, t₂⁶)\nIf 2 tokens are assigned per vertex:\nSequence: (t₁¹, t₁², t₁³, t₁⁴, t₁⁵, t₁⁶, t₂¹, t₂², t₂³, t₂⁴, t₂⁵, t₂⁶)\nRepetition of tokens", + "sub_type": "text_image", + "bbox": [ + 500, + 128, + 893, + 277 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "We evaluate the effect of various choices – how much does the positional encoding at input help, effect of using continuous predictions instead of discrete as outputs, using vector quantization (1 token per face) instead of residual quantization (D tokens per face), encoder architecture as a point encoder, or different graph convolution operators, and decoder architecture as either ResNet19 or Point-Net decoder. Note that even though for encoder-decoder reconstruction, ‘w/o per Vertex Quantization’ performs best, this variant works significantly worse than with per Vertex Quantization, as shown in the main paper. Fig. 16 describes an intuition of why the embeddings from this variant are more transformer friendly.", + "bbox": [ + 498, + 430, + 892, + 627 + ], + "page_idx": 15 + }, + { + "type": "header", + "text": "MeshGPT User Study", + "bbox": [ + 81, + 90, + 137, + 97 + ], + "page_idx": 15 + }, + { + "type": "page_number", + "text": "16", + "bbox": [ + 475, + 924, + 495, + 936 + ], + "page_idx": 15 + } +] \ No newline at end of file diff --git a/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_content_list_v2.json b/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_content_list_v2.json new file mode 100644 index 0000000000000000000000000000000000000000..4556cbe6df40f155a416548c34283c5a9fcc9b2d --- /dev/null +++ b/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_content_list_v2.json @@ -0,0 +1,4347 @@ +[ + [ + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers" + } + ], + "level": 1 + }, + "bbox": [ + 112, + 92, + 854, + 113 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Yawar Siddiqui1 Antonio Alliegro2 Alexey Artemov1" + } + ] + }, + "bbox": [ + 254, + 142, + 702, + 160 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Tatiana Tommasi2 Daniele Sirigatti3 Vladislav Rosov3 Angela Dai1 Matthias Nießner1" + } + ] + }, + "bbox": [ + 106, + 160, + 841, + 179 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Technical University of Munich1 Politecnico di Torino2 AUDI AG3" + } + ] + }, + "bbox": [ + 209, + 185, + 754, + 203 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/3545e4e678461da72e464d2647815436fc502f261b64157952c11a9676ecbf7e.jpg" + }, + "content": "```mermaid\ngraph LR\n A[\"Shape Dataset\"] --> B[\"Face Encoder\"]\n B --> C[\"Embedding Codebook\"]\n C --> D[\"Token Decoder\"]\n D --> E[\"GPT-Style Transformer\"]\n E --> F[\"MeshGPT: Autoregressive Mesh Generation\"]\n```", + "image_caption": [ + { + "type": "text", + "content": "Figure 1. Our method creates triangle meshes by autoregressively sampling from a transformer model that has been trained to produce tokens from a learned geometric vocabulary. These tokens can then be decoded into the faces of a triangle mesh. Our method generates clean, coherent, and compact meshes, characterized by sharp edges and high fidelity." + } + ], + "image_footnote": [] + }, + "sub_type": "flowchart", + "bbox": [ + 81, + 220, + 883, + 385 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "Abstract" + } + ], + "level": 2 + }, + "bbox": [ + 233, + 449, + 313, + 465 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We introduce MeshGPT, a new approach for generating triangle meshes that reflects the compactness typical of artist-created meshes, in contrast to dense triangle meshes extracted by iso-surfacing methods from neural fields. Inspired by recent advances in powerful large language models, we adopt a sequence-based approach to autoregressively generate triangle meshes as sequences of triangles. Wefirst learn a vocabulary oflatent quantized embeddings, using graph convolutions, which inform these embeddings ofthe local mesh geometry and topology. These embeddings are sequenced and decoded into triangles by a decoder, ensuring that they can effectively reconstruct the mesh. A transformer is then trained on this learned vocabulary to predict the index of the next embedding given previous embeddings. Once trained, our model can be autoregressively sampled to generate new triangle meshes, directly generating compact meshes with sharp edges, more closely imitating the efficient triangulation patterns of human-crafted meshes. MeshGPT demonstrates a notable improvement over state of the art mesh generation methods, with a 9% increase in shape coverage and a 30-point enhancement in FID scores across various categories." + } + ] + }, + "bbox": [ + 75, + 481, + 473, + 815 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "1. Introduction" + } + ], + "level": 2 + }, + "bbox": [ + 76, + 829, + 209, + 845 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Triangle meshes are the main representation for 3D geometry in computer graphics. They are the predominant representation for 3D assets used in video games, movies, and virtual reality interfaces. Compared to alternative 3D shape representations such as point clouds or voxels, meshes provide a more coherent surface representation; they are more controllable, easier to manipulate, more compact, and fit directly into modern rendering pipelines, attaining high visual quality with far fewer primitives. In this paper, we tackle the task of automated generation of triangle meshes, streamlining the process of crafting 3D assets." + } + ] + }, + "bbox": [ + 75, + 854, + 468, + 900 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 496, + 450, + 890, + 571 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Recently, 3D vision research has seen great interest in generative 3D models using representations such as voxels [3, 62], point clouds [37, 67, 68], and neural fields [14, 19, 31, 35, 41]. However, these representations must then be converted into meshes through a post-process for use in downstream applications, for instance by iso-surfacing with Marching Cubes [36]. Unfortunately, this results in dense, over-tessellated meshes that often exhibit oversmoothing and bumpy artifacts from the iso-surfacing, as shown in Figure 2. In contrast, artist-modeled 3D meshes are compact in representation, while maintaining sharp details with much fewer triangles." + } + ] + }, + "bbox": [ + 496, + 571, + 892, + 753 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Thus, we propose MeshGPT1 to generate a mesh representation directly, as a set of triangles. Inspired by powerful recent advances in generative models for language, we adopt a direct sequence generation approach to synthesize triangle meshes as sequences of triangles. Following text generation paradigms, we first learn a vocabulary of triangles. Triangles are encoded into latent quantized embeddings through an encoder. To encourage learned triangle embeddings to maintain local geometric and topological features, we employ a graph convolutional encoder. These triangle embeddings are then decoded by a ResNet [22] decoder that processes the sequence of tokens representing a triangle to produce its vertex coordinates. We can then train a GPT-based architecture on this learned vocabulary to autoregressively produce sequences of triangles representing a mesh. Experiments across multiple categories of the ShapeNet dataset demonstrate that our method significantly improves 3D mesh generation quality in comparison with state of the art, with an average 9% increase in shape coverage and a 30-point improvement in FID scores." + } + ] + }, + "bbox": [ + 496, + 753, + 893, + 875 + ] + }, + { + "type": "page_aside_text", + "content": { + "page_aside_text_content": [ + { + "type": "text", + "content": "arXiv:2311.15475v1 [cs.CV] 27 Nov 2023" + } + ] + }, + "bbox": [ + 22, + 258, + 57, + 707 + ] + }, + { + "type": "page_footnote", + "content": { + "page_footnote_content": [ + { + "type": "text", + "content": "1nihalsid.github.io/mesh-gpt" + } + ] + }, + "bbox": [ + 517, + 887, + 671, + 900 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "1" + } + ] + }, + "bbox": [ + 480, + 924, + 488, + 936 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/9c49a05ead13fc277ddba7a5d49bbf787caf1c0d5ba8613e0e8d8d464e85ac30.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "Figure 2. Meshes generated by our method (top) for chairs, tables, benches, and lamps when trained on ShapeNet [5]. MeshGPT meshes tend to be compact, with the ability to represent both sharp details and curved boundaries. This contrasts with neural fieldbased approaches that yield dense triangulations not easily simplified through decimation (bottom)." + } + ], + "image_footnote": [] + }, + "bbox": [ + 86, + 87, + 465, + 327 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 75, + 435, + 468, + 616 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In summary, our contributions are:" + } + ] + }, + "bbox": [ + 76, + 617, + 307, + 630 + ] + }, + { + "type": "list", + "content": { + "list_type": "text_list", + "list_items": [ + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "• A new generative formulation for meshes as a sequence of triangles, tailoring a GPT-inspired decoder-only transformer, to produce compact meshes with sharp edges." + } + ] + }, + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "• Triangles are represented as a vocabulary of latent geometric tokens to enable coherent mesh generation in an autoregressive fashion." + } + ] + } + ] + }, + "bbox": [ + 76, + 631, + 468, + 720 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "2. Related Work" + } + ], + "level": 2 + }, + "bbox": [ + 76, + 734, + 218, + 750 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Voxel-based 3D Shape Generation. Early shape generation approaches generated shapes as a grid of low-resolution voxels [3, 9, 26, 62] or, more recently, as high-resolution grids using efficient representations such as Octrees [57] and sparse voxels [50], with generative models such as GANs [17]. These methods pioneered the extension of 2D generative techniques into the 3D domain. However, the voxel representation inherently constrains them with gridlike artifacts and high memory requirements, limiting their practical utility in capturing fine details and complex geometries." + } + ] + }, + "bbox": [ + 75, + 763, + 468, + 900 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 498, + 90, + 890, + 119 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Point Cloud Generation. Methods in this category represent 3D shapes by point samples on their surfaces, aiming to learn point distributions across shape datasets. Early works involved GANs for synthesizing point locations [30, 54, 59] and latent shape codes [1]. Flow-based [64] and gradient field-based models [4] also yield impressive results. Recently, diffusion-based techniques have been adapted for point cloud generation [44, 67, 68], showing competitive performance in shape generation. However, point clouds, while useful, are not the ideal format for downstream applications requiring 3D content, as converting them to meshes, which apart from being non-trivial [42, 47, 51, 65], can often fail to accurately reflect the characteristics of the underlying mesh datasets." + } + ] + }, + "bbox": [ + 498, + 128, + 892, + 339 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Neural Implicit Fields. Implicit representation of shapes as volumetric functions (e.g., signed distance functions) has become popular for encoding arbitrary topologies at any resolution [39, 45]. Various implicit generative methods have shown impressive performance using adversarial [6, 53] and diffusion-based [8, 14, 41] models. Diffusion-based neural field synthesis in MLP weight spaces [13] and triplanes [55] have also been explored, alongside leveraging image-based models for optimizing NeRFs [25, 34, 48, 63]. However, like point clouds, these methods require mesh conversion [12, 32, 36, 49, 53] for downstream applications, often leading to dense meshes that don’t capture the properties of the underlying datasets (e.g., edge lengths, dihedral angles). In contrast, we directly fit a generative model to triangulated meshes, explicitly modeling the training data, resulting in clean, compact and coherent meshes as outputs." + } + ] + }, + "bbox": [ + 498, + 345, + 892, + 589 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "3D Mesh Generation. While several discriminative approaches capable of learning signals directly on mesh structure were proposed over the recent years [16, 21, 23, 33, 40, 52, 56], direct mesh generation remains underexplored. Mesh generation has been approached with various learning-based methods [7, 11, 18, 43]. AtlasNet [18] and BSPNet [7], for example, produce mesh patches and compact meshes through binary space partitioning, respectively. However, as we demonstrate in Sec. 4, these struggle with accurately capturing shape detail." + } + ] + }, + "bbox": [ + 498, + 595, + 890, + 746 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Closely related to our work, PolyGen [43] employs two autoregressively trained networks to create explicit mesh structures. In contrast, our method utilizes a single decoderonly network, representing triangles through learned tokens for a more streamlined generation process compared to PolyGen’s separate vertex-and-face sequence approach. Additionally, we observe that PolyGen’s vertex generator, oblivious to face generation, and the face generator, not exposed to the generated vertex distribution during training, exhibit limited robustness during inference." + } + ] + }, + "bbox": [ + 496, + 750, + 892, + 900 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "2" + } + ] + }, + "bbox": [ + 478, + 924, + 491, + 936 + ] + } + ], + [ + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "3. Method" + } + ], + "level": 2 + }, + "bbox": [ + 76, + 89, + 168, + 104 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Inspired by advancements in large language models, we develop a sequence-based approach to autoregressively generate triangle meshes as sequences of triangles. We first learn a vocabulary of geometric embeddings from a large collection of 3D object meshes, enabling triangles to be encoded to and decoded from this embedding. We then train a transformer for mesh generation as autoregressive nextindex prediction over the learned vocabulary embeddings." + } + ] + }, + "bbox": [ + 75, + 114, + 468, + 234 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "To learn the triangle vocabulary, we employ a graph convolution encoder operating on triangles of a mesh and their neighborhood to extract geometrically rich features that capture the intricate details of 3D shapes. These features are quantized as embeddings of a codebook using residual quantization [27, 38], effectively reducing sequence lengths of the mesh representation. These embeddings are sequenced and then decoded by a 1D ResNet [22] guided by a reconstruction loss. This phase lays the groundwork for the subsequent training of the transformer." + } + ] + }, + "bbox": [ + 75, + 236, + 470, + 385 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We then train a GPT-style decoder-only transformer, which leverages these quantized geometric embeddings. Given a sequence of geometric embeddings extracted from the triangles of a mesh, the transformer is trained to predict the codebook index of the next embedding in the sequence. Once trained, the transformer can be auto-regressively sampled to predict sequences of embeddings. These embeddings can then be decoded to generate novel and diverse mesh structures that display efficient, irregular triangulations similar to human-crafted meshes." + } + ] + }, + "bbox": [ + 75, + 386, + 468, + 537 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "3.1. Learning Quantized Triangle Embeddings" + } + ], + "level": 2 + }, + "bbox": [ + 76, + 545, + 437, + 561 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Autoregressive generative models, such as transformers, synthesize sequences of tokens where each new token is conditioned on previously generated tokens. For generating meshes using transformers, we must then define the ordering convention of generation, along with the tokens." + } + ] + }, + "bbox": [ + 75, + 569, + 468, + 643 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "For sequence ordering, Polygen [43] suggests a convention where faces are ordered based on their lowest vertex index, followed by the next lowest, and so forth. Vertices are sorted in " + }, + { + "type": "equation_inline", + "content": "z - y - x" + }, + { + "type": "text", + "content": "order (z representing the vertical axis), progressing from lowest to highest. Within each face, indices are cyclically permuted to place the lowest index first. In our method, we also adopt this sequencing approach." + } + ] + }, + "bbox": [ + 75, + 643, + 468, + 750 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "To define the tokens to generate, we consider a practical approach to represent a mesh M for autoregressive generation: a sequence of triangles," + } + ] + }, + "bbox": [ + 75, + 750, + 468, + 795 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {M} := (f _ {1}, f _ {2}, f _ {3}, \\dots , f _ {N}), \\tag {1}", + "math_type": "latex", + "image_source": { + "path": "images/5c4bb9c1739b322c7f7055205013c2478b8b04bc8af7df9e8b6e416bbbe36845.jpg" + } + }, + "bbox": [ + 179, + 801, + 468, + 819 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "with N faces (triangles), " + }, + { + "type": "equation_inline", + "content": "f _ { i } \\in \\mathbb { R } ^ { n _ { \\mathrm { i n } } }" + }, + { + "type": "text", + "content": "having " + }, + { + "type": "equation_inline", + "content": "n _ { \\mathrm { i n } }" + }, + { + "type": "text", + "content": "features. A simple approach to describe each triangle is as its three vertices, comprising nine total coordinates. Upon discretization, these coordinates can be treated as tokens. The sequence length in this case would be 9N." + } + ] + }, + "bbox": [ + 75, + 824, + 468, + 901 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/68bf00eef4f292ec6f6d2b982ffb3ea487e15df8e5bbe5ed3e13d7f0d3653820.jpg" + }, + "content": "```mermaid\ngraph LR\n InputMesh[\"Input Mesh\"] -->|\"| F| × C_in\"| GraphConv[\"Graph Convolutional Encoder\"]\n ReconstructedMesh[\"Reconstructed Mesh\"] -->|\"| F| × 9\"| ResNetDecoder[\"ResNet Decoder\"]\n GraphConv -->|\"| F| × C_e\"| ResidualFaceQuant[\"Residual Face Quantization Module\"]\n ResNetDecoder --> SequenceOfFaces[\"Sequence Of Faces\"]\n SequenceOfFaces -->|\"| F| × C_e\"| ResidualFaceQuant\n ResidualFaceQuant -->|\"| F| ×\"| ResidualFaceQuantModule[\"Residual Face Quantization Module\"]\n ResidualFaceQuantModule -->|\"C_e\"| SumResidualFeatures[\"Sum Residual Features\"]\n ResidualFaceQuantModule -->|\"D × C_e\"| Reshape[\"Reshape\"]\n Reshape --> FeatureCodebook[\"Feature Codebook\"]\n FeatureCodebook --> MeanAcrossSharedVertices[\"Mean across Shared Vertices\"]\n MeanAcrossSharedVertices --> SplitFeature[\"Split Feature\"]\n SplitFeature -->|\"C_e\"| SumResidualFeatures\n```", + "image_caption": [ + { + "type": "text", + "content": "Figure 3. We employ a graph convolutional encoder to process mesh faces, leveraging geometric neighborhood information to capture strong features representing intricate details of 3D shapes. These features are then quantized into codebook embeddings using residual quantization [27, 38]. In contrast to naive vector quantization, this ensures better reconstruction quality. The quantized embeddings are subsequently sequenced and decoded through a 1D ResNet [22], guided by a reconstruction loss." + } + ], + "image_footnote": [] + }, + "sub_type": "flowchart", + "bbox": [ + 498, + 88, + 893, + 289 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "However, we observe two major challenges when using coordinates directly as tokens. First, the sequence lengths become excessively long, as each face is represented by nine values. This length does not scale well with transformer architectures, which often have limited context windows. Second, representing discrete positions of a triangle as tokens fails to capture geometric patterns effectively. This is because such a representation lacks information about neighboring triangles and does not incorporate any priors from mesh distributions." + } + ] + }, + "bbox": [ + 496, + 436, + 890, + 587 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "To address the aforementioned challenges, we propose to learn geometric embeddings from a collection of triangular meshes, utilizing an encoder-decoder architecture with residual vector quantization at its bottleneck (Fig. 3)." + } + ] + }, + "bbox": [ + 496, + 588, + 890, + 648 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The network’s encoder E employs graph convolutions on mesh faces, where each face forms a node and neighboring faces are connected by undirected edges. The input face node features are comprised of the nine positionally encoded coordinates of its vertices, face normal, angles between its edges, and area. These features undergo processing through a stack of SAGEConv [20] layers, extracting a feature vector for each face. This graph convolutional approach enables the extraction of geometrically enriched features " + }, + { + "type": "equation_inline", + "content": "z _ { i } \\in \\mathbb { R } ^ { n _ { \\mathrm { z } } }" + }, + { + "type": "text", + "content": "for each face," + } + ] + }, + "bbox": [ + 496, + 648, + 892, + 799 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathbf {Z} = (z _ {1}, z _ {2}, \\dots , z _ {N}) = E (\\mathcal {M}), \\tag {2}", + "math_type": "latex", + "image_source": { + "path": "images/82d4e72d4e8d649d3636f6144bb77ac91aef8d1e44d74065821e17d32fa397b1.jpg" + } + }, + "bbox": [ + 586, + 811, + 890, + 828 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "fusing neighborhood information into the learned embeddings." + } + ] + }, + "bbox": [ + 496, + 839, + 890, + 869 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "For quantization, we employ residual vector quantization (RQ) [38]. We found that using a single code per face is insufficient for accurate reconstruction. Instead, we use a stack of D codes per face. Further, we find that instead of directly using D codes per face, it is more effective to first divide the feature channels among the vertices, aggregate the features by shared vertex indices, and then quantize these vertex-based features, giving " + }, + { + "type": "equation_inline", + "content": "\\frac { \\mathrm { D } } { 3 }" + }, + { + "type": "text", + "content": "codes per vertex, and therefore effectively D codes per face. This leads to sequences that are easier to learn for the transformer trained subsequently (see Tab. 3 and Fig. 10 for comparison). Formally, given a codebook C, RQ with depth D represents features Z as" + } + ] + }, + "bbox": [ + 498, + 869, + 890, + 901 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "3" + } + ] + }, + "bbox": [ + 478, + 924, + 490, + 936 + ] + } + ], + [ + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 75, + 90, + 472, + 256 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathbf {T} = (t _ {1}, t _ {2}, \\dots , t _ {N}) = \\mathrm{RQ} (\\mathbf {Z}; \\mathcal {C}, D), \\tag {3}", + "math_type": "latex", + "image_source": { + "path": "images/1a4e40dfbd00b2c45bc5e73d5e0b75471caacda63352d27eac8e8b12c8b372aa.jpg" + } + }, + "bbox": [ + 145, + 258, + 468, + 276 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "t _ {i} = (t _ {i} ^ {1}, t _ {i} ^ {2}, \\dots , t _ {i} ^ {D}), \\tag {4}", + "math_type": "latex", + "image_source": { + "path": "images/4b410f778db16b9611323e0b65d0ee020987feb5fd828442e863817eb6447446.jpg" + } + }, + "bbox": [ + 200, + 286, + 468, + 305 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "where " + }, + { + "type": "equation_inline", + "content": "t _ { i }" + }, + { + "type": "text", + "content": "is a stack of tokens, each token " + }, + { + "type": "equation_inline", + "content": "t _ { i } ^ { d }" + }, + { + "type": "text", + "content": "being an index to an embedding " + }, + { + "type": "equation_inline", + "content": "\\mathbf { e } ( t _ { i } ^ { d } )" + }, + { + "type": "text", + "content": "in the codebook C." + } + ] + }, + "bbox": [ + 76, + 313, + 468, + 344 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The decoder then decodes the quantized face embeddings to triangles. First, the stack of D features is reduced to a single feature per face through summation across embeddings and concatenation across vertices," + } + ] + }, + "bbox": [ + 76, + 345, + 468, + 405 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\hat {\\mathbf {Z}} = (\\hat {z} _ {1}, \\dots , \\hat {z} _ {N}), \\text {with} \\hat {z} _ {i} = \\oplus_ {v = 0} ^ {2} \\sum_ {d = 1} ^ {\\frac {D}{3}} \\mathbf {e} (t _ {i} ^ {3. v + d}). \\tag {5}", + "math_type": "latex", + "image_source": { + "path": "images/43b5e648f07febbbc0a254ece4b7fc6a37fc84f43f98b8c1776a4405fb0f36b0.jpg" + } + }, + "bbox": [ + 94, + 419, + 468, + 464 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The face embeddings are arranged in the previously described order, and a 1D ResNet34 decoding head G processes the resulting sequence to output the reconstructed mesh " + }, + { + "type": "equation_inline", + "content": "{ \\hat { \\mathcal { M } } } = G ( { \\hat { \\mathbf { Z } } } )" + }, + { + "type": "text", + "content": "with 9 coordinates representing each face. We observe that predicting these coordinates as discrete variables, i.e. as a probability distribution over a set of discrete values, leads to a more accurate reconstruction compared to regressing them as real values (Fig. 4). A cross-entropy loss on the discrete mesh coordinates and a commitment loss for the embeddings guides the reconstruction process. More details can be found in supplementary." + } + ] + }, + "bbox": [ + 75, + 476, + 472, + 643 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/ee8d3956b2fa1fe0a598529c608460da65258fd9b5188ac3e5354bbc23759131.jpg" + }, + "content": "Three 3D wireframe models of a chair: one with real-valued outputs, one with discrete outputs, and the ground truth (no text or symbols on the models themselves)", + "image_caption": [ + { + "type": "text", + "content": "Figure 4. Our method utilizes a ResNet [22] decoder that outputs mesh faces as a distribution over discretized coordinate values (center), as opposed to regression of continuous values (left). This significantly reduces floating face artifacts, leading to reconstructions that more closely resemble the ground truth (right)." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 98, + 657, + 450, + 818 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "After training, the graph encoder E and codebook C are incorporated into the transformer training, using T from Eq. 3 as the token sequence. With " + }, + { + "type": "equation_inline", + "content": "| \\mathbf { T } | = D N" + }, + { + "type": "text", + "content": ", this sequence is more concise than the naive 9N-length tokenization when " + }, + { + "type": "equation_inline", + "content": "D \\ < \\ 9 ." + }, + { + "type": "text", + "content": "Thus, we obtain geometrically rich embeddings with shorter sequence lengths, overcoming our initial challenges and paving the way for efficient mesh generation." + } + ] + }, + "bbox": [ + 498, + 90, + 893, + 198 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "3.2. Mesh Generation with Transformers" + } + ], + "level": 2 + }, + "bbox": [ + 500, + 205, + 818, + 220 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/72cb966cd94dd8b5076080c802a06cda11de1a0168b09a46a1aa9944576b1ec9.jpg" + }, + "content": "```mermaid\ngraph LR\n A[\"Face Graph + Input Features\"] --> B[\"Graph Convolutional Encoder\"]\n B --> C[\"Residual Face Quantization Module\"]\n C --> D[\"Sequence & Flatten\"]\n D --> E[\"GPT-Style Transformer\"]\n E --> F[\"Predicted Codebook Indices\"]\n F --> G[\"GT Codebook Indices\"]\n G --> H[\"CE Loss\"]\n```", + "image_caption": [ + { + "type": "text", + "content": "Figure 5. We employ a transformer to generate mesh sequences as token indices from a pre-learned codebook vocabulary. During training, a graph encoder extracts features from mesh faces, which are quantized into a set of face embeddings. These embeddings are flattened, bookended with start and end tokens, and fed into a GPTstyle transformer. This decoder predicts the subsequent codebook index for each embedding, optimized via cross-entropy loss." + } + ], + "image_footnote": [] + }, + "sub_type": "flowchart", + "bbox": [ + 501, + 237, + 893, + 354 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We employ a decoder-only transformer architecture from the GPT family of models to predict meshes as sequences of indices from the learned codebook in Sec. 3.1. The input to this transformer consists of embeddings " + }, + { + "type": "equation_inline", + "content": "\\mathbf { e } ( t _ { i } ^ { d } )" + }, + { + "type": "text", + "content": "extracted from the mesh M using the GraphConv encoder E and quantized using RQ (Eq. 3). The embeddings are prefixed and suffixed with a learned start and end embedding. Additionally, learned discrete positional encodings are added, indicating the position of each face in the sequence and the index of each embedding within the face. The features then pass through a stack of multiheaded self-attention layers, where the transformer is trained to predict the codebook index of the next embedding in the sequence (Fig. 5). Essentially, we maximize the log probability of the training sequences with respect to the transformer parameters θ," + } + ] + }, + "bbox": [ + 496, + 479, + 893, + 705 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\prod_ {i = 1} ^ {N} \\prod_ {d = 1} ^ {D} p (t _ {i} ^ {d} \\mid \\mathbf {e} (t _ {< i} ^ {d}), \\mathbf {e} (t _ {i} ^ {< d}); \\theta). \\tag {6}", + "math_type": "latex", + "image_source": { + "path": "images/1550d35f45f33a9ad3318f5fee4db2c6cc9f0ffd97ab6276c575e77eaf44f3e7.jpg" + } + }, + "bbox": [ + 584, + 714, + 890, + 757 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Once the transformer is trained, it can autoregressively generate a sequence of tokens, starting with a start token and continuing until a stop token is encountered using beam sampling. The codebook embeddings indexed by this sequence of tokens is then decoded by decoder G to produce the generated mesh. As this output initially forms a ‘triangle soup’ with duplicate vertices for neighboring faces, we apply a simple post-processing operation to merge close vertices (e.g., with MeshLab), to yield the final mesh." + } + ] + }, + "bbox": [ + 496, + 763, + 893, + 901 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "4" + } + ] + }, + "bbox": [ + 478, + 924, + 491, + 936 + ] + } + ], + [ + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "3.3. Implementation Details" + } + ], + "level": 2 + }, + "bbox": [ + 76, + 90, + 294, + 107 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In learning the triangle vocabulary, our residual quantization layer features a depth of 2, yielding D = 6 embeddings per face, each with dimension 192. The codebook is dynamically updated using an exponential moving average of the clustered features. Following [29], we incorporate stochastic sampling of codes and employ a shared codebook across all levels. The decoder predicts the coordinates of the faces across 128 classes, resulting in a discretization of space to 1283 possible values. This encoder-decoder network is trained using 2 A100 GPUs for ≈ 2 days." + } + ] + }, + "bbox": [ + 75, + 114, + 468, + 265 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "For our transformer, we use a GPT2-medium model, equipped with a context window of up to 4608 embeddings. The model is trained on 4 A100 GPUs, for ≈ 5 days." + } + ] + }, + "bbox": [ + 76, + 266, + 468, + 311 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Both the encoder-decoder network and the transformer are written using the Pytorch [46] and are trained utilizing the ADAM optimizer [28]. We set the learning rate at 1 × " + }, + { + "type": "equation_inline", + "content": "1 0 ^ { - 4 }" + }, + { + "type": "text", + "content": "and use an effective batch size of 64." + } + ] + }, + "bbox": [ + 76, + 311, + 468, + 372 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "4. Experiments" + } + ], + "level": 2 + }, + "bbox": [ + 76, + 388, + 209, + 406 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "4.1. Dataset and Metrics" + } + ], + "level": 2 + }, + "bbox": [ + 76, + 414, + 267, + 429 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Data. We present our results on the ShapeNetV2 dataset. Both the encoder-decoder network and the GPT model are trained across all 55 categories of this dataset. Additionally, we fine-tune the GPT model specifically on four categories: Chair, Table, Bench, and Lamp. The results are reported on these categories. During training, we employ augmentation techniques including random shifts and random scaling to enhance the diversity of the training meshes. Similar to Polygen [43], we also apply planar decimation to further augment the shapes. To ensure that the entire mesh fits into the transformer’s context window, we select only those meshes for training that have fewer than 800 faces post-decimation. Detailed information regarding the augmentation processes, decimation techniques, and data splits are provided in the supplementary material." + } + ] + }, + "bbox": [ + 75, + 441, + 468, + 669 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Metrics. Evaluating the unconditional synthesis of 3D shapes presents challenges due to the absence of direct ground truth correspondence. Hence, we utilize established metrics for assessment, consistent with previous works [37, 67, 68]. These include Minimum Matching Distance (MMD), Coverage (COV), and 1-Nearest-Neighbor Accuracy (1-NNA). For MMD, lower is better; for COV, higher is better; for 1-NNA, 50% is the optimal. We use a Chamfer Distance (CD) distance measure for computing these metrics in 3D. More details about these metrics can be found in the supplementary." + } + ] + }, + "bbox": [ + 75, + 672, + 468, + 839 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The aforementioned metrics effectively measure the quality of shapes but do not address the visual similarity of the generated meshes to the real distribution. To assess this aspect, we render both the generated meshes and the" + } + ] + }, + "bbox": [ + 75, + 839, + 468, + 900 + ] + }, + { + "type": "table", + "content": { + "image_source": { + "path": "images/8b871bacf5cfff1883e75b5abcb4c81fe4a612a1d79d755738c7bec1d17f5365.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 1. Quantitative comparison on the task of unconditional mesh generation on a subset of categories from the ShapeNet [5] dataset. GET3D* refers to meshes simplified to 400 faces using QEM [15]. MMD values are multiplied by 103. We outperform the baselines on shape quality, visual and compactness metrics." + } + ], + "table_footnote": [], + "html": "
ClassMethodCOV↑MMD↓1-NNAFID↓KID↓|V||F|
ChairAtlasNet [18]9.034.0595.13170.710.16925004050
BSPNet [7]16.483.6291.7546.730.0306731165
Polygen [43]31.224.4193.5661.100.043248603
GET3D [14]40.853.5683.0481.450.0541372527457
GET3D*38.753.5784.0778.290.065199399
MeshGPT43.283.2975.5118.460.010125228
TableAtlasNet [18]7.163.8596.30161.380.15025004050
BSPNet [7]16.833.1493.5830.780.017420699
Polygen [43]32.993.0088.6538.530.029147454
GET3D [14]41.702.7885.5493.930.0761376727537
GET3D*37.952.8581.9350.460.037199399
MeshGPT45.682.3672.886.240.00299187
BenchAtlasNet [18]20.532.4790.58189.390.16325004050
BSPNet [7]28.742.0588.4459.110.030457756
Polygen [43]51.921.9776.9849.340.031172430
MeshGPT55.231.4468.248.720.001159291
LampAtlasNet [18]19.974.6891.85177.910.13925004050
BSPNet [7]18.385.3293.13112.650.0775871011
Polygen [43]47.864.1881.4252.480.025185558
MeshGPT53.883.9465.7319.910.004150288
", + "table_type": "complex_table", + "table_nest_level": 1 + }, + "bbox": [ + 504, + 90, + 890, + 323 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "ShapeNet meshes as images from eight different viewpoints using Blender, applying a metallic material to emphasize the geometric structures. Subsequently, we calculate the FID (Frechet Inception Distance) and KID (Kernel Incep-´ tion Distance) scores for these image sets. For both FID and KID, lower scores indicate better performance. We further report compactness as the average number of vertices and faces in the generated meshes." + } + ] + }, + "bbox": [ + 498, + 414, + 890, + 536 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "4.2. Results" + } + ], + "level": 2 + }, + "bbox": [ + 500, + 545, + 591, + 559 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We benchmark our approach against leading mesh generation methods: Polygen [43], which generates polygonal meshes by first generating vertices followed by faces conditioned on the vertices; BSPNet [7], which represents a mesh through convex decompositions; and AtlasNet [18], which represents a 3D mesh as a deformation of multiple 2D planes. We additionally compare with a state-of-the-art neural field-based method, GET3D [14], that creates shapes as 3D signed distance fields (SDFs) from which a mesh is extracted by differentiable marching tetrahedra. For BSP-Net and AtlasNet, which are built on autoencoder backbones, we follow [1] to fit a Gaussian mixture model with 32 components to enable unconditional sampling of shapes." + } + ] + }, + "bbox": [ + 498, + 568, + 890, + 763 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "As shown in Fig. 6, Fig. 7 and Tab. 1, our method outperforms all baselines in all four categories. Our method can generate sharp and compact meshes with high geometric details. Compared to Polygen, our approach creates shapes with more intricate details. Additionally, Polygen’s separate training for vertex and face models, with the latter only exposed to ground truth vertex distributions, makes it more susceptible to error accumulation during inference. Atlas-Net often suffers from folding artifacts, resulting in lower diversity and shape quality. BSPNet’s use of BSP tree of planes tends to produce blocky shapes with unusual triangulation patterns. GET3D generates good high-level shape structures, but over-triangulated and with imperfect flat surfaces. Simplifying GET3D-generated meshes with algorithms such as QEM [15] results in a loss of fine structures." + } + ] + }, + "bbox": [ + 498, + 765, + 890, + 900 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "5" + } + ] + }, + "bbox": [ + 478, + 924, + 490, + 936 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/76068c6dfb1898f16de88ae3f72de3ea3ccab75df28511e16f84b9e6bd9d5116.jpg" + }, + "content": "GT Samples\nAtlasNet\tBSPNetGET3DGET3D-QEMPolygenOurs\n100000000000000000000000000000000000000000000000000000000000000000000000000", + "image_caption": [ + { + "type": "text", + "content": "Figure 6. Qualitative comparison of Chair and Table meshes from ShapeNet [5]. Our approach produces compact meshes with sharp geometric details. In contrast, baselines often either miss these details, produce over-triangulated meshes, or output too simplistic shapes." + } + ], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 81, + 89, + 890, + 688 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 75, + 736, + 470, + 828 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "User Study. We further conducted a user study, in Tab. 2, to assess generated mesh quality. 49 participants were shown pairs of four meshes, randomly selected from our method and each baseline method. Additionally, users were presented with ground truth ShapeNet meshes for comparison. Participants were asked their preference between our method and the baseline in terms of both overall shape quality and similarity of triangulation patterns to the ground truth meshes. This resulted in 784 total question responses. Our method was significantly preferred over Atlas-Net, Polygen, and BSPNet in both shape and triangulation quality. Moreover, a majority of users (68%) favored our method over neural field-based GET3D in shape quality, with even higher preference (73%) for triangulation quality. This underscores our ability to generate high-quality meshes that align with human users’ preferences. Further user study details are provided in the supplemental." + } + ] + }, + "bbox": [ + 75, + 839, + 470, + 902 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 496, + 736, + 893, + 888 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "6" + } + ] + }, + "bbox": [ + 478, + 924, + 491, + 936 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/45b493818f6537a57fadcb2454130c2c50c5a184adc6d1ed712e535a4a05c269.jpg" + }, + "content": "GT Samples\nAtlasNet\tBSPNet\tPolygen\tOurs", + "image_caption": [], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 80, + 89, + 460, + 415 + ] + }, + { + "type": "table", + "content": { + "image_source": { + "path": "images/469b0707a1d0c24a76a461e6a0fbb95c58ce28348c8e9ee5a08dff8e39ee4713.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Figure 7. Qualitative comparison of Bench and Lamp meshes from the ShapeNet [5] dataset. Compared to baselines, our method produces valid meshes with high geometric fidelity." + } + ], + "table_footnote": [], + "html": "
PreferenceAtlasNet [18]BSPNet [7]Polygen [43]GET3D [14]
Our Shape82.65%78.57%85.71%68.37%
Our Triangulation84.69%71.43%84.69%73.47%
", + "table_type": "simple_table", + "table_nest_level": 1 + }, + "bbox": [ + 80, + 472, + 468, + 518 + ] + }, + { + "type": "table", + "content": { + "image_source": { + "path": "images/0500b44c57dd1a58136123af0b3f1b93b7cfad5e8dead5b38ee8706f0c22e0c7.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 2. Percentage of users who prefer our method over the baselines in terms of shape quality and the triangulation quality. Our generated meshes are preferred significantly more often." + }, + { + "type": "text", + "content": "Table 3. Ablations of our design choices on the Chair category of the ShapeNet [5] dataset. As highlighted by the drop in performance by removing any of them, each of these contribute to the final method." + } + ], + "table_footnote": [], + "html": "
MethodCOV↑MMD↓1-NNAFID↓KID↓
w/o Learned Tokens27.504.5193.1540.200.024
w/o Encoder Features39.243.4384.4830.350.017
w/o Pretraining36.973.7384.6927.540.014
w/o Sequence Compression30.984.1588.9838.760.023
w/o per Vertex Quantization23.575.4998.3574.940.050
MeshGPT43.283.2975.5118.460.010
", + "table_type": "simple_table", + "table_nest_level": 1 + }, + "bbox": [ + 80, + 580, + 468, + 679 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 76, + 760, + 468, + 806 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Shape Novelty Analysis. We investigate whether our method can generate novel shapes that extend beyond the training dataset, ensuring the model is not merely retrieving existing shapes. Following the methodology in previous studies [13, 24], we generate 500 shapes using our model. For each generated shape, we identify the top three nearest neighbors from the training set based on Chamfer Distance (CD). To ensure a fair distance computation, accounting for potential discrepancies due to scale or shift in the augmented generations, we normalize all generated and train shapes to be centered within [0, 1]3." + } + ] + }, + "bbox": [ + 76, + 810, + 470, + 901 + ] + }, + { + "type": "chart", + "content": { + "image_source": { + "path": "images/c529395af6d980051ddecada4916f283df5a930f3e3dfe3b5e19f6ee6a2f96a9.jpg" + }, + "content": "| Chamfer Distance (x10^3) | Proportion of Generated Shapes |\n| --- | --- |\n| 0 | ~0.5 |\n| 1 | ~4.5 |\n| 2 | ~6.5 |\n| 3 | ~3.5 |\n| 4 | ~2.5 |\n| 5 | ~1.5 |\n| 6 | ~1.5 |\n| 7 | ~1.5 |\n| 8 | ~1.0 |\n| 9 | ~0.5 |\n| 10+ | ~4.5 |", + "chart_caption": [], + "chart_footnote": [] + }, + "sub_type": "bar", + "bbox": [ + 498, + 85, + 890, + 402 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/5b3a33b4221fb57854918e5b77130294ccf40f3adc775ccf038ce130eb125645.jpg" + }, + "content": "3D model of wooden furniture with various shapes and layouts, including chairs, tables, and blocks (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "Figure 8. Shape novelty analysis on ShapeNet [5] chair category. We show the 3 nearest neighbors in terms of Chamfer Distance (CD) for a generated shape (top). We also plot the distribution of 500 generated chair samples from our method and their closeness to training distribution. Our method can generate shapes that are similar (low CD) as well as different (high CD) from the training distribution, with shapes at the 50th percentile looking different from closest train shape." + }, + { + "type": "text", + "content": "Figure 9. Given a partial mesh, our method can infer multiple possible shape completions." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 500, + 527, + 885, + 715 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 498, + 763, + 893, + 839 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Fig. 8 displays the most similar shapes from the train set corresponding to a sample generated by our model. We conduct a detailed analysis of the shape similarity distribution between the retrieved and generated shapes on the" + } + ] + }, + "bbox": [ + 498, + 840, + 893, + 901 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "7" + } + ] + }, + "bbox": [ + 480, + 924, + 490, + 936 + ] + } + ], + [ + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Chair category in Fig. 8. The CD distribution reveals that our method not only covers shapes in the training set, indicated by low CD values, but also successfully generates novel and realistic-looking shapes, indicated by high CD values. In the supplemental, we present further analysis of the novelty of all meshes generated by our method, which are featured in the figures of this paper." + } + ] + }, + "bbox": [ + 75, + 90, + 472, + 196 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Shape Completion. Our model can infer multiple possible completions for a given partial shape, leveraging its probabilistic nature to generate diverse shape hypotheses. Fig. 9 illustrates examples of chair and table completions." + } + ] + }, + "bbox": [ + 75, + 200, + 470, + 262 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "4.2.1 Ablations" + } + ], + "level": 2 + }, + "bbox": [ + 76, + 281, + 199, + 294 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In Tab. 3, we show a set of ablations on the task of unconditional mesh generation on ShapeNet Chair category. Further ablations are detailed in the supplementary." + } + ] + }, + "bbox": [ + 75, + 305, + 470, + 351 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/c106cef48f10754a10c06872decaa8bd01f67062fb929d7f25e9990aa5bda13f.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "w/o Encoder Features" + }, + { + "type": "text", + "content": "w/o Pretraining" + } + ], + "image_footnote": [] + }, + "bbox": [ + 78, + 362, + 460, + 508 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/ad9fafe54b97a2db08791ed1d9d6d5fc1f9740c532fa025b564f6f99b7850f35.jpg" + }, + "content": "3D illustration of a wooden chair with vertical supports and a curved top (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "w/o Learned Tokens" + }, + { + "type": "text", + "content": "w/o Sequence Compression" + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 86, + 531, + 189, + 671 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/7cd31a0f47e47c84d92e08dca904b6c960a3e46e34d19fe04d035df0379c8406.jpg" + }, + "content": "3D illustration of a wooden chair with geometric panel design (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "w/o per Vertex Quantization" + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 207, + 532, + 318, + 671 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/a1fcd1221add5906336612abb60dd62afe146092c590f7e919b6ddaee9d492a5.jpg" + }, + "content": "3D illustration of a wooden chair with yellow cushion and side legs (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "Ours (Complete)" + }, + { + "type": "text", + "content": "Figure 10. Ablation over our method’s components. Naive tokenization (w/o Learned Tokens) and naive per face quantization (w/o per-vertex quantization) markedly diminishes shape quality. Longer sequences without sequence compression (w/o Sequence Compression) lead to the model forgetting the context and repeating shape elements in the output." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 336, + 531, + 439, + 671 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Do learned geometric embeddings help? Using our geometric embeddings in vocabulary learning significantly improves over naive coordinate tokenization (w/o Learned Tokens), as shown in Tab. 3 and Fig. 3." + } + ] + }, + "bbox": [ + 75, + 806, + 468, + 867 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Does sequence length compression help? As evidenced by Tab. 3 and Fig. 3, a model with a shorter sequence length performs better than without (w/o Sequence Compression), as shorter sequence lengths fit transformer context windows better. Visually, with longer sequences, shapes exhibit repeating structures due to limited context." + } + ] + }, + "bbox": [ + 75, + 869, + 470, + 901 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 496, + 90, + 890, + 151 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "What is the effect of aggregation and quantization across vertex indices instead of faces? As discussed in Section 3, an alternative to having embeddings aggregated and quantized across vertex indices, is to simply have the same number of embeddings directly per face (w/o per Vertex Quantization). In Tab. 3, we observe that this makes sequences much harder to learn with the transformer." + } + ] + }, + "bbox": [ + 496, + 155, + 893, + 261 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Do features from graph convolutional encoder help in mesh generation? An alternative to using embeddings from the graph encoder and the codebook is to only use the codebook indices of these tokens as input to the transformer, and let the transformer learn the discrete token embeddings (w/o Encoder Features). While the transformer is able to still learn meaningful embeddings, these are still not as effective as using graph encoder features." + } + ] + }, + "bbox": [ + 496, + 265, + 892, + 385 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "What is the effect of large-scale shape pretraining? Tab. 3 shows that training only on shapes from individual categories (w/o Pretraining) leads to overfitting and subobtimal performance, in contrast to pre-training our GPT transformer on all ShapeNet train shapes." + } + ] + }, + "bbox": [ + 496, + 388, + 890, + 465 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Limitations. MeshGPT significantly advances direct mesh generation but faces several limitations. Its autoregressive nature leads to slower sampling performance, with mesh generation times taking 30 to 90 seconds. Despite our learned tokenization approach reducing sequence lengths, which suffices for single object generation, it may not be as effective for scene-scale generation, suggesting an area for future enhancement. Moreover, our current computational resources limit us to using a GPT2-medium transformer, which is smaller than more sophisticated models like Llama2 [58]. Given that larger language models benefit from increased data and computational power, expanding these resources could significantly boost MeshGPT’s performance and capabilities." + } + ] + }, + "bbox": [ + 496, + 468, + 892, + 680 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "5. Conclusion" + } + ], + "level": 2 + }, + "bbox": [ + 500, + 694, + 617, + 709 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We have introduced MeshGPT, a novel shape generation approach that outputs meshes directly as triangles. We learn a vocabulary of geometric embeddings over a distribution of meshes, over which a transformer is trained to predict meshes autoregressively as a sequence of triangles. In contrast to existing mesh generation approaches, our method generates clean, coherent meshes which are compact and follow the triangulation patterns in real data more closely. We believe that MeshGPT will not only elevate the current landscape of mesh generation but also inspire new research in the area, offering a unique alternative to the more commonly explored representations for 3D content creation." + } + ] + }, + "bbox": [ + 496, + 719, + 893, + 900 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "8" + } + ] + }, + "bbox": [ + 480, + 924, + 488, + 936 + ] + } + ], + [ + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "Acknowledgements" + } + ], + "level": 2 + }, + "bbox": [ + 78, + 90, + 243, + 107 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "This work was funded by AUDI AG. Matthias Nießner was supported by the ERC Starting Grant Scan2CAD (804724). Angela Dai was supported by the Bavarian State Ministry of Science and the Arts coordinated by the Bavarian Research Institute for Digital Transformation (BIDT). We would like to thank Ziya Erkoc¸, Quyet-Chien Nguyen, Haoxuan Li and Artem Sevastopolsky for the helpful discussions." + } + ] + }, + "bbox": [ + 76, + 114, + 468, + 213 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "References" + } + ], + "level": 2 + }, + "bbox": [ + 78, + 244, + 173, + 258 + ] + }, + { + "type": "list", + "content": { + "list_type": "reference_list", + "list_items": [ + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40–49. 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We provide implementation details of our method, loss functions, and the baselines in Section B. Additional details about the user study are provided in Section C. We also provide further qualitative and quantitative results (Section E), including a shape novelty analysis (Section D) for shapes from the main paper. We further encourage the readers to check out the supplemental video for a summary of the method and an overview of results." + } + ] + }, + "bbox": [ + 75, + 114, + 472, + 267 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "A. Data" + } + ], + "level": 2 + }, + "bbox": [ + 76, + 284, + 147, + 300 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Selection. We use the ShapeNetV2 [5] dataset for all our experiments. We first apply planar decimation to each shape using Blender [10], with the angle tolerance parameter α set within [1, 60]. The impact of this decimation is assessed by calculating the Hausdorff distance [2] between the decimated and original shapes. We then choose, for each original shape, the decimated version with the Hausdorff distance closest to, but below, a pre-set threshold " + }, + { + "type": "equation_inline", + "content": "\\delta _ { \\mathrm { h a u s d o r f f } } ." + }, + { + "type": "text", + "content": "Shapes with more than 800 faces are excluded, resulting in a final count of 28980 shapes across all categories. The Chair, Table, Bench, and Lamp categories are further divided into a 9:1 train-test split. All shapes from rest of the categories are used for pretraining phase, while only the training subset from specific categories is used for pretraining and finetuning. All shapes are normalized to be centered at the origin and scaled to ensure the longest side is of unit length." + } + ] + }, + "bbox": [ + 75, + 314, + 472, + 556 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Augmentation. During the training of both the encoderdecoder and the transformer, multiple augmentation techniques are applied to all train shapes. Scaling augmentation, ranging from 0.75 to 1.25, is independently applied across each axis. Post-scaling, meshes are resized to keep the longest side at unit length. Additionally, jitter-shift augmentation in the range of [−0.1, 0.1] is used, adjusted to maintain the mesh within the unit bounding box around the origin. We also implement varying levels of planar decimation for training shapes, provided the distortion remains below " + }, + { + "type": "equation_inline", + "content": "\\delta _ { \\mathrm { h a u s d o r f f } } ." + } + ] + }, + "bbox": [ + 75, + 561, + 472, + 729 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "B. Method Details" + } + ], + "level": 2 + }, + "bbox": [ + 76, + 744, + 233, + 758 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "B.1. Architecture" + } + ], + "level": 2 + }, + "bbox": [ + 76, + 770, + 215, + 785 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The architecture of our encoder-decoder network is elaborated in Fig. 14. The encoder comprises a series of SAGE-Conv [20] graph convolution layers, processing the mesh in the form of a face graph. For each graph node, input features include the positionally encoded 9 coordinates of the face triangle, its area, the angles between its edges, and the normal of the face. The decoder is essentially a 1D" + } + ] + }, + "bbox": [ + 75, + 794, + 470, + 901 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "ResNet-34 [22] network, applied to the face features interpreted as a 1D sequence. It outputs logits corresponding to the 9 discrete coordinates of each face triangle, which are discretized within a " + }, + { + "type": "equation_inline", + "content": "1 2 8 ^ { 3 }" + }, + { + "type": "text", + "content": "space. The codebook C has a size of 16384. The architecture of the transformer is simply a GPT-2 medium architecture, i.e. 24 multi-headed self attention layers, 16 heads, 768 as feature width, with context length of 4608." + } + ] + }, + "bbox": [ + 496, + 90, + 893, + 212 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "B.2. Residual Vector Quantization" + } + ], + "level": 2 + }, + "bbox": [ + 500, + 219, + 767, + 234 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Fundamentals. For quantization, we employ residual vector quantization (RQ) [29, 38]. RQ discretizes a vector z with a stack of D ordered codes. Starting with the " + }, + { + "type": "equation_inline", + "content": "0 ^ { \\mathrm { t h } }" + }, + { + "type": "text", + "content": "residual " + }, + { + "type": "equation_inline", + "content": "\\mathbf { r } ^ { 0 } = \\mathbf { z } ," + }, + { + "type": "text", + "content": ", RQ recursively computes " + }, + { + "type": "equation_inline", + "content": "t ^ { d }" + }, + { + "type": "text", + "content": "as the code of the residual " + }, + { + "type": "equation_inline", + "content": "\\mathbf { r } ^ { d - 1 }" + }, + { + "type": "text", + "content": ", and the next residual " + }, + { + "type": "equation_inline", + "content": "\\mathbf { r } ^ { d }" + }, + { + "type": "text", + "content": "as" + } + ] + }, + "bbox": [ + 498, + 246, + 893, + 321 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "t ^ {d} = \\mathcal {Q} \\left(\\mathbf {r} ^ {d - 1}; \\mathcal {C}\\right) \\tag {7}", + "math_type": "latex", + "image_source": { + "path": "images/44cba733956d05a27ab445cb9cb1e2599b41d866b2c754ec0f9901640971ab03.jpg" + } + }, + "bbox": [ + 632, + 328, + 890, + 345 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathbf {r} ^ {d} = \\mathbf {r} ^ {d - 1} - \\mathbf {e} (t ^ {d}) \\tag {8}", + "math_type": "latex", + "image_source": { + "path": "images/020437d77367d0bc4899d24ebb8dacec3203a9bc0c95e8e837961340b0918a5e.jpg" + } + }, + "bbox": [ + 630, + 349, + 890, + 367 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "where " + }, + { + "type": "equation_inline", + "content": "\\mathcal { Q } ( \\mathbf { z } ; \\mathcal { C } )" + }, + { + "type": "text", + "content": "denotes vector quantization of z with codebook " + }, + { + "type": "equation_inline", + "content": "{ \\mathcal { C } } ," + }, + { + "type": "text", + "content": ", and " + }, + { + "type": "equation_inline", + "content": "\\mathbf { e } ( t ^ { d } )" + }, + { + "type": "text", + "content": "is the embedding in the codebook C. Further, we define" + } + ] + }, + "bbox": [ + 498, + 375, + 890, + 417 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\hat {\\mathbf {z}} ^ {(d)} = \\sum_ {1} ^ {d} \\mathbf {e} (t ^ {d}) \\tag {9}", + "math_type": "latex", + "image_source": { + "path": "images/2211427a900f3cc85d32b0c0e542da3e1d541c41761a79d2b19bc6a2838d11a7.jpg" + } + }, + "bbox": [ + 637, + 419, + 890, + 458 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "as the partial sum of up to d code embeddings, and " + }, + { + "type": "equation_inline", + "content": "\\hat { \\mathbf { z } } = \\hat { \\mathbf { z } } ^ { D }" + }, + { + "type": "text", + "content": "is the quantized vector of z. The recursive quantization of RQ thus approximates the vector z in a coarse-to-fine manner [29]. The commitment loss can now be defined between vector z and its quantization zˆ as" + } + ] + }, + "bbox": [ + 498, + 462, + 893, + 539 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {L} _ {\\text {commit}} (\\mathbf {z}, \\hat {\\mathbf {z}}) = \\sum_ {d = 1} ^ {D} \\| \\mathbf {z} - \\mathrm{sg} [ \\hat {\\mathbf {z}} ^ {(d)} ] \\| _ {2} ^ {2} \\tag {10}", + "math_type": "latex", + "image_source": { + "path": "images/1ea5a6505d55a2fe4afb157ac943d526b5b89fc808b0ceeb1ce853c0a809c5b8.jpg" + } + }, + "bbox": [ + 576, + 546, + 890, + 587 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "where sg denotes the stop gradient operation." + } + ] + }, + "bbox": [ + 500, + 593, + 799, + 608 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Per Vertex Residual Vector Quantization. Instead of directly applying RQ, for a face feature " + }, + { + "type": "equation_inline", + "content": "\\mathbf { z _ { i } }" + }, + { + "type": "text", + "content": "extracted by the graph encoder, we first split this 576 dimension face feature " + }, + { + "type": "equation_inline", + "content": "\\mathbf { z _ { i } }" + }, + { + "type": "text", + "content": "into 3 features, " + }, + { + "type": "equation_inline", + "content": "( \\mathbf { z } _ { i } ^ { 1 } , \\mathbf { z } _ { i } ^ { 2 } , \\mathbf { z } _ { i } ^ { 3 } )" + }, + { + "type": "text", + "content": "), each of 192 dimensions representing the features of the face triangle’s 3 vertices. The features the fall on vertices that are shared across faces are averaged. On these per vertex index feature " + }, + { + "type": "equation_inline", + "content": "\\mathbf { z } _ { i } ^ { j }" + }, + { + "type": "text", + "content": ", RQ quantizes them into a stack of " + }, + { + "type": "equation_inline", + "content": "\\textstyle { \\frac { D } { 3 } }" + }, + { + "type": "text", + "content": "features," + } + ] + }, + "bbox": [ + 498, + 611, + 890, + 733 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathrm{RQ} (\\mathbf {z _ {i}}; \\mathcal {C}, D) = (\\mathrm{RQ} (\\mathbf {z _ {i} ^ {1}}; \\mathcal {C}, \\frac {D}{3}), \\dots , \\mathrm{RQ} (\\mathbf {z _ {i} ^ {3}}; \\mathcal {C}, \\frac {D}{3})) \\tag {11}", + "math_type": "latex", + "image_source": { + "path": "images/b4b99368e6d72d15d8330d70bdec6bbef080804b6993055984ad1f0503981ead.jpg" + } + }, + "bbox": [ + 506, + 739, + 890, + 771 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "for codebook C, with" + } + ] + }, + "bbox": [ + 500, + 775, + 643, + 789 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathrm{RQ} (\\mathbf {z} _ {\\mathbf {i}} ^ {\\mathbf {j}}; \\mathcal {C}, \\frac {D}{3}) = (t _ {i} ^ {2 j - \\frac {D}{3} + 1}, t _ {i} ^ {2 j - \\frac {D}{3} + 2}, \\dots , t _ {i} ^ {2 j}), \\tag {12}", + "math_type": "latex", + "image_source": { + "path": "images/d40998845b921b4e3b22fb9514967b79d12ae17b67a17f7a2995beff4baf0146.jpg" + } + }, + "bbox": [ + 522, + 795, + 890, + 825 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "where " + }, + { + "type": "equation_inline", + "content": "t _ { i } ^ { d }" + }, + { + "type": "text", + "content": "is the index to the embedding " + }, + { + "type": "equation_inline", + "content": "\\mathbf { e } ( t _ { i } ^ { d } )" + }, + { + "type": "text", + "content": "in the codebook C. Taken together for each vertex, these form a stack of D features," + } + ] + }, + "bbox": [ + 498, + 830, + 890, + 876 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathrm{RQ} (\\mathbf {z _ {i}}; \\mathcal {C}, D) = (t _ {i} ^ {1}, t _ {i} ^ {2}, \\dots , t _ {i} ^ {D}) = t _ {i}. \\tag {13}", + "math_type": "latex", + "image_source": { + "path": "images/868036cb80a50a21a3a70fb106cbc05589657be145e987ff796893ef5582e3a2.jpg" + } + }, + "bbox": [ + 568, + 883, + 890, + 902 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "12" + } + ] + }, + "bbox": [ + 475, + 924, + 495, + 936 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/22c1035334c0e2d06f3f6dff66da36e08b29b61356c3f3ee05ec77a5c69fdd7e.jpg" + }, + "content": "Collection of 3D architectural and furniture models including wooden chairs, tables, benches, and decorative objects (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "Figure 11. Additional novel shapes on Chairs, Tables, Benches and Lamps generated by our method." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 138, + 85, + 836, + 583 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Thus, the residual quantization for the features extracted for all the N faces of the mesh " + }, + { + "type": "equation_inline", + "content": "\\mathbf { Z } = ( z _ { 1 } , z _ { 2 } , \\ldots , z _ { N } )" + }, + { + "type": "text", + "content": "is given as" + } + ] + }, + "bbox": [ + 75, + 632, + 470, + 676 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathrm{RQ} (\\mathbf {Z}; \\mathcal {C}, D) = \\mathrm{RQ} (\\mathbf {z _ {1}} \\dots \\mathbf {z _ {N}}; \\mathcal {C}, D) \\tag {14}", + "math_type": "latex", + "image_source": { + "path": "images/9f4304f09188d4d264ab7afae1c07ec7011758ec3aa2284281ff49cf23a07f07.jpg" + } + }, + "bbox": [ + 158, + 686, + 468, + 703 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathrm{RQ} (\\mathbf {z _ {1}} \\dots \\mathbf {z _ {N}}; \\mathcal {C}, D) = (t _ {0}, t _ {1}, \\dots , t _ {N}). \\tag {15}", + "math_type": "latex", + "image_source": { + "path": "images/def86cdbe7e7d40f29d70ca4ab576f7313ff826374d637551d21e5751a7ebb9a.jpg" + } + }, + "bbox": [ + 138, + 705, + 468, + 722 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Fig. 16 gives an intuition on why ‘per vertex’ tokenization is better than ‘per face’ tokenization, with ablations in the main paper confirming it." + } + ] + }, + "bbox": [ + 75, + 729, + 468, + 775 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "B.3. Loss Functions" + } + ], + "level": 2 + }, + "bbox": [ + 76, + 782, + 233, + 797 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Vocabulary Learning. Let " + }, + { + "type": "equation_inline", + "content": "\\mathcal { P } _ { n i j k }" + }, + { + "type": "text", + "content": "be the predicted probability distribution over the discrete coordinates, where n is the face index, i is the vertex index inside the face, " + }, + { + "type": "equation_inline", + "content": "j" + }, + { + "type": "text", + "content": "is the coordinate’s axis index " + }, + { + "type": "equation_inline", + "content": "( x , y \\ \\mathrm { o r } \\ z )" + }, + { + "type": "text", + "content": ", and k goes over the discretized positions " + }, + { + "type": "equation_inline", + "content": "\\in \\{ 1 , 2 , 3 , \\ldots , 1 2 8 \\}" + }, + { + "type": "text", + "content": ". If " + }, + { + "type": "equation_inline", + "content": "V _ { n i j }" + }, + { + "type": "text", + "content": "is the target discretized position, then the reconstruction loss for the encoder-decoder network is given as" + } + ] + }, + "bbox": [ + 75, + 809, + 470, + 901 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 500, + 633, + 743, + 648 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {L} _ {\\text {recon}} = \\sum_ {n = 1} ^ {N} \\sum_ {i = 1} ^ {3} \\sum_ {j = 1} ^ {3} \\sum_ {k = 1} ^ {1 2 8} \\mathrm{w} _ {n i j k} \\log \\mathcal {P} _ {n i j k} \\tag {16}", + "math_type": "latex", + "image_source": { + "path": "images/fb92775219515f035c625846a8e9c7ac63788b512340dd0f74ef75e600381dd7.jpg" + } + }, + "bbox": [ + 557, + 660, + 890, + 704 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "with" + } + ] + }, + "bbox": [ + 500, + 715, + 535, + 729 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathrm{w} _ {n i j k} = \\text {smooth} \\left(\\text {one - hot} _ {1 2 8} \\left(V _ {n i j}\\right)\\right) \\tag {17}", + "math_type": "latex", + "image_source": { + "path": "images/3f4d9f31af7db6eedbdf6cce5a529185b922de8afe61c6e444b878f3a7a0341e.jpg" + } + }, + "bbox": [ + 573, + 744, + 890, + 762 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "is a smoothening kernel applied across the one-hot probability distribution over the targets, encouraging physically close coordinates to be penalized less. The loss over the encoder-decoder network is the sum of " + }, + { + "type": "equation_inline", + "content": "{ \\mathcal { L } } _ { \\mathrm { r e c o n } }" + }, + { + "type": "text", + "content": "and " + }, + { + "type": "equation_inline", + "content": "\\mathcal { L } _ { \\mathrm { c o m m i t } }" + }, + { + "type": "text", + "content": "previously described." + } + ] + }, + "bbox": [ + 496, + 775, + 890, + 851 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Transformer. Given a target sequence " + }, + { + "type": "equation_inline", + "content": "\\begin{array} { r l } { \\mathbf T } & { { } = } \\end{array}" + }, + { + "type": "equation_inline", + "content": "( t _ { 0 } , t _ { 1 } , \\ldots , t _ { N } )" + }, + { + "type": "text", + "content": "with " + }, + { + "type": "equation_inline", + "content": "\\begin{array} { c c l } { t _ { i } } & { = } & { ( t _ { i } ^ { 1 } , \\bar { t } _ { i } ^ { 2 } , \\dots , \\bar { t } _ { i } ^ { D } ) } \\end{array}" + }, + { + "type": "text", + "content": ", and " + }, + { + "type": "equation_inline", + "content": "s _ { i } ^ { j } \\mathrm { i s }" + }, + { + "type": "text", + "content": "the corresponding predicted sequence element, then the transformer is trained with the loss" + } + ] + }, + "bbox": [ + 500, + 854, + 893, + 901 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "13" + } + ] + }, + "bbox": [ + 475, + 924, + 493, + 936 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/af8b3cd584542eb6776b8e675298e42cc5c1a00283f7ad4d41092a1e2cc3a20a.jpg" + }, + "content": "Grid of 3D-rendered wooden chairs with varying colors and line textures, no text or symbols present.", + "image_caption": [ + { + "type": "text", + "content": "Generated Shape" + }, + { + "type": "text", + "content": "Most similar shapes retrieved from training set" + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 80, + 89, + 428, + 532 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/d00aabe098c8a3f3b7dac3186467ea197ed472f32e2fee65cd05d4e034e6f1e2.jpg" + }, + "content": "Collection of 3D-rendered wooden table and chair models in various colors, showing different shapes and sizes (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "Generated Shape" + }, + { + "type": "text", + "content": "Most similar shapes retrieved from training set" + }, + { + "type": "text", + "content": "Figure 12. Shape novelty analysis on ShapeNet [5] chair and table category for shapes generated by our method shown in main paper. We show the 3 nearest neighbors in terms of Chamfer Distance (CD) for a generated shape. Shapes are scaled to a unit length along all axes to account for augmented generations before computing CD." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 450, + 90, + 890, + 532 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 76, + 633, + 308, + 646 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {L} _ {\\mathrm{recon}} = \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {D} \\sum_ {k = 1} ^ {| \\mathcal {C} |} \\log p (s _ {i} ^ {k} = t _ {i} ^ {j}). \\tag {18}", + "math_type": "latex", + "image_source": { + "path": "images/3a9012a3740ff174fd6f405856953c28f453ecfb2a8ab86ac8ee48cff8bd4e4b.jpg" + } + }, + "bbox": [ + 151, + 666, + 468, + 710 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "B.4. Baselines" + } + ], + "level": 2 + }, + "bbox": [ + 76, + 736, + 187, + 750 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We utilize the official implementations for BSPNet [7], AtlasNet [18], and GET3D [14]. For Polygen [43], we reimplement it following the details in their paper. To align its architecture with our method, we employ the same GPT2- medium architecture for the vertex model in Polygen. Additionally, mirroring our approach, Polygen undergoes pretraining on all categories and is finetuned for each evaluated category, applying the same train-time augmentations as used in our method." + } + ] + }, + "bbox": [ + 75, + 763, + 470, + 900 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "C. User Study Details" + } + ], + "level": 2 + }, + "bbox": [ + 500, + 630, + 684, + 648 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We develop a Django-based web application for the user study. In Fig. 15, we show the interface for the questionnaire. We randomly select 16 pairs of meshes from each baseline and our method across the Chair and Table categories, half of which are used for a question on preference based on shape quality, and the other half for preference based on triangulation quality. After the samples are prepared, we ask the users to pick the sample which they prefer more based on the question. To avoid biases in this user study, we shuffle the pairs so that there is no positional hint to our method. We also show a collection of ground-truth meshes to the user for them to get an idea of the real distribution. In the end, we gather 784 responses from 49 participants to calculate the preferences." + } + ] + }, + "bbox": [ + 496, + 689, + 893, + 900 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "14" + } + ] + }, + "bbox": [ + 475, + 924, + 493, + 936 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/95d2fd7dc948e6e373c37d2368438952d9cd7875e959f9b4d76310b4db266b77.jpg" + }, + "content": "Generated Shape\nMost similar shapes retrieved from training set", + "image_caption": [], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 76, + 89, + 500, + 420 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/7e8ea87daf63578d77b643fe27855345f3b330fc8382177835e2da7c30cd4d4c.jpg" + }, + "content": "Generated Shape\nMost similar shapes retrieved from training set", + "image_caption": [ + { + "type": "text", + "content": "Figure 13. Shape novelty analysis on ShapeNet [5] bench and lamp category for shapes generated by our method shown in main paper. We show the 3 nearest neighbors in terms of Chamfer Distance (CD) for a generated shape. Shapes are scaled to a unit length along all axes to account for augmented generations before computing CD." + } + ], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 540, + 103, + 893, + 420 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/4ec5ee7755bd6f8b5c1ddbe9d84366f8031e24b91ec1d239bef0eaaa83da18f7.jpg" + }, + "content": "```mermaid\ngraph LR\n InputMesh[\"Input Mesh\"] -->|\"F| x196\"| GraphConvEncoder[\"Graph Conv Encoder\"]\n GraphConvEncoder -->|\"F| x576\"| ResidualQuantizationModule[\"Residual Face Quantization Module\"]\n SequenceOfFaces[\"Sequence Of Faces\"] -->|\"F| x576\"| ResNet34Decoder[\"ResNet34 Decoder\"]\n ResNet34Decoder --> ReconstructedMesh[\"Reconstructed Mesh\"]\n```", + "image_caption": [ + { + "type": "text", + "content": "Figure 14. Our encoder-decoder network features an encoder with SAGEConv [20] layers processing mesh faces as a graph. Each node inputs positionally encoded face triangle coordinates, area, edge angles, and normal. The decoder, a 1D ResNet-34 [22], interprets face features as a sequence, outputting logits for the discretized face triangle coordinates in a 1283 space." + } + ], + "image_footnote": [] + }, + "sub_type": "flowchart", + "bbox": [ + 78, + 502, + 467, + 661 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "D. Shape Novelty Analysis" + } + ], + "level": 2 + }, + "bbox": [ + 76, + 780, + 302, + 797 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Fig. 12 and 13 displays the top-3 most similar shapes from the train set corresponding to all samples used in the main paper that were generated by our model. These nearest neighbor shapes are identified based on Chamfer Distance (CD). To ensure a fair distance computation, accounting for potential discrepancies due to scale or shift in the augmented generations, we normalize all generated and train shapes to be centered within [0, 1]3 and scaled to the extremes of this cube." + } + ] + }, + "bbox": [ + 75, + 809, + 470, + 902 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 498, + 503, + 890, + 549 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "E. Additional Results" + } + ], + "level": 2 + }, + "bbox": [ + 500, + 566, + 684, + 582 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Metrics. Following recent works for unconditional shape generation [13, 66, 67] for calculating the shape metrics we define" + } + ] + }, + "bbox": [ + 500, + 597, + 890, + 641 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\begin{array}{l} \\mathrm{MMD} (S _ {g}, S _ {r}) = \\frac {1}{| S _ {r} |} \\sum_ {Y \\in S _ {r}} \\min _ {X \\in S _ {g}} D (X, Y), \\\\ \\operatorname{COV} (S _ {g}, S _ {r}) = \\frac {| \\{\\operatorname{argmin} _ {Y \\in S _ {r}} D (X , Y) | X \\in S _ {g} \\} |}{| S _ {r} |}, \\\\ 1 \\text {-NNA} (S _ {g}, S _ {r}) = \\frac {\\sum_ {X \\in S _ {g}} \\mathbb {1} _ {X} + \\sum_ {Y \\in S _ {r}} \\mathbb {1} _ {Y}}{| S _ {g} | + | S _ {r} |}, \\\\ \\mathbb {1} _ {X} = \\mathbb {1} [ N _ {X} \\in S _ {g} ], \\\\ \\mathbb {1} _ {Y} = \\mathbb {1} [ N _ {Y} \\in S _ {r} ], \\\\ \\end{array}", + "math_type": "latex", + "image_source": { + "path": "images/19c6197c76d7bc7cf778195faf70a0af545cf9c3d8ba819c98ba311568451adf.jpg" + } + }, + "bbox": [ + 516, + 667, + 879, + 819 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "where in the 1-NNA metric N is a point cloud that is closest to X in both generated and reference dataset, i.e.," + } + ] + }, + "bbox": [ + 498, + 832, + 890, + 862 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "N _ {X} = \\underset {K \\in S _ {r} \\cup S _ {g}} {\\operatorname{argmin}} D (X, K)", + "math_type": "latex", + "image_source": { + "path": "images/0de2feb3a7d26f051457f5a3ccc07c749b076715468812b6386426b03394b547.jpg" + } + }, + "bbox": [ + 607, + 876, + 784, + 902 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "15" + } + ] + }, + "bbox": [ + 475, + 924, + 493, + 936 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/9c8f17f2ed164e56329aa2345718e115db7f4d94e1cb5a94b39d1e155c6a929e.jpg" + }, + "content": "I filter your name\nwere are some artist designed mesh of the category chair:\nPlease answer the following questions keeping these in mind.\n• which of the objects is a better quality mesh for this category?\n• which of the objects better matches the quality of artist meshes in this category!", + "image_caption": [ + { + "type": "text", + "content": "Figure 15. User study interface. We show users a set of random ground-truth shapes for a category and then ask users for shape quality and triangulation preference among meshed generated by two methods." + } + ], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 81, + 99, + 467, + 396 + ] + }, + { + "type": "table", + "content": { + "image_source": { + "path": "images/49f0a0b67bf0922c8a8f7cf55a35efdf69ee6af7dd796a2f5d42c77189f570d4.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 4. Ablations of our design choices for the encoder-decoder network on the Chair category of the ShapeNet [5] dataset." + } + ], + "table_footnote": [], + "html": "
VariantTriangle Accuracy (%) ↑Cross-Entropy ↓
w/o Positional Encoding79.330.2484
w/o Output Discretization22.030.5705
w/o Residual Quantization1.294.6679
w/o per Vertex Quantization98.640.1413
w/ PointNet Encoder88.730.1896
w/ GAT [60] Encoder86.140.2015
w/ EdgeConv [61] Encoder91.230.1702
w/ ResNet19 Decoder96.290.1492
w/ PointNet Decoder95.470.1528
MeshGPT98.490.1473
", + "table_type": "simple_table", + "table_nest_level": 1 + }, + "bbox": [ + 81, + 479, + 468, + 625 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We use a Chamfer Distance (CD) distance measure " + }, + { + "type": "equation_inline", + "content": "D ( X , Y )" + }, + { + "type": "text", + "content": "for computing these metrics in 3D. To evaluate these point-based measures, we sample 2048 points randomly from all baseline outputs; and use 6000, 1200, 1000, 8000 generated shapes from chair, bench, lamp and table categories." + } + ] + }, + "bbox": [ + 76, + 680, + 468, + 770 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Qualitative Results. Fig. 11 shows more unconditional generations from our model across different ShapeNet categories." + } + ] + }, + "bbox": [ + 76, + 775, + 468, + 821 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Encoder-Decoder Ablations. In Tab. 4, we show a set of ablations on the design choice for our encoder-decoder network used for learning the triangle embeddings. We measure the performance in terms of triangle accuracy, which measures average accuracy with which all 9 coordinates of faces are correctly predicted, and the cross-entropy loss on the test set." + } + ] + }, + "bbox": [ + 76, + 825, + 468, + 900 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 498, + 90, + 890, + 119 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/93ed53b8c4f1a77bc0a632004090c5a0533351b6ab70863f6b98e63b4c7c521a.jpg" + }, + "content": "Sequence of Faces = (F₁, F₂) = ((V₁, V₂, V₃), (V₂, V₄, V₃))\nIf 6 tokens are assigned per face:\nSequence: (t₁¹, t₁², t₁³, t₁⁴, t₁⁵, t₁⁶, t₂¹, t₂², t₂³, t₂⁴, t₂⁵, t₂⁶)\nIf 2 tokens are assigned per vertex:\nSequence: (t₁¹, t₁², t₁³, t₁⁴, t₁⁵, t₁⁶, t₂¹, t₂², t₂³, t₂⁴, t₂⁵, t₂⁶)\nRepetition of tokens", + "image_caption": [ + { + "type": "text", + "content": "Figure 16. The effectiveness of per-vertex quantization over perface quantization can be understood through an example where two faces share an edge as shown above. With per-face tokenization assigning 6 tokens per face, the sequence yields 12 unique tokens. In contrast, per-vertex tokenization leads to repeated tokens in the sequence due to shared vertices between faces. This repetition makes the sequence easier for the transformer to learn compared to a wholly unique sequence per face, especially when both sequences are of equal length." + } + ], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 500, + 128, + 893, + 277 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We evaluate the effect of various choices – how much does the positional encoding at input help, effect of using continuous predictions instead of discrete as outputs, using vector quantization (1 token per face) instead of residual quantization (D tokens per face), encoder architecture as a point encoder, or different graph convolution operators, and decoder architecture as either ResNet19 or Point-Net decoder. Note that even though for encoder-decoder reconstruction, ‘w/o per Vertex Quantization’ performs best, this variant works significantly worse than with per Vertex Quantization, as shown in the main paper. Fig. 16 describes an intuition of why the embeddings from this variant are more transformer friendly." + } + ] + }, + "bbox": [ + 498, + 430, + 892, + 627 + ] + }, + { + "type": "page_header", + "content": { + "page_header_content": [ + { + "type": "text", + "content": "MeshGPT User Study" + } + ] + }, + "bbox": [ + 81, + 90, + 137, + 97 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "16" + } + ] + }, + "bbox": [ + 475, + 924, + 495, + 936 + ] + } + ] +] \ No newline at end of file diff --git a/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_layout.pdf b/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_layout.pdf new file mode 100644 index 0000000000000000000000000000000000000000..acd1cb9525e432f1961bc3ec5459101b9817a422 --- /dev/null +++ b/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_layout.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f5511d31c643b31e539fabd1dc82d8cd36a4409d7f25b5110d43e7fc55fbe5f1 +size 11616909 diff --git a/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_middle.json b/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_middle.json new file mode 100644 index 0000000000000000000000000000000000000000..df3be877a2a126dcd269671901ff85197698e005 --- /dev/null +++ b/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_middle.json @@ -0,0 +1,57246 @@ +{ + "pdf_info": [ + { + "preproc_blocks": [ + { + "bbox": [ + 69, + 73, + 523, + 90 + ], + "type": "title", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 72, + 76, + 523, + 89 + ], + "spans": [ + { + "bbox": [ + 72, + 76, + 523, + 89 + ], + "type": "text", + "content": "MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers", + "score": 1.0 + } + ] + } + ], + "level": 1 + }, + { + "bbox": [ + 156, + 113, + 430, + 127 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 157, + 114, + 430, + 127 + ], + "spans": [ + { + "bbox": [ + 157, + 114, + 430, + 127 + ], + "type": "text", + "content": "Yawar Siddiqui1 Antonio Alliegro2 Alexey Artemov1", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 65, + 127, + 515, + 142 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 66, + 126, + 515, + 141 + ], + "spans": [ + { + "bbox": [ + 66, + 126, + 515, + 141 + ], + "type": "text", + "content": "Tatiana Tommasi2 Daniele Sirigatti3 Vladislav Rosov3 Angela Dai1 Matthias Nießner1", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 128, + 147, + 462, + 161 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 129, + 148, + 462, + 159 + ], + "spans": [ + { + "bbox": [ + 129, + 148, + 462, + 159 + ], + "type": "text", + "content": "Technical University of Munich1 Politecnico di Torino2 AUDI AG3", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "image", + "bbox": [ + 50, + 175, + 541, + 305 + ], + "blocks": [ + { + "bbox": [ + 50, + 175, + 541, + 305 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 175, + 541, + 305 + ], + "spans": [ + { + "bbox": [ + 50, + 175, + 541, + 305 + ], + "type": "image", + "content": "```mermaid\ngraph LR\n A[\"Shape Dataset\"] --> B[\"Face Encoder\"]\n B --> C[\"Embedding Codebook\"]\n C --> D[\"Token Decoder\"]\n D --> E[\"GPT-Style Transformer\"]\n E --> F[\"MeshGPT: Autoregressive Mesh Generation\"]\n```", + "image_path": "3545e4e678461da72e464d2647815436fc502f261b64157952c11a9676ecbf7e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 312, + 546, + 346 + ], + "type": "image_caption", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 49, + 315, + 544, + 322 + ], + "spans": [ + { + "bbox": [ + 49, + 315, + 544, + 322 + ], + "type": "text", + "content": "Figure 1. 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Various implicit generative methods", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 324, + 544, + 333 + ], + "spans": [ + { + "bbox": [ + 307, + 324, + 544, + 333 + ], + "type": "text", + "content": "have shown impressive performance using adversarial [6,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 336, + 545, + 345 + ], + "spans": [ + { + "bbox": [ + 308, + 336, + 545, + 345 + ], + "type": "text", + "content": "53] and diffusion-based [8, 14, 41] models. Diffusion-based", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 348, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 307, + 348, + 545, + 357 + ], + "type": "text", + "content": "neural field synthesis in MLP weight spaces [13] and tri-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 360, + 545, + 370 + ], + "spans": [ + { + "bbox": [ + 307, + 360, + 545, + 370 + ], + "type": "text", + "content": "planes [55] have also been explored, alongside leveraging", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 373, + 544, + 381 + ], + "spans": [ + { + "bbox": [ + 308, + 373, + 544, + 381 + ], + "type": "text", + "content": "image-based models for optimizing NeRFs [25, 34, 48, 63].", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 384, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 307, + 384, + 545, + 393 + ], + "type": "text", + "content": "However, like point clouds, these methods require mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 396, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 307, + 396, + 545, + 406 + ], + "type": "text", + "content": "conversion [12, 32, 36, 49, 53] for downstream applications,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 407, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 307, + 407, + 545, + 418 + ], + "type": "text", + "content": "often leading to dense meshes that don’t capture the proper-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 420, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 308, + 420, + 545, + 429 + ], + "type": "text", + "content": "ties of the underlying datasets (e.g., edge lengths, dihedral", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 433, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 308, + 433, + 545, + 441 + ], + "type": "text", + "content": "angles). In contrast, we directly fit a generative model to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 445, + 544, + 453 + ], + "spans": [ + { + "bbox": [ + 308, + 445, + 544, + 453 + ], + "type": "text", + "content": "triangulated meshes, explicitly modeling the training data,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 456, + 544, + 464 + ], + "spans": [ + { + "bbox": [ + 308, + 456, + 544, + 464 + ], + "type": "text", + "content": "resulting in clean, compact and coherent meshes as outputs.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 305, + 472, + 545, + 591 + ], + "type": "text", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 307, + 472, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 307, + 472, + 545, + 483 + ], + "type": "text", + "content": "3D Mesh Generation. While several discriminative ap-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 486, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 308, + 486, + 545, + 495 + ], + "type": "text", + "content": "proaches capable of learning signals directly on mesh struc-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 498, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 308, + 498, + 545, + 506 + ], + "type": "text", + "content": "ture were proposed over the recent years [16, 21, 23,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 510, + 544, + 517 + ], + "spans": [ + { + "bbox": [ + 308, + 510, + 544, + 517 + ], + "type": "text", + "content": "33, 40, 52, 56], direct mesh generation remains underex-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 521, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 308, + 521, + 545, + 531 + ], + "type": "text", + "content": "plored. Mesh generation has been approached with various", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 534, + 544, + 542 + ], + "spans": [ + { + "bbox": [ + 308, + 534, + 544, + 542 + ], + "type": "text", + "content": "learning-based methods [7, 11, 18, 43]. AtlasNet [18] and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 545, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 307, + 545, + 545, + 555 + ], + "type": "text", + "content": "BSPNet [7], for example, produce mesh patches and com-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 557, + 544, + 567 + ], + "spans": [ + { + "bbox": [ + 308, + 557, + 544, + 567 + ], + "type": "text", + "content": "pact meshes through binary space partitioning, respectively.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 569, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 307, + 569, + 545, + 578 + ], + "type": "text", + "content": "However, as we demonstrate in Sec. 4, these struggle with", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 582, + 441, + 590 + ], + "spans": [ + { + "bbox": [ + 308, + 582, + 441, + 590 + ], + "type": "text", + "content": "accurately capturing shape detail.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 320, + 595, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 320, + 595, + 545, + 605 + ], + "type": "text", + "content": "Closely related to our work, PolyGen [43] employs two", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 608, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 308, + 608, + 545, + 617 + ], + "type": "text", + "content": "autoregressively trained networks to create explicit mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 620, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 307, + 620, + 545, + 629 + ], + "type": "text", + "content": "structures. In contrast, our method utilizes a single decoder-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 631, + 544, + 640 + ], + "spans": [ + { + "bbox": [ + 308, + 631, + 544, + 640 + ], + "type": "text", + "content": "only network, representing triangles through learned to-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 643, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 307, + 643, + 545, + 653 + ], + "type": "text", + "content": "kens for a more streamlined generation process compared", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 654, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 307, + 654, + 545, + 666 + ], + "type": "text", + "content": "to PolyGen’s separate vertex-and-face sequence approach.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 667, + 544, + 677 + ], + "spans": [ + { + "bbox": [ + 308, + 667, + 544, + 677 + ], + "type": "text", + "content": "Additionally, we observe that PolyGen’s vertex generator,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 678, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 307, + 678, + 545, + 689 + ], + "type": "text", + "content": "oblivious to face generation, and the face generator, not ex-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 692, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 307, + 692, + 545, + 700 + ], + "type": "text", + "content": "posed to the generated vertex distribution during training,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 703, + 482, + 712 + ], + "spans": [ + { + "bbox": [ + 307, + 703, + 482, + 712 + ], + "type": "text", + "content": "exhibit limited robustness during inference.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 301, + 742 + ], + "type": "page_number", + "angle": 0, + "index": 16, + "lines": [ + { + "bbox": [ + 293, + 732, + 300, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 300, + 742 + ], + "type": "text", + "content": "2", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1, + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 69, + 285, + 259 + ], + "blocks": [ + { + "bbox": [ + 53, + 69, + 285, + 259 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 69, + 285, + 259 + ], + "spans": [ + { + "bbox": [ + 53, + 69, + 285, + 259 + ], + "type": "image", + "image_path": "9c49a05ead13fc277ddba7a5d49bbf787caf1c0d5ba8613e0e8d8d464e85ac30.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 266, + 287, + 332 + ], + "type": "image_caption", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 49, + 268, + 286, + 277 + ], + "spans": [ + { + "bbox": [ + 49, + 268, + 286, + 277 + ], + "type": "text", + "content": "Figure 2. Meshes generated by our method (top) for chairs, tables,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 279, + 285, + 287 + ], + "spans": [ + { + "bbox": [ + 48, + 279, + 285, + 287 + ], + "type": "text", + "content": "benches, and lamps when trained on ShapeNet [5]. MeshGPT", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 290, + 285, + 299 + ], + "spans": [ + { + "bbox": [ + 48, + 290, + 285, + 299 + ], + "type": "text", + "content": "meshes tend to be compact, with the ability to represent both sharp", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 300, + 286, + 309 + ], + "spans": [ + { + "bbox": [ + 49, + 300, + 286, + 309 + ], + "type": "text", + "content": "details and curved boundaries. This contrasts with neural field-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 312, + 286, + 320 + ], + "spans": [ + { + "bbox": [ + 49, + 312, + 286, + 320 + ], + "type": "text", + "content": "based approaches that yield dense triangulations not easily simpli-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 323, + 171, + 331 + ], + "spans": [ + { + "bbox": [ + 49, + 323, + 171, + 331 + ], + "type": "text", + "content": "fied through decimation (bottom).", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_images": [ + { + "type": "image", + "bbox": [ + 0.013, + 0.0, + 0.966, + 0.516 + ] + }, + { + "type": "image", + "bbox": [ + 0.013, + 0.563, + 1.0, + 1.0 + ] + } + ] + }, + { + "bbox": [ + 46, + 345, + 287, + 488 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 47, + 489, + 188, + 499 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 48, + 489, + 187, + 500 + ], + "spans": [ + { + "bbox": [ + 48, + 489, + 187, + 500 + ], + "type": "text", + "content": "In summary, our contributions are:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 47, + 500, + 287, + 571 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 500, + 287, + 536 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 49, + 501, + 286, + 512 + ], + "spans": [ + { + "bbox": [ + 49, + 501, + 286, + 512 + ], + "type": "text", + "content": "• A new generative formulation for meshes as a sequence", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 58, + 514, + 286, + 523 + ], + "spans": [ + { + "bbox": [ + 58, + 514, + 286, + 523 + ], + "type": "text", + "content": "of triangles, tailoring a GPT-inspired decoder-only trans-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 58, + 526, + 271, + 536 + ], + "spans": [ + { + "bbox": [ + 58, + 526, + 271, + 536 + ], + "type": "text", + "content": "former, to produce compact meshes with sharp edges.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 47, + 536, + 287, + 571 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 49, + 537, + 286, + 548 + ], + "spans": [ + { + "bbox": [ + 49, + 537, + 286, + 548 + ], + "type": "text", + "content": "• Triangles are represented as a vocabulary of latent geo-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 57, + 549, + 286, + 559 + ], + "spans": [ + { + "bbox": [ + 57, + 549, + 286, + 559 + ], + "type": "text", + "content": "metric tokens to enable coherent mesh generation in an", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 58, + 562, + 149, + 571 + ], + "spans": [ + { + "bbox": [ + 58, + 562, + 149, + 571 + ], + "type": "text", + "content": "autoregressive fashion.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 582, + 134, + 594 + ], + "type": "title", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 49, + 583, + 133, + 594 + ], + "spans": [ + { + "bbox": [ + 49, + 583, + 133, + 594 + ], + "type": "text", + "content": "2. Related Work", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 49, + 606, + 286, + 617 + ], + "spans": [ + { + "bbox": [ + 49, + 606, + 286, + 617 + ], + "type": "text", + "content": "Voxel-based 3D Shape Generation. Early shape genera-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 619, + 286, + 629 + ], + "spans": [ + { + "bbox": [ + 48, + 619, + 286, + 629 + ], + "type": "text", + "content": "tion approaches generated shapes as a grid of low-resolution", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 632, + 286, + 641 + ], + "spans": [ + { + "bbox": [ + 49, + 632, + 286, + 641 + ], + "type": "text", + "content": "voxels [3, 9, 26, 62] or, more recently, as high-resolution", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 643, + 286, + 653 + ], + "spans": [ + { + "bbox": [ + 49, + 643, + 286, + 653 + ], + "type": "text", + "content": "grids using efficient representations such as Octrees [57]", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 655, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 49, + 655, + 286, + 665 + ], + "type": "text", + "content": "and sparse voxels [50], with generative models such as", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 667, + 286, + 676 + ], + "spans": [ + { + "bbox": [ + 49, + 667, + 286, + 676 + ], + "type": "text", + "content": "GANs [17]. These methods pioneered the extension of 2D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 679, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 48, + 679, + 287, + 689 + ], + "type": "text", + "content": "generative techniques into the 3D domain. 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Methods in this category repre-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 116, + 545, + 125 + ], + "spans": [ + { + "bbox": [ + 308, + 116, + 545, + 125 + ], + "type": "text", + "content": "sent 3D shapes by point samples on their surfaces, aiming to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 128, + 545, + 137 + ], + "spans": [ + { + "bbox": [ + 308, + 128, + 545, + 137 + ], + "type": "text", + "content": "learn point distributions across shape datasets. Early works", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 139, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 307, + 139, + 545, + 148 + ], + "type": "text", + "content": "involved GANs for synthesizing point locations [30, 54, 59]", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 151, + 545, + 161 + ], + "spans": [ + { + "bbox": [ + 307, + 151, + 545, + 161 + ], + "type": "text", + "content": "and latent shape codes [1]. Flow-based [64] and gradient", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 164, + 544, + 172 + ], + "spans": [ + { + "bbox": [ + 308, + 164, + 544, + 172 + ], + "type": "text", + "content": "field-based models [4] also yield impressive results. Re-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 176, + 545, + 185 + ], + "spans": [ + { + "bbox": [ + 308, + 176, + 545, + 185 + ], + "type": "text", + "content": "cently, diffusion-based techniques have been adapted for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 187, + 545, + 197 + ], + "spans": [ + { + "bbox": [ + 307, + 187, + 545, + 197 + ], + "type": "text", + "content": "point cloud generation [44, 67, 68], showing competitive", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 199, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 307, + 199, + 545, + 209 + ], + "type": "text", + "content": "performance in shape generation. However, point clouds,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 210, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 307, + 210, + 545, + 220 + ], + "type": "text", + "content": "while useful, are not the ideal format for downstream appli-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 224, + 544, + 232 + ], + "spans": [ + { + "bbox": [ + 308, + 224, + 544, + 232 + ], + "type": "text", + "content": "cations requiring 3D content, as converting them to meshes,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 236, + 544, + 244 + ], + "spans": [ + { + "bbox": [ + 308, + 236, + 544, + 244 + ], + "type": "text", + "content": "which apart from being non-trivial [42, 47, 51, 65], can of-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 247, + 544, + 256 + ], + "spans": [ + { + "bbox": [ + 308, + 247, + 544, + 256 + ], + "type": "text", + "content": "ten fail to accurately reflect the characteristics of the under-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 259, + 389, + 269 + ], + "spans": [ + { + "bbox": [ + 307, + 259, + 389, + 269 + ], + "type": "text", + "content": "lying mesh datasets.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 305, + 274, + 546, + 467 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 307, + 276, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 307, + 276, + 545, + 285 + ], + "type": "text", + "content": "Neural Implicit Fields. Implicit representation of shapes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 289, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 308, + 289, + 545, + 297 + ], + "type": "text", + "content": "as volumetric functions (e.g., signed distance functions) has", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 300, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 307, + 300, + 545, + 310 + ], + "type": "text", + "content": "become popular for encoding arbitrary topologies at any", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 312, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 307, + 312, + 545, + 322 + ], + "type": "text", + "content": "resolution [39, 45]. Various implicit generative methods", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 324, + 544, + 333 + ], + "spans": [ + { + "bbox": [ + 307, + 324, + 544, + 333 + ], + "type": "text", + "content": "have shown impressive performance using adversarial [6,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 336, + 545, + 345 + ], + "spans": [ + { + "bbox": [ + 308, + 336, + 545, + 345 + ], + "type": "text", + "content": "53] and diffusion-based [8, 14, 41] models. Diffusion-based", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 348, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 307, + 348, + 545, + 357 + ], + "type": "text", + "content": "neural field synthesis in MLP weight spaces [13] and tri-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 360, + 545, + 370 + ], + "spans": [ + { + "bbox": [ + 307, + 360, + 545, + 370 + ], + "type": "text", + "content": "planes [55] have also been explored, alongside leveraging", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 373, + 544, + 381 + ], + "spans": [ + { + "bbox": [ + 308, + 373, + 544, + 381 + ], + "type": "text", + "content": "image-based models for optimizing NeRFs [25, 34, 48, 63].", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 384, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 307, + 384, + 545, + 393 + ], + "type": "text", + "content": "However, like point clouds, these methods require mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 396, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 307, + 396, + 545, + 406 + ], + "type": "text", + "content": "conversion [12, 32, 36, 49, 53] for downstream applications,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 407, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 307, + 407, + 545, + 418 + ], + "type": "text", + "content": "often leading to dense meshes that don’t capture the proper-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 420, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 308, + 420, + 545, + 429 + ], + "type": "text", + "content": "ties of the underlying datasets (e.g., edge lengths, dihedral", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 433, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 308, + 433, + 545, + 441 + ], + "type": "text", + "content": "angles). In contrast, we directly fit a generative model to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 445, + 544, + 453 + ], + "spans": [ + { + "bbox": [ + 308, + 445, + 544, + 453 + ], + "type": "text", + "content": "triangulated meshes, explicitly modeling the training data,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 456, + 544, + 464 + ], + "spans": [ + { + "bbox": [ + 308, + 456, + 544, + 464 + ], + "type": "text", + "content": "resulting in clean, compact and coherent meshes as outputs.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 305, + 472, + 545, + 591 + ], + "type": "text", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 307, + 472, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 307, + 472, + 545, + 483 + ], + "type": "text", + "content": "3D Mesh Generation. While several discriminative ap-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 486, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 308, + 486, + 545, + 495 + ], + "type": "text", + "content": "proaches capable of learning signals directly on mesh struc-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 498, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 308, + 498, + 545, + 506 + ], + "type": "text", + "content": "ture were proposed over the recent years [16, 21, 23,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 510, + 544, + 517 + ], + "spans": [ + { + "bbox": [ + 308, + 510, + 544, + 517 + ], + "type": "text", + "content": "33, 40, 52, 56], direct mesh generation remains underex-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 521, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 308, + 521, + 545, + 531 + ], + "type": "text", + "content": "plored. Mesh generation has been approached with various", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 534, + 544, + 542 + ], + "spans": [ + { + "bbox": [ + 308, + 534, + 544, + 542 + ], + "type": "text", + "content": "learning-based methods [7, 11, 18, 43]. AtlasNet [18] and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 545, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 307, + 545, + 545, + 555 + ], + "type": "text", + "content": "BSPNet [7], for example, produce mesh patches and com-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 557, + 544, + 567 + ], + "spans": [ + { + "bbox": [ + 308, + 557, + 544, + 567 + ], + "type": "text", + "content": "pact meshes through binary space partitioning, respectively.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 569, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 307, + 569, + 545, + 578 + ], + "type": "text", + "content": "However, as we demonstrate in Sec. 4, these struggle with", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 582, + 441, + 590 + ], + "spans": [ + { + "bbox": [ + 308, + 582, + 441, + 590 + ], + "type": "text", + "content": "accurately capturing shape detail.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 320, + 595, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 320, + 595, + 545, + 605 + ], + "type": "text", + "content": "Closely related to our work, PolyGen [43] employs two", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 608, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 308, + 608, + 545, + 617 + ], + "type": "text", + "content": "autoregressively trained networks to create explicit mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 620, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 307, + 620, + 545, + 629 + ], + "type": "text", + "content": "structures. In contrast, our method utilizes a single decoder-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 631, + 544, + 640 + ], + "spans": [ + { + "bbox": [ + 308, + 631, + 544, + 640 + ], + "type": "text", + "content": "only network, representing triangles through learned to-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 643, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 307, + 643, + 545, + 653 + ], + "type": "text", + "content": "kens for a more streamlined generation process compared", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 654, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 307, + 654, + 545, + 666 + ], + "type": "text", + "content": "to PolyGen’s separate vertex-and-face sequence approach.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 667, + 544, + 677 + ], + "spans": [ + { + "bbox": [ + 308, + 667, + 544, + 677 + ], + "type": "text", + "content": "Additionally, we observe that PolyGen’s vertex generator,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 678, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 307, + 678, + 545, + 689 + ], + "type": "text", + "content": "oblivious to face generation, and the face generator, not ex-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 692, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 307, + 692, + 545, + 700 + ], + "type": "text", + "content": "posed to the generated vertex distribution during training,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 703, + 482, + 712 + ], + "spans": [ + { + "bbox": [ + 307, + 703, + 482, + 712 + ], + "type": "text", + "content": "exhibit limited robustness during inference.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "bbox": [ + 47, + 71, + 103, + 83 + ], + "type": "title", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 102, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 102, + 84 + ], + "type": "text", + "content": "3. Method", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 46, + 91, + 287, + 186 + ], + "type": "text", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 49, + 93, + 286, + 102 + ], + "spans": [ + { + "bbox": [ + 49, + 93, + 286, + 102 + ], + "type": "text", + "content": "Inspired by advancements in large language models, we de-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 105, + 286, + 114 + ], + "spans": [ + { + "bbox": [ + 49, + 105, + 286, + 114 + ], + "type": "text", + "content": "velop a sequence-based approach to autoregressively gen-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 118, + 287, + 126 + ], + "spans": [ + { + "bbox": [ + 49, + 118, + 287, + 126 + ], + "type": "text", + "content": "erate triangle meshes as sequences of triangles. We first", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 129, + 286, + 138 + ], + "spans": [ + { + "bbox": [ + 48, + 129, + 286, + 138 + ], + "type": "text", + "content": "learn a vocabulary of geometric embeddings from a large", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 140, + 286, + 150 + ], + "spans": [ + { + "bbox": [ + 49, + 140, + 286, + 150 + ], + "type": "text", + "content": "collection of 3D object meshes, enabling triangles to be en-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 153, + 285, + 162 + ], + "spans": [ + { + "bbox": [ + 49, + 153, + 285, + 162 + ], + "type": "text", + "content": "coded to and decoded from this embedding. We then train", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 165, + 286, + 174 + ], + "spans": [ + { + "bbox": [ + 49, + 165, + 286, + 174 + ], + "type": "text", + "content": "a transformer for mesh generation as autoregressive next-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 177, + 280, + 186 + ], + "spans": [ + { + "bbox": [ + 48, + 177, + 280, + 186 + ], + "type": "text", + "content": "index prediction over the learned vocabulary embeddings.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 46, + 187, + 288, + 305 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 60, + 187, + 286, + 198 + ], + "spans": [ + { + "bbox": [ + 60, + 187, + 286, + 198 + ], + "type": "text", + "content": "To learn the triangle vocabulary, we employ a graph con-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 201, + 286, + 209 + ], + "spans": [ + { + "bbox": [ + 49, + 201, + 286, + 209 + ], + "type": "text", + "content": "volution encoder operating on triangles of a mesh and their", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 213, + 287, + 221 + ], + "spans": [ + { + "bbox": [ + 49, + 213, + 287, + 221 + ], + "type": "text", + "content": "neighborhood to extract geometrically rich features that", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 224, + 287, + 234 + ], + "spans": [ + { + "bbox": [ + 48, + 224, + 287, + 234 + ], + "type": "text", + "content": "capture the intricate details of 3D shapes. These features", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 236, + 286, + 246 + ], + "spans": [ + { + "bbox": [ + 48, + 236, + 286, + 246 + ], + "type": "text", + "content": "are quantized as embeddings of a codebook using resid-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 249, + 286, + 258 + ], + "spans": [ + { + "bbox": [ + 49, + 249, + 286, + 258 + ], + "type": "text", + "content": "ual quantization [27, 38], effectively reducing sequence", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 261, + 286, + 270 + ], + "spans": [ + { + "bbox": [ + 48, + 261, + 286, + 270 + ], + "type": "text", + "content": "lengths of the mesh representation. These embeddings are", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 273, + 286, + 281 + ], + "spans": [ + { + "bbox": [ + 49, + 273, + 286, + 281 + ], + "type": "text", + "content": "sequenced and then decoded by a 1D ResNet [22] guided", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 285, + 286, + 293 + ], + "spans": [ + { + "bbox": [ + 49, + 285, + 286, + 293 + ], + "type": "text", + "content": "by a reconstruction loss. This phase lays the groundwork", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 297, + 232, + 305 + ], + "spans": [ + { + "bbox": [ + 48, + 297, + 232, + 305 + ], + "type": "text", + "content": "for the subsequent training of the transformer.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 46, + 306, + 287, + 426 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 61, + 308, + 286, + 317 + ], + "spans": [ + { + "bbox": [ + 61, + 308, + 286, + 317 + ], + "type": "text", + "content": "We then train a GPT-style decoder-only transformer,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 320, + 286, + 330 + ], + "spans": [ + { + "bbox": [ + 49, + 320, + 286, + 330 + ], + "type": "text", + "content": "which leverages these quantized geometric embeddings.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 332, + 286, + 341 + ], + "spans": [ + { + "bbox": [ + 49, + 332, + 286, + 341 + ], + "type": "text", + "content": "Given a sequence of geometric embeddings extracted from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 344, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 49, + 344, + 287, + 354 + ], + "type": "text", + "content": "the triangles of a mesh, the transformer is trained to predict", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 356, + 286, + 365 + ], + "spans": [ + { + "bbox": [ + 48, + 356, + 286, + 365 + ], + "type": "text", + "content": "the codebook index of the next embedding in the sequence.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 368, + 286, + 377 + ], + "spans": [ + { + "bbox": [ + 48, + 368, + 286, + 377 + ], + "type": "text", + "content": "Once trained, the transformer can be auto-regressively sam-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 380, + 286, + 389 + ], + "spans": [ + { + "bbox": [ + 49, + 380, + 286, + 389 + ], + "type": "text", + "content": "pled to predict sequences of embeddings. These embed-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 392, + 286, + 400 + ], + "spans": [ + { + "bbox": [ + 49, + 392, + 286, + 400 + ], + "type": "text", + "content": "dings can then be decoded to generate novel and diverse", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 404, + 286, + 413 + ], + "spans": [ + { + "bbox": [ + 49, + 404, + 286, + 413 + ], + "type": "text", + "content": "mesh structures that display efficient, irregular triangula-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 416, + 204, + 424 + ], + "spans": [ + { + "bbox": [ + 49, + 416, + 204, + 424 + ], + "type": "text", + "content": "tions similar to human-crafted meshes.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 47, + 432, + 268, + 445 + ], + "type": "title", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 49, + 433, + 266, + 444 + ], + "spans": [ + { + "bbox": [ + 49, + 433, + 266, + 444 + ], + "type": "text", + "content": "3.1. Learning Quantized Triangle Embeddings", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 46, + 451, + 287, + 510 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 50, + 453, + 285, + 461 + ], + "spans": [ + { + "bbox": [ + 50, + 453, + 285, + 461 + ], + "type": "text", + "content": "Autoregressive generative models, such as transformers,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 464, + 286, + 473 + ], + "spans": [ + { + "bbox": [ + 49, + 464, + 286, + 473 + ], + "type": "text", + "content": "synthesize sequences of tokens where each new token is", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 476, + 286, + 485 + ], + "spans": [ + { + "bbox": [ + 49, + 476, + 286, + 485 + ], + "type": "text", + "content": "conditioned on previously generated tokens. For generating", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 488, + 286, + 497 + ], + "spans": [ + { + "bbox": [ + 48, + 488, + 286, + 497 + ], + "type": "text", + "content": "meshes using transformers, we must then define the order-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 500, + 257, + 509 + ], + "spans": [ + { + "bbox": [ + 49, + 500, + 257, + 509 + ], + "type": "text", + "content": "ing convention of generation, along with the tokens.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 46, + 510, + 287, + 594 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 61, + 512, + 286, + 521 + ], + "spans": [ + { + "bbox": [ + 61, + 512, + 286, + 521 + ], + "type": "text", + "content": "For sequence ordering, Polygen [43] suggests a conven-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 524, + 286, + 533 + ], + "spans": [ + { + "bbox": [ + 49, + 524, + 286, + 533 + ], + "type": "text", + "content": "tion where faces are ordered based on their lowest vertex", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 536, + 286, + 544 + ], + "spans": [ + { + "bbox": [ + 49, + 536, + 286, + 544 + ], + "type": "text", + "content": "index, followed by the next lowest, and so forth. Vertices", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 548, + 286, + 558 + ], + "spans": [ + { + "bbox": [ + 49, + 548, + 100, + 557 + ], + "type": "text", + "content": "are sorted in", + "score": 1.0 + }, + { + "bbox": [ + 101, + 548, + 126, + 558 + ], + "type": "inline_equation", + "content": "z - y - x", + "score": 0.7253 + }, + { + "bbox": [ + 127, + 548, + 286, + 557 + ], + "type": "text", + "content": "order (z representing the vertical axis),", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 559, + 286, + 569 + ], + "spans": [ + { + "bbox": [ + 48, + 559, + 286, + 569 + ], + "type": "text", + "content": "progressing from lowest to highest. Within each face, in-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 572, + 286, + 581 + ], + "spans": [ + { + "bbox": [ + 49, + 572, + 286, + 581 + ], + "type": "text", + "content": "dices are cyclically permuted to place the lowest index first.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 582, + 272, + 594 + ], + "spans": [ + { + "bbox": [ + 48, + 582, + 272, + 594 + ], + "type": "text", + "content": "In our method, we also adopt this sequencing approach.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 61, + 595, + 286, + 605 + ], + "spans": [ + { + "bbox": [ + 61, + 595, + 286, + 605 + ], + "type": "text", + "content": "To define the tokens to generate, we consider a practical", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 607, + 286, + 617 + ], + "spans": [ + { + "bbox": [ + 49, + 607, + 286, + 617 + ], + "type": "text", + "content": "approach to represent a mesh M for autoregressive genera-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 620, + 164, + 629 + ], + "spans": [ + { + "bbox": [ + 49, + 620, + 164, + 629 + ], + "type": "text", + "content": "tion: a sequence of triangles,", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 110, + 635, + 287, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 635, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 110, + 635, + 287, + 649 + ], + "type": "interline_equation", + "content": "\\mathcal {M} := (f _ {1}, f _ {2}, f _ {3}, \\dots , f _ {N}), \\tag {1}", + "image_path": "5c4bb9c1739b322c7f7055205013c2478b8b04bc8af7df9e8b6e416bbbe36845.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 49, + 654, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 49, + 655, + 149, + 665 + ], + "type": "text", + "content": "with N faces (triangles),", + "score": 1.0 + }, + { + "bbox": [ + 152, + 654, + 191, + 665 + ], + "type": "inline_equation", + "content": "f _ { i } \\in \\mathbb { R } ^ { n _ { \\mathrm { i n } } }", + "score": 0.911 + }, + { + "bbox": [ + 193, + 654, + 223, + 665 + ], + "type": "text", + "content": "having", + "score": 1.0 + }, + { + "bbox": [ + 223, + 656, + 237, + 665 + ], + "type": "inline_equation", + "content": "n _ { \\mathrm { i n } }", + "score": 0.8383 + }, + { + "bbox": [ + 238, + 654, + 286, + 665 + ], + "type": "text", + "content": "features. A", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 666, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 48, + 666, + 287, + 677 + ], + "type": "text", + "content": "simple approach to describe each triangle is as its three ver-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 680, + 286, + 689 + ], + "spans": [ + { + "bbox": [ + 49, + 680, + 286, + 689 + ], + "type": "text", + "content": "tices, comprising nine total coordinates. Upon discretiza-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 692, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 49, + 692, + 286, + 700 + ], + "type": "text", + "content": "tion, these coordinates can be treated as tokens. The se-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 703, + 211, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 703, + 211, + 712 + ], + "type": "text", + "content": "quence length in this case would be 9N.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "image", + "bbox": [ + 305, + 70, + 547, + 229 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 547, + 229 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 70, + 547, + 229 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 547, + 229 + ], + "type": "image", + "content": "```mermaid\ngraph LR\n InputMesh[\"Input Mesh\"] -->|\"| F| × C_in\"| GraphConv[\"Graph Convolutional Encoder\"]\n ReconstructedMesh[\"Reconstructed Mesh\"] -->|\"| F| × 9\"| ResNetDecoder[\"ResNet Decoder\"]\n GraphConv -->|\"| F| × C_e\"| ResidualFaceQuant[\"Residual Face Quantization Module\"]\n ResNetDecoder --> SequenceOfFaces[\"Sequence Of Faces\"]\n SequenceOfFaces -->|\"| F| × C_e\"| ResidualFaceQuant\n ResidualFaceQuant -->|\"| F| ×\"| ResidualFaceQuantModule[\"Residual Face Quantization Module\"]\n ResidualFaceQuantModule -->|\"C_e\"| SumResidualFeatures[\"Sum Residual Features\"]\n ResidualFaceQuantModule -->|\"D × C_e\"| Reshape[\"Reshape\"]\n Reshape --> FeatureCodebook[\"Feature Codebook\"]\n FeatureCodebook --> MeanAcrossSharedVertices[\"Mean across Shared Vertices\"]\n MeanAcrossSharedVertices --> SplitFeature[\"Split Feature\"]\n SplitFeature -->|\"C_e\"| SumResidualFeatures\n```", + "image_path": "68bf00eef4f292ec6f6d2b982ffb3ea487e15df8e5bbe5ed3e13d7f0d3653820.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 236, + 547, + 326 + ], + "type": "image_caption", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 308, + 239, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 308, + 239, + 545, + 247 + ], + "type": "text", + "content": "Figure 3. We employ a graph convolutional encoder to process", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 250, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 308, + 250, + 545, + 258 + ], + "type": "text", + "content": "mesh faces, leveraging geometric neighborhood information to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 261, + 544, + 270 + ], + "spans": [ + { + "bbox": [ + 308, + 261, + 544, + 270 + ], + "type": "text", + "content": "capture strong features representing intricate details of 3D shapes.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 271, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 307, + 271, + 545, + 281 + ], + "type": "text", + "content": "These features are then quantized into codebook embeddings using", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 282, + 544, + 291 + ], + "spans": [ + { + "bbox": [ + 308, + 282, + 544, + 291 + ], + "type": "text", + "content": "residual quantization [27, 38]. In contrast to naive vector quanti-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 294, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 308, + 294, + 545, + 302 + ], + "type": "text", + "content": "zation, this ensures better reconstruction quality. The quantized", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 304, + 545, + 313 + ], + "spans": [ + { + "bbox": [ + 308, + 304, + 545, + 313 + ], + "type": "text", + "content": "embeddings are subsequently sequenced and decoded through a", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 309, + 316, + 483, + 323 + ], + "spans": [ + { + "bbox": [ + 309, + 316, + 483, + 323 + ], + "type": "text", + "content": "1D ResNet [22], guided by a reconstruction loss.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 10, + "sub_type": "flowchart" + }, + { + "bbox": [ + 304, + 346, + 545, + 465 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 319, + 348, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 319, + 348, + 545, + 357 + ], + "type": "text", + "content": "However, we observe two major challenges when using", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 360, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 308, + 360, + 545, + 369 + ], + "type": "text", + "content": "coordinates directly as tokens. First, the sequence lengths", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 372, + 544, + 381 + ], + "spans": [ + { + "bbox": [ + 307, + 372, + 544, + 381 + ], + "type": "text", + "content": "become excessively long, as each face is represented by", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 384, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 307, + 384, + 545, + 392 + ], + "type": "text", + "content": "nine values. This length does not scale well with trans-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 396, + 544, + 405 + ], + "spans": [ + { + "bbox": [ + 307, + 396, + 544, + 405 + ], + "type": "text", + "content": "former architectures, which often have limited context win-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 408, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 308, + 408, + 545, + 417 + ], + "type": "text", + "content": "dows. Second, representing discrete positions of a trian-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 420, + 544, + 429 + ], + "spans": [ + { + "bbox": [ + 308, + 420, + 544, + 429 + ], + "type": "text", + "content": "gle as tokens fails to capture geometric patterns effectively.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 431, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 308, + 431, + 545, + 441 + ], + "type": "text", + "content": "This is because such a representation lacks information", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 444, + 544, + 453 + ], + "spans": [ + { + "bbox": [ + 308, + 444, + 544, + 453 + ], + "type": "text", + "content": "about neighboring triangles and does not incorporate any", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 456, + 432, + 464 + ], + "spans": [ + { + "bbox": [ + 308, + 456, + 432, + 464 + ], + "type": "text", + "content": "priors from mesh distributions.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 304, + 466, + 545, + 514 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 319, + 467, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 319, + 467, + 545, + 478 + ], + "type": "text", + "content": "To address the aforementioned challenges, we propose", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 479, + 544, + 489 + ], + "spans": [ + { + "bbox": [ + 308, + 479, + 544, + 489 + ], + "type": "text", + "content": "to learn geometric embeddings from a collection of triangu-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 491, + 545, + 501 + ], + "spans": [ + { + "bbox": [ + 307, + 491, + 545, + 501 + ], + "type": "text", + "content": "lar meshes, utilizing an encoder-decoder architecture with", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 502, + 519, + 514 + ], + "spans": [ + { + "bbox": [ + 307, + 502, + 519, + 514 + ], + "type": "text", + "content": "residual vector quantization at its bottleneck (Fig. 3).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 304, + 514, + 546, + 633 + ], + "type": "text", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 319, + 515, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 319, + 515, + 545, + 525 + ], + "type": "text", + "content": "The network’s encoder E employs graph convolutions", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 528, + 544, + 536 + ], + "spans": [ + { + "bbox": [ + 308, + 528, + 544, + 536 + ], + "type": "text", + "content": "on mesh faces, where each face forms a node and neigh-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 540, + 545, + 549 + ], + "spans": [ + { + "bbox": [ + 307, + 540, + 545, + 549 + ], + "type": "text", + "content": "boring faces are connected by undirected edges. The input", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 552, + 544, + 561 + ], + "spans": [ + { + "bbox": [ + 307, + 552, + 544, + 561 + ], + "type": "text", + "content": "face node features are comprised of the nine positionally", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 563, + 545, + 573 + ], + "spans": [ + { + "bbox": [ + 307, + 563, + 545, + 573 + ], + "type": "text", + "content": "encoded coordinates of its vertices, face normal, angles be-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 575, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 307, + 575, + 545, + 585 + ], + "type": "text", + "content": "tween its edges, and area. These features undergo process-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 587, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 307, + 587, + 545, + 597 + ], + "type": "text", + "content": "ing through a stack of SAGEConv [20] layers, extracting", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 599, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 307, + 599, + 545, + 609 + ], + "type": "text", + "content": "a feature vector for each face. This graph convolutional", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 612, + 545, + 621 + ], + "spans": [ + { + "bbox": [ + 307, + 612, + 545, + 621 + ], + "type": "text", + "content": "approach enables the extraction of geometrically enriched", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 622, + 435, + 633 + ], + "spans": [ + { + "bbox": [ + 307, + 624, + 340, + 632 + ], + "type": "text", + "content": "features", + "score": 1.0 + }, + { + "bbox": [ + 342, + 622, + 376, + 633 + ], + "type": "inline_equation", + "content": "z _ { i } \\in \\mathbb { R } ^ { n _ { \\mathrm { z } } }", + "score": 0.876 + }, + { + "bbox": [ + 378, + 624, + 435, + 633 + ], + "type": "text", + "content": "for each face,", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 359, + 643, + 545, + 656 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 643, + 545, + 656 + ], + "spans": [ + { + "bbox": [ + 359, + 643, + 545, + 656 + ], + "type": "interline_equation", + "content": "\\mathbf {Z} = (z _ {1}, z _ {2}, \\dots , z _ {N}) = E (\\mathcal {M}), \\tag {2}", + "image_path": "82d4e72d4e8d649d3636f6144bb77ac91aef8d1e44d74065821e17d32fa397b1.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 545, + 689 + ], + "type": "text", + "angle": 0, + "index": 16, + "lines": [ + { + "bbox": [ + 307, + 666, + 544, + 677 + ], + "spans": [ + { + "bbox": [ + 307, + 666, + 544, + 677 + ], + "type": "text", + "content": "fusing neighborhood information into the learned embed-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 677, + 334, + 690 + ], + "spans": [ + { + "bbox": [ + 307, + 677, + 334, + 690 + ], + "type": "text", + "content": "dings.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "index": 17, + "lines": [ + { + "bbox": [ + 320, + 692, + 544, + 700 + ], + "spans": [ + { + "bbox": [ + 320, + 692, + 544, + 700 + ], + "type": "text", + "content": "For quantization, we employ residual vector quantiza-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 703, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 703, + 544, + 712 + ], + "type": "text", + "content": "tion (RQ) [38]. We found that using a single code per face", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 300, + 742 + ], + "type": "page_number", + "angle": 0, + "index": 18, + "lines": [ + { + "bbox": [ + 294, + 732, + 300, + 743 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 300, + 743 + ], + "type": "text", + "content": "3", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2, + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 103, + 83 + ], + "type": "title", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 102, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 102, + 84 + ], + "type": "text", + "content": "3. Method", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 46, + 91, + 287, + 186 + ], + "type": "text", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 49, + 93, + 286, + 102 + ], + "spans": [ + { + "bbox": [ + 49, + 93, + 286, + 102 + ], + "type": "text", + "content": "Inspired by advancements in large language models, we de-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 105, + 286, + 114 + ], + "spans": [ + { + "bbox": [ + 49, + 105, + 286, + 114 + ], + "type": "text", + "content": "velop a sequence-based approach to autoregressively gen-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 118, + 287, + 126 + ], + "spans": [ + { + "bbox": [ + 49, + 118, + 287, + 126 + ], + "type": "text", + "content": "erate triangle meshes as sequences of triangles. We first", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 129, + 286, + 138 + ], + "spans": [ + { + "bbox": [ + 48, + 129, + 286, + 138 + ], + "type": "text", + "content": "learn a vocabulary of geometric embeddings from a large", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 140, + 286, + 150 + ], + "spans": [ + { + "bbox": [ + 49, + 140, + 286, + 150 + ], + "type": "text", + "content": "collection of 3D object meshes, enabling triangles to be en-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 153, + 285, + 162 + ], + "spans": [ + { + "bbox": [ + 49, + 153, + 285, + 162 + ], + "type": "text", + "content": "coded to and decoded from this embedding. We then train", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 165, + 286, + 174 + ], + "spans": [ + { + "bbox": [ + 49, + 165, + 286, + 174 + ], + "type": "text", + "content": "a transformer for mesh generation as autoregressive next-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 177, + 280, + 186 + ], + "spans": [ + { + "bbox": [ + 48, + 177, + 280, + 186 + ], + "type": "text", + "content": "index prediction over the learned vocabulary embeddings.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 46, + 187, + 288, + 305 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 60, + 187, + 286, + 198 + ], + "spans": [ + { + "bbox": [ + 60, + 187, + 286, + 198 + ], + "type": "text", + "content": "To learn the triangle vocabulary, we employ a graph con-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 201, + 286, + 209 + ], + "spans": [ + { + "bbox": [ + 49, + 201, + 286, + 209 + ], + "type": "text", + "content": "volution encoder operating on triangles of a mesh and their", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 213, + 287, + 221 + ], + "spans": [ + { + "bbox": [ + 49, + 213, + 287, + 221 + ], + "type": "text", + "content": "neighborhood to extract geometrically rich features that", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 224, + 287, + 234 + ], + "spans": [ + { + "bbox": [ + 48, + 224, + 287, + 234 + ], + "type": "text", + "content": "capture the intricate details of 3D shapes. These features", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 236, + 286, + 246 + ], + "spans": [ + { + "bbox": [ + 48, + 236, + 286, + 246 + ], + "type": "text", + "content": "are quantized as embeddings of a codebook using resid-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 249, + 286, + 258 + ], + "spans": [ + { + "bbox": [ + 49, + 249, + 286, + 258 + ], + "type": "text", + "content": "ual quantization [27, 38], effectively reducing sequence", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 261, + 286, + 270 + ], + "spans": [ + { + "bbox": [ + 48, + 261, + 286, + 270 + ], + "type": "text", + "content": "lengths of the mesh representation. These embeddings are", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 273, + 286, + 281 + ], + "spans": [ + { + "bbox": [ + 49, + 273, + 286, + 281 + ], + "type": "text", + "content": "sequenced and then decoded by a 1D ResNet [22] guided", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 285, + 286, + 293 + ], + "spans": [ + { + "bbox": [ + 49, + 285, + 286, + 293 + ], + "type": "text", + "content": "by a reconstruction loss. This phase lays the groundwork", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 297, + 232, + 305 + ], + "spans": [ + { + "bbox": [ + 48, + 297, + 232, + 305 + ], + "type": "text", + "content": "for the subsequent training of the transformer.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 46, + 306, + 287, + 426 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 61, + 308, + 286, + 317 + ], + "spans": [ + { + "bbox": [ + 61, + 308, + 286, + 317 + ], + "type": "text", + "content": "We then train a GPT-style decoder-only transformer,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 320, + 286, + 330 + ], + "spans": [ + { + "bbox": [ + 49, + 320, + 286, + 330 + ], + "type": "text", + "content": "which leverages these quantized geometric embeddings.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 332, + 286, + 341 + ], + "spans": [ + { + "bbox": [ + 49, + 332, + 286, + 341 + ], + "type": "text", + "content": "Given a sequence of geometric embeddings extracted from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 344, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 49, + 344, + 287, + 354 + ], + "type": "text", + "content": "the triangles of a mesh, the transformer is trained to predict", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 356, + 286, + 365 + ], + "spans": [ + { + "bbox": [ + 48, + 356, + 286, + 365 + ], + "type": "text", + "content": "the codebook index of the next embedding in the sequence.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 368, + 286, + 377 + ], + "spans": [ + { + "bbox": [ + 48, + 368, + 286, + 377 + ], + "type": "text", + "content": "Once trained, the transformer can be auto-regressively sam-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 380, + 286, + 389 + ], + "spans": [ + { + "bbox": [ + 49, + 380, + 286, + 389 + ], + "type": "text", + "content": "pled to predict sequences of embeddings. These embed-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 392, + 286, + 400 + ], + "spans": [ + { + "bbox": [ + 49, + 392, + 286, + 400 + ], + "type": "text", + "content": "dings can then be decoded to generate novel and diverse", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 404, + 286, + 413 + ], + "spans": [ + { + "bbox": [ + 49, + 404, + 286, + 413 + ], + "type": "text", + "content": "mesh structures that display efficient, irregular triangula-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 416, + 204, + 424 + ], + "spans": [ + { + "bbox": [ + 49, + 416, + 204, + 424 + ], + "type": "text", + "content": "tions similar to human-crafted meshes.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 47, + 432, + 268, + 445 + ], + "type": "title", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 49, + 433, + 266, + 444 + ], + "spans": [ + { + "bbox": [ + 49, + 433, + 266, + 444 + ], + "type": "text", + "content": "3.1. Learning Quantized Triangle Embeddings", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 46, + 451, + 287, + 510 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 50, + 453, + 285, + 461 + ], + "spans": [ + { + "bbox": [ + 50, + 453, + 285, + 461 + ], + "type": "text", + "content": "Autoregressive generative models, such as transformers,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 464, + 286, + 473 + ], + "spans": [ + { + "bbox": [ + 49, + 464, + 286, + 473 + ], + "type": "text", + "content": "synthesize sequences of tokens where each new token is", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 476, + 286, + 485 + ], + "spans": [ + { + "bbox": [ + 49, + 476, + 286, + 485 + ], + "type": "text", + "content": "conditioned on previously generated tokens. For generating", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 488, + 286, + 497 + ], + "spans": [ + { + "bbox": [ + 48, + 488, + 286, + 497 + ], + "type": "text", + "content": "meshes using transformers, we must then define the order-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 500, + 257, + 509 + ], + "spans": [ + { + "bbox": [ + 49, + 500, + 257, + 509 + ], + "type": "text", + "content": "ing convention of generation, along with the tokens.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 46, + 510, + 287, + 594 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 61, + 512, + 286, + 521 + ], + "spans": [ + { + "bbox": [ + 61, + 512, + 286, + 521 + ], + "type": "text", + "content": "For sequence ordering, Polygen [43] suggests a conven-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 524, + 286, + 533 + ], + "spans": [ + { + "bbox": [ + 49, + 524, + 286, + 533 + ], + "type": "text", + "content": "tion where faces are ordered based on their lowest vertex", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 536, + 286, + 544 + ], + "spans": [ + { + "bbox": [ + 49, + 536, + 286, + 544 + ], + "type": "text", + "content": "index, followed by the next lowest, and so forth. Vertices", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 548, + 286, + 558 + ], + "spans": [ + { + "bbox": [ + 49, + 548, + 100, + 557 + ], + "type": "text", + "content": "are sorted in", + "score": 1.0 + }, + { + "bbox": [ + 101, + 548, + 126, + 558 + ], + "type": "inline_equation", + "content": "z - y - x", + "score": 0.7253 + }, + { + "bbox": [ + 127, + 548, + 286, + 557 + ], + "type": "text", + "content": "order (z representing the vertical axis),", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 559, + 286, + 569 + ], + "spans": [ + { + "bbox": [ + 48, + 559, + 286, + 569 + ], + "type": "text", + "content": "progressing from lowest to highest. Within each face, in-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 572, + 286, + 581 + ], + "spans": [ + { + "bbox": [ + 49, + 572, + 286, + 581 + ], + "type": "text", + "content": "dices are cyclically permuted to place the lowest index first.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 582, + 272, + 594 + ], + "spans": [ + { + "bbox": [ + 48, + 582, + 272, + 594 + ], + "type": "text", + "content": "In our method, we also adopt this sequencing approach.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 61, + 595, + 286, + 605 + ], + "spans": [ + { + "bbox": [ + 61, + 595, + 286, + 605 + ], + "type": "text", + "content": "To define the tokens to generate, we consider a practical", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 607, + 286, + 617 + ], + "spans": [ + { + "bbox": [ + 49, + 607, + 286, + 617 + ], + "type": "text", + "content": "approach to represent a mesh M for autoregressive genera-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 620, + 164, + 629 + ], + "spans": [ + { + "bbox": [ + 49, + 620, + 164, + 629 + ], + "type": "text", + "content": "tion: a sequence of triangles,", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 110, + 635, + 287, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 635, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 110, + 635, + 287, + 649 + ], + "type": "interline_equation", + "content": "\\mathcal {M} := (f _ {1}, f _ {2}, f _ {3}, \\dots , f _ {N}), \\tag {1}", + "image_path": "5c4bb9c1739b322c7f7055205013c2478b8b04bc8af7df9e8b6e416bbbe36845.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 49, + 654, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 49, + 655, + 149, + 665 + ], + "type": "text", + "content": "with N faces (triangles),", + "score": 1.0 + }, + { + "bbox": [ + 152, + 654, + 191, + 665 + ], + "type": "inline_equation", + "content": "f _ { i } \\in \\mathbb { R } ^ { n _ { \\mathrm { i n } } }", + "score": 0.911 + }, + { + "bbox": [ + 193, + 654, + 223, + 665 + ], + "type": "text", + "content": "having", + "score": 1.0 + }, + { + "bbox": [ + 223, + 656, + 237, + 665 + ], + "type": "inline_equation", + "content": "n _ { \\mathrm { i n } }", + "score": 0.8383 + }, + { + "bbox": [ + 238, + 654, + 286, + 665 + ], + "type": "text", + "content": "features. A", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 666, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 48, + 666, + 287, + 677 + ], + "type": "text", + "content": "simple approach to describe each triangle is as its three ver-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 680, + 286, + 689 + ], + "spans": [ + { + "bbox": [ + 49, + 680, + 286, + 689 + ], + "type": "text", + "content": "tices, comprising nine total coordinates. Upon discretiza-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 692, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 49, + 692, + 286, + 700 + ], + "type": "text", + "content": "tion, these coordinates can be treated as tokens. The se-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 703, + 211, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 703, + 211, + 712 + ], + "type": "text", + "content": "quence length in this case would be 9N.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "image", + "bbox": [ + 305, + 70, + 547, + 229 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 547, + 229 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 70, + 547, + 229 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 547, + 229 + ], + "type": "image", + "content": "```mermaid\ngraph LR\n InputMesh[\"Input Mesh\"] -->|\"| F| × C_in\"| GraphConv[\"Graph Convolutional Encoder\"]\n ReconstructedMesh[\"Reconstructed Mesh\"] -->|\"| F| × 9\"| ResNetDecoder[\"ResNet Decoder\"]\n GraphConv -->|\"| F| × C_e\"| ResidualFaceQuant[\"Residual Face Quantization Module\"]\n ResNetDecoder --> SequenceOfFaces[\"Sequence Of Faces\"]\n SequenceOfFaces -->|\"| F| × C_e\"| ResidualFaceQuant\n ResidualFaceQuant -->|\"| F| ×\"| ResidualFaceQuantModule[\"Residual Face Quantization Module\"]\n ResidualFaceQuantModule -->|\"C_e\"| SumResidualFeatures[\"Sum Residual Features\"]\n ResidualFaceQuantModule -->|\"D × C_e\"| Reshape[\"Reshape\"]\n Reshape --> FeatureCodebook[\"Feature Codebook\"]\n FeatureCodebook --> MeanAcrossSharedVertices[\"Mean across Shared Vertices\"]\n MeanAcrossSharedVertices --> SplitFeature[\"Split Feature\"]\n SplitFeature -->|\"C_e\"| SumResidualFeatures\n```", + "image_path": "68bf00eef4f292ec6f6d2b982ffb3ea487e15df8e5bbe5ed3e13d7f0d3653820.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 236, + 547, + 326 + ], + "type": "image_caption", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 308, + 239, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 308, + 239, + 545, + 247 + ], + "type": "text", + "content": "Figure 3. We employ a graph convolutional encoder to process", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 250, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 308, + 250, + 545, + 258 + ], + "type": "text", + "content": "mesh faces, leveraging geometric neighborhood information to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 261, + 544, + 270 + ], + "spans": [ + { + "bbox": [ + 308, + 261, + 544, + 270 + ], + "type": "text", + "content": "capture strong features representing intricate details of 3D shapes.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 271, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 307, + 271, + 545, + 281 + ], + "type": "text", + "content": "These features are then quantized into codebook embeddings using", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 282, + 544, + 291 + ], + "spans": [ + { + "bbox": [ + 308, + 282, + 544, + 291 + ], + "type": "text", + "content": "residual quantization [27, 38]. In contrast to naive vector quanti-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 294, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 308, + 294, + 545, + 302 + ], + "type": "text", + "content": "zation, this ensures better reconstruction quality. The quantized", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 304, + 545, + 313 + ], + "spans": [ + { + "bbox": [ + 308, + 304, + 545, + 313 + ], + "type": "text", + "content": "embeddings are subsequently sequenced and decoded through a", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 309, + 316, + 483, + 323 + ], + "spans": [ + { + "bbox": [ + 309, + 316, + 483, + 323 + ], + "type": "text", + "content": "1D ResNet [22], guided by a reconstruction loss.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 10, + "sub_type": "flowchart" + }, + { + "bbox": [ + 304, + 346, + 545, + 465 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 319, + 348, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 319, + 348, + 545, + 357 + ], + "type": "text", + "content": "However, we observe two major challenges when using", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 360, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 308, + 360, + 545, + 369 + ], + "type": "text", + "content": "coordinates directly as tokens. First, the sequence lengths", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 372, + 544, + 381 + ], + "spans": [ + { + "bbox": [ + 307, + 372, + 544, + 381 + ], + "type": "text", + "content": "become excessively long, as each face is represented by", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 384, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 307, + 384, + 545, + 392 + ], + "type": "text", + "content": "nine values. This length does not scale well with trans-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 396, + 544, + 405 + ], + "spans": [ + { + "bbox": [ + 307, + 396, + 544, + 405 + ], + "type": "text", + "content": "former architectures, which often have limited context win-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 408, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 308, + 408, + 545, + 417 + ], + "type": "text", + "content": "dows. Second, representing discrete positions of a trian-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 420, + 544, + 429 + ], + "spans": [ + { + "bbox": [ + 308, + 420, + 544, + 429 + ], + "type": "text", + "content": "gle as tokens fails to capture geometric patterns effectively.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 431, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 308, + 431, + 545, + 441 + ], + "type": "text", + "content": "This is because such a representation lacks information", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 444, + 544, + 453 + ], + "spans": [ + { + "bbox": [ + 308, + 444, + 544, + 453 + ], + "type": "text", + "content": "about neighboring triangles and does not incorporate any", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 456, + 432, + 464 + ], + "spans": [ + { + "bbox": [ + 308, + 456, + 432, + 464 + ], + "type": "text", + "content": "priors from mesh distributions.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 304, + 466, + 545, + 514 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 319, + 467, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 319, + 467, + 545, + 478 + ], + "type": "text", + "content": "To address the aforementioned challenges, we propose", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 479, + 544, + 489 + ], + "spans": [ + { + "bbox": [ + 308, + 479, + 544, + 489 + ], + "type": "text", + "content": "to learn geometric embeddings from a collection of triangu-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 491, + 545, + 501 + ], + "spans": [ + { + "bbox": [ + 307, + 491, + 545, + 501 + ], + "type": "text", + "content": "lar meshes, utilizing an encoder-decoder architecture with", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 502, + 519, + 514 + ], + "spans": [ + { + "bbox": [ + 307, + 502, + 519, + 514 + ], + "type": "text", + "content": "residual vector quantization at its bottleneck (Fig. 3).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 304, + 514, + 546, + 633 + ], + "type": "text", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 319, + 515, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 319, + 515, + 545, + 525 + ], + "type": "text", + "content": "The network’s encoder E employs graph convolutions", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 528, + 544, + 536 + ], + "spans": [ + { + "bbox": [ + 308, + 528, + 544, + 536 + ], + "type": "text", + "content": "on mesh faces, where each face forms a node and neigh-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 540, + 545, + 549 + ], + "spans": [ + { + "bbox": [ + 307, + 540, + 545, + 549 + ], + "type": "text", + "content": "boring faces are connected by undirected edges. 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Mesh Generation with Transformers", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "type": "image", + "bbox": [ + 307, + 188, + 547, + 281 + ], + "blocks": [ + { + "bbox": [ + 307, + 188, + 547, + 281 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 188, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 307, + 188, + 547, + 281 + ], + "type": "image", + "content": "```mermaid\ngraph LR\n A[\"Face Graph + Input Features\"] --> B[\"Graph Convolutional Encoder\"]\n B --> C[\"Residual Face Quantization Module\"]\n C --> D[\"Sequence & Flatten\"]\n D --> E[\"GPT-Style Transformer\"]\n E --> F[\"Predicted Codebook Indices\"]\n F --> G[\"GT Codebook Indices\"]\n G --> H[\"CE Loss\"]\n```", + "image_path": "72cb966cd94dd8b5076080c802a06cda11de1a0168b09a46a1aa9944576b1ec9.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 288, + 547, + 366 + ], + "type": "image_caption", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 307, + 290, + 545, + 298 + ], + "spans": [ + { + "bbox": [ + 307, + 290, + 545, + 298 + ], + "type": "text", + "content": "Figure 5. 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These embeddings are", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 334, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 307, + 334, + 545, + 342 + ], + "type": "text", + "content": "flattened, bookended with start and end tokens, and fed into a GPT-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 345, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 308, + 345, + 545, + 354 + ], + "type": "text", + "content": "style transformer. 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Es-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 537, + 545, + 546 + ], + "spans": [ + { + "bbox": [ + 308, + 537, + 545, + 546 + ], + "type": "text", + "content": "sentially, we maximize the log probability of the training", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 549, + 529, + 558 + ], + "spans": [ + { + "bbox": [ + 308, + 549, + 529, + 558 + ], + "type": "text", + "content": "sequences with respect to the transformer parameters θ,", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 358, + 566, + 545, + 600 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 566, + 545, + 600 + ], + "spans": [ + { + "bbox": [ + 358, + 566, + 545, + 600 + ], + "type": "interline_equation", + "content": "\\prod_ {i = 1} ^ {N} \\prod_ {d = 1} ^ {D} p (t _ {i} ^ {d} \\mid \\mathbf {e} (t _ {< i} ^ {d}), \\mathbf {e} (t _ {i} ^ {< d}); \\theta). \\tag {6}", + "image_path": "1550d35f45f33a9ad3318f5fee4db2c6cc9f0ffd97ab6276c575e77eaf44f3e7.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 320, + 607, + 544, + 616 + ], + "spans": [ + { + "bbox": [ + 320, + 607, + 544, + 616 + ], + "type": "text", + "content": "Once the transformer is trained, it can autoregressively", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 620, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 307, + 620, + 545, + 629 + ], + "type": "text", + "content": "generate a sequence of tokens, starting with a start token", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 632, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 308, + 632, + 545, + 640 + ], + "type": "text", + "content": "and continuing until a stop token is encountered using beam", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 643, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 307, + 643, + 545, + 653 + ], + "type": "text", + "content": "sampling. 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A", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 475, + 286, + 483 + ], + "spans": [ + { + "bbox": [ + 48, + 475, + 286, + 483 + ], + "type": "text", + "content": "cross-entropy loss on the discrete mesh coordinates and a", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 487, + 285, + 495 + ], + "spans": [ + { + "bbox": [ + 49, + 487, + 285, + 495 + ], + "type": "text", + "content": "commitment loss for the embeddings guides the reconstruc-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 498, + 280, + 508 + ], + "spans": [ + { + "bbox": [ + 48, + 498, + 280, + 508 + ], + "type": "text", + "content": "tion process. More details can be found in supplementary.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "image", + "bbox": [ + 60, + 521, + 276, + 648 + ], + "blocks": [ + { + "bbox": [ + 60, + 521, + 276, + 648 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 521, + 276, + 648 + ], + "spans": [ + { + "bbox": [ + 60, + 521, + 276, + 648 + ], + "type": "image", + "content": "Three 3D wireframe models of a chair: one with real-valued outputs, one with discrete outputs, and the ground truth (no text or symbols on the models themselves)", + "image_path": "ee8d3956b2fa1fe0a598529c608460da65258fd9b5188ac3e5354bbc23759131.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 654, + 287, + 711 + ], + "type": "image_caption", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 49, + 657, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 49, + 657, + 286, + 665 + ], + "type": "text", + "content": "Figure 4. Our method utilizes a ResNet [22] decoder that out-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 668, + 286, + 676 + ], + "spans": [ + { + "bbox": [ + 48, + 668, + 286, + 676 + ], + "type": "text", + "content": "puts mesh faces as a distribution over discretized coordinate val-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 679, + 286, + 687 + ], + "spans": [ + { + "bbox": [ + 49, + 679, + 286, + 687 + ], + "type": "text", + "content": "ues (center), as opposed to regression of continuous values (left).", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 689, + 286, + 698 + ], + "spans": [ + { + "bbox": [ + 49, + 689, + 286, + 698 + ], + "type": "text", + "content": "This significantly reduces floating face artifacts, leading to recon-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 700, + 271, + 709 + ], + "spans": [ + { + "bbox": [ + 49, + 700, + 271, + 709 + ], + "type": "text", + "content": "structions that more closely resemble the ground truth (right).", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 7, + "sub_type": "natural_image" + }, + { + "bbox": [ + 305, + 72, + 547, + 157 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 320, + 74, + 545, + 83 + ], + "spans": [ + { + "bbox": [ + 320, + 74, + 545, + 83 + ], + "type": "text", + "content": "After training, the graph encoder E and codebook C are", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 87, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 308, + 87, + 545, + 95 + ], + "type": "text", + "content": "incorporated into the transformer training, using T from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 96, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 307, + 98, + 441, + 107 + ], + "type": "text", + "content": "Eq. 3 as the token sequence. With", + "score": 1.0 + }, + { + "bbox": [ + 443, + 96, + 486, + 107 + ], + "type": "inline_equation", + "content": "| \\mathbf { T } | = D N", + "score": 0.7008 + }, + { + "bbox": [ + 486, + 98, + 545, + 108 + ], + "type": "text", + "content": ", this sequence", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 110, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 307, + 110, + 545, + 119 + ], + "type": "text", + "content": "is more concise than the naive 9N-length tokenization when", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 121, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 308, + 121, + 340, + 131 + ], + "type": "inline_equation", + "content": "D \\ < \\ 9 .", + "score": 0.7276 + }, + { + "bbox": [ + 346, + 121, + 545, + 132 + ], + "type": "text", + "content": "Thus, we obtain geometrically rich embeddings", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 134, + 544, + 143 + ], + "spans": [ + { + "bbox": [ + 308, + 134, + 544, + 143 + ], + "type": "text", + "content": "with shorter sequence lengths, overcoming our initial chal-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 146, + 533, + 156 + ], + "spans": [ + { + "bbox": [ + 308, + 146, + 533, + 156 + ], + "type": "text", + "content": "lenges and paving the way for efficient mesh generation.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 306, + 163, + 501, + 175 + ], + "type": "title", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 307, + 163, + 499, + 174 + ], + "spans": [ + { + "bbox": [ + 307, + 163, + 499, + 174 + ], + "type": "text", + "content": "3.2. Mesh Generation with Transformers", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "type": "image", + "bbox": [ + 307, + 188, + 547, + 281 + ], + "blocks": [ + { + "bbox": [ + 307, + 188, + 547, + 281 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 188, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 307, + 188, + 547, + 281 + ], + "type": "image", + "content": "```mermaid\ngraph LR\n A[\"Face Graph + Input Features\"] --> B[\"Graph Convolutional Encoder\"]\n B --> C[\"Residual Face Quantization Module\"]\n C --> D[\"Sequence & Flatten\"]\n D --> E[\"GPT-Style Transformer\"]\n E --> F[\"Predicted Codebook Indices\"]\n F --> G[\"GT Codebook Indices\"]\n G --> H[\"CE Loss\"]\n```", + "image_path": "72cb966cd94dd8b5076080c802a06cda11de1a0168b09a46a1aa9944576b1ec9.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 288, + 547, + 366 + ], + "type": "image_caption", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 307, + 290, + 545, + 298 + ], + "spans": [ + { + "bbox": [ + 307, + 290, + 545, + 298 + ], + "type": "text", + "content": "Figure 5. We employ a transformer to generate mesh sequences", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 300, + 545, + 309 + ], + "spans": [ + { + "bbox": [ + 307, + 300, + 545, + 309 + ], + "type": "text", + "content": "as token indices from a pre-learned codebook vocabulary. During", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 312, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 307, + 312, + 545, + 320 + ], + "type": "text", + "content": "training, a graph encoder extracts features from mesh faces, which", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 323, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 307, + 323, + 545, + 331 + ], + "type": "text", + "content": "are quantized into a set of face embeddings. These embeddings are", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 334, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 307, + 334, + 545, + 342 + ], + "type": "text", + "content": "flattened, bookended with start and end tokens, and fed into a GPT-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 345, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 308, + 345, + 545, + 354 + ], + "type": "text", + "content": "style transformer. This decoder predicts the subsequent codebook", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 355, + 525, + 364 + ], + "spans": [ + { + "bbox": [ + 307, + 355, + 525, + 364 + ], + "type": "text", + "content": "index for each embedding, optimized via cross-entropy loss.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 11, + "sub_type": "flowchart" + }, + { + "bbox": [ + 304, + 380, + 547, + 559 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 320, + 381, + 545, + 391 + ], + "spans": [ + { + "bbox": [ + 320, + 381, + 545, + 391 + ], + "type": "text", + "content": "We employ a decoder-only transformer architecture from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 392, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 307, + 392, + 545, + 403 + ], + "type": "text", + "content": "the GPT family of models to predict meshes as sequences", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 405, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 308, + 405, + 545, + 414 + ], + "type": "text", + "content": "of indices from the learned codebook in Sec. 3.1. 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Es-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 537, + 545, + 546 + ], + "spans": [ + { + "bbox": [ + 308, + 537, + 545, + 546 + ], + "type": "text", + "content": "sentially, we maximize the log probability of the training", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 549, + 529, + 558 + ], + "spans": [ + { + "bbox": [ + 308, + 549, + 529, + 558 + ], + "type": "text", + "content": "sequences with respect to the transformer parameters θ,", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 358, + 566, + 545, + 600 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 566, + 545, + 600 + ], + "spans": [ + { + "bbox": [ + 358, + 566, + 545, + 600 + ], + "type": "interline_equation", + "content": "\\prod_ {i = 1} ^ {N} \\prod_ {d = 1} ^ {D} p (t _ {i} ^ {d} \\mid \\mathbf {e} (t _ {< i} ^ {d}), \\mathbf {e} (t _ {i} ^ {< d}); \\theta). \\tag {6}", + "image_path": "1550d35f45f33a9ad3318f5fee4db2c6cc9f0ffd97ab6276c575e77eaf44f3e7.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 320, + 607, + 544, + 616 + ], + "spans": [ + { + "bbox": [ + 320, + 607, + 544, + 616 + ], + "type": "text", + "content": "Once the transformer is trained, it can autoregressively", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 620, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 307, + 620, + 545, + 629 + ], + "type": "text", + "content": "generate a sequence of tokens, starting with a start token", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 632, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 308, + 632, + 545, + 640 + ], + "type": "text", + "content": "and continuing until a stop token is encountered using beam", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 643, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 307, + 643, + 545, + 653 + ], + "type": "text", + "content": "sampling. 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ClassMethodCOV↑MMD↓1-NNAFID↓KID↓|V||F|
ChairAtlasNet [18]9.034.0595.13170.710.16925004050
BSPNet [7]16.483.6291.7546.730.0306731165
Polygen [43]31.224.4193.5661.100.043248603
GET3D [14]40.853.5683.0481.450.0541372527457
GET3D*38.753.5784.0778.290.065199399
MeshGPT43.283.2975.5118.460.010125228
TableAtlasNet [18]7.163.8596.30161.380.15025004050
BSPNet [7]16.833.1493.5830.780.017420699
Polygen [43]32.993.0088.6538.530.029147454
GET3D [14]41.702.7885.5493.930.0761376727537
GET3D*37.952.8581.9350.460.037199399
MeshGPT45.682.3672.886.240.00299187
BenchAtlasNet [18]20.532.4790.58189.390.16325004050
BSPNet [7]28.742.0588.4459.110.030457756
Polygen [43]51.921.9776.9849.340.031172430
MeshGPT55.231.4468.248.720.001159291
LampAtlasNet [18]19.974.6891.85177.910.13925004050
BSPNet [7]18.385.3293.13112.650.0775871011
Polygen [43]47.864.1881.4252.480.025185558
MeshGPT53.883.9465.7319.910.004150288
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ClassMethodCOV↑MMD↓1-NNAFID↓KID↓|V||F|
ChairAtlasNet [18]9.034.0595.13170.710.16925004050
BSPNet [7]16.483.6291.7546.730.0306731165
Polygen [43]31.224.4193.5661.100.043248603
GET3D [14]40.853.5683.0481.450.0541372527457
GET3D*38.753.5784.0778.290.065199399
MeshGPT43.283.2975.5118.460.010125228
TableAtlasNet [18]7.163.8596.30161.380.15025004050
BSPNet [7]16.833.1493.5830.780.017420699
Polygen [43]32.993.0088.6538.530.029147454
GET3D [14]41.702.7885.5493.930.0761376727537
GET3D*37.952.8581.9350.460.037199399
MeshGPT45.682.3672.886.240.00299187
BenchAtlasNet [18]20.532.4790.58189.390.16325004050
BSPNet [7]28.742.0588.4459.110.030457756
Polygen [43]51.921.9776.9849.340.031172430
MeshGPT55.231.4468.248.720.001159291
LampAtlasNet [18]19.974.6891.85177.910.13925004050
BSPNet [7]18.385.3293.13112.650.0775871011
Polygen [43]47.864.1881.4252.480.025185558
MeshGPT53.883.9465.7319.910.004150288
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We additionally compare with a state-of-the-art", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 535, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 307, + 535, + 545, + 545 + ], + "type": "text", + "content": "neural field-based method, GET3D [14], that creates shapes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 548, + 544, + 555 + ], + "spans": [ + { + "bbox": [ + 308, + 548, + 544, + 555 + ], + "type": "text", + "content": "as 3D signed distance fields (SDFs) from which a mesh is", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 559, + 544, + 568 + ], + "spans": [ + { + "bbox": [ + 308, + 559, + 544, + 568 + ], + "type": "text", + "content": "extracted by differentiable marching tetrahedra. For BSP-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 572, + 544, + 581 + ], + "spans": [ + { + "bbox": [ + 308, + 572, + 544, + 581 + ], + "type": "text", + "content": "Net and AtlasNet, which are built on autoencoder back-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 584, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 308, + 584, + 545, + 593 + ], + "type": "text", + "content": "bones, we follow [1] to fit a Gaussian mixture model with", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 595, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 307, + 595, + 545, + 605 + ], + "type": "text", + "content": "32 components to enable unconditional sampling of shapes.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 305, + 606, + 545, + 713 + ], + "type": "text", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 320, + 608, + 544, + 616 + ], + "spans": [ + { + "bbox": [ + 320, + 608, + 544, + 616 + ], + "type": "text", + "content": "As shown in Fig. 6, Fig. 7 and Tab. 1, our method outper-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 620, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 308, + 620, + 545, + 628 + ], + "type": "text", + "content": "forms all baselines in all four categories. 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GET3D generates good high-level shape", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 49, + 621, + 286, + 630 + ], + "spans": [ + { + "bbox": [ + 49, + 621, + 286, + 630 + ], + "type": "text", + "content": "structures, but over-triangulated and with imperfect flat sur-", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 49, + 633, + 285, + 642 + ], + "spans": [ + { + "bbox": [ + 49, + 633, + 285, + 642 + ], + "type": "text", + "content": "faces. 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Qualitative comparison of Chair and Table meshes from ShapeNet [5]. Our approach produces compact meshes with sharp", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 567, + 541, + 575 + ], + "spans": [ + { + "bbox": [ + 49, + 567, + 541, + 575 + ], + "type": "text", + "content": "geometric details. In contrast, baselines often either miss these details, produce over-triangulated meshes, or output too simplistic shapes.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_type": "text_image" + }, + { + "bbox": [ + 46, + 583, + 288, + 656 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 48, + 585, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 48, + 585, + 287, + 594 + ], + "type": "text", + "content": "diversity and shape quality. 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Participants were asked their preference be-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 609, + 544, + 618 + ], + "spans": [ + { + "bbox": [ + 308, + 609, + 544, + 618 + ], + "type": "text", + "content": "tween our method and the baseline in terms of both overall", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 621, + 545, + 631 + ], + "spans": [ + { + "bbox": [ + 308, + 621, + 545, + 631 + ], + "type": "text", + "content": "shape quality and similarity of triangulation patterns to the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 633, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 308, + 633, + 545, + 643 + ], + "type": "text", + "content": "ground truth meshes. This resulted in 784 total question re-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 645, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 307, + 645, + 545, + 654 + ], + "type": "text", + "content": "sponses. 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Further", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 49, + 628, + 253, + 637 + ], + "spans": [ + { + "bbox": [ + 49, + 628, + 253, + 637 + ], + "type": "text", + "content": "user study details are provided in the supplemental.", + "score": 1.0, + "cross_page": true + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 304, + 583, + 547, + 704 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [], + "merge_prev": false, + "lines_deleted": true + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 282, + 329 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 282, + 329 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 71, + 282, + 329 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 282, + 329 + ], + "type": "image", + "content": "GT Samples\nAtlasNet\tBSPNet\tPolygen\tOurs", + "image_path": "45b493818f6537a57fadcb2454130c2c50c5a184adc6d1ed712e535a4a05c269.jpg" + } + ] + } + ], + "index": 0 + } + ], + "index": 0, + "sub_type": "text_image" + }, + { + "type": "table", + "bbox": [ + 49, + 374, + 287, + 411 + ], + "blocks": [ + { + "bbox": [ + 47, + 337, + 287, + 370 + ], + "type": "table_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 49, + 338, + 286, + 347 + ], + "spans": [ + { + "bbox": [ + 49, + 338, + 286, + 347 + ], + "type": "text", + "content": "Figure 7. Qualitative comparison of Bench and Lamp meshes from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 350, + 286, + 358 + ], + "spans": [ + { + "bbox": [ + 49, + 350, + 286, + 358 + ], + "type": "text", + "content": "the ShapeNet [5] dataset. Compared to baselines, our method pro-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 361, + 222, + 369 + ], + "spans": [ + { + "bbox": [ + 49, + 361, + 222, + 369 + ], + "type": "text", + "content": "duces valid meshes with high geometric fidelity.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 49, + 374, + 287, + 411 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 374, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 49, + 374, + 287, + 411 + ], + "type": "table", + "html": "
PreferenceAtlasNet [18]BSPNet [7]Polygen [43]GET3D [14]
Our Shape82.65%78.57%85.71%68.37%
Our Triangulation84.69%71.43%84.69%73.47%
", + "image_path": "469b0707a1d0c24a76a461e6a0fbb95c58ce28348c8e9ee5a08dff8e39ee4713.jpg" + } + ] + } + ], + "index": 2 + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 49, + 460, + 287, + 538 + ], + "blocks": [ + { + "bbox": [ + 47, + 418, + 287, + 452 + ], + "type": "table_caption", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 49, + 420, + 286, + 428 + ], + "spans": [ + { + "bbox": [ + 49, + 420, + 286, + 428 + ], + "type": "text", + "content": "Table 2. Percentage of users who prefer our method over the base-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 431, + 286, + 440 + ], + "spans": [ + { + "bbox": [ + 49, + 431, + 286, + 440 + ], + "type": "text", + "content": "lines in terms of shape quality and the triangulation quality. Our", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 442, + 252, + 451 + ], + "spans": [ + { + "bbox": [ + 49, + 442, + 252, + 451 + ], + "type": "text", + "content": "generated meshes are preferred significantly more often.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 49, + 460, + 287, + 538 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 460, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 49, + 460, + 287, + 538 + ], + "type": "table", + "html": "
MethodCOV↑MMD↓1-NNAFID↓KID↓
w/o Learned Tokens27.504.5193.1540.200.024
w/o Encoder Features39.243.4384.4830.350.017
w/o Pretraining36.973.7384.6927.540.014
w/o Sequence Compression30.984.1588.9838.760.023
w/o per Vertex Quantization23.575.4998.3574.940.050
MeshGPT43.283.2975.5118.460.010
", + "image_path": "0500b44c57dd1a58136123af0b3f1b93b7cfad5e8dead5b38ee8706f0c22e0c7.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 546, + 287, + 589 + ], + "type": "table_caption", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 48, + 547, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 48, + 547, + 287, + 556 + ], + "type": "text", + "content": "Table 3. Ablations of our design choices on the Chair category of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 559, + 286, + 567 + ], + "spans": [ + { + "bbox": [ + 49, + 559, + 286, + 567 + ], + "type": "text", + "content": "the ShapeNet [5] dataset. As highlighted by the drop in perfor-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 570, + 286, + 578 + ], + "spans": [ + { + "bbox": [ + 49, + 570, + 286, + 578 + ], + "type": "text", + "content": "mance by removing any of them, each of these contribute to the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 580, + 97, + 589 + ], + "spans": [ + { + "bbox": [ + 49, + 580, + 97, + 589 + ], + "type": "text", + "content": "final method.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 602, + 287, + 639 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 48, + 603, + 285, + 614 + ], + "spans": [ + { + "bbox": [ + 48, + 603, + 285, + 614 + ], + "type": "text", + "content": "ity. This underscores our ability to generate high-quality", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 616, + 286, + 625 + ], + "spans": [ + { + "bbox": [ + 49, + 616, + 286, + 625 + ], + "type": "text", + "content": "meshes that align with human users’ preferences. Further", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 628, + 253, + 637 + ], + "spans": [ + { + "bbox": [ + 49, + 628, + 253, + 637 + ], + "type": "text", + "content": "user study details are provided in the supplemental.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 49, + 643, + 286, + 652 + ], + "spans": [ + { + "bbox": [ + 49, + 643, + 286, + 652 + ], + "type": "text", + "content": "Shape Novelty Analysis. We investigate whether our", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 655, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 49, + 655, + 286, + 664 + ], + "type": "text", + "content": "method can generate novel shapes that extend beyond the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 667, + 286, + 677 + ], + "spans": [ + { + "bbox": [ + 49, + 667, + 286, + 677 + ], + "type": "text", + "content": "training dataset, ensuring the model is not merely retriev-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 679, + 285, + 689 + ], + "spans": [ + { + "bbox": [ + 49, + 679, + 285, + 689 + ], + "type": "text", + "content": "ing existing shapes. Following the methodology in pre-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 691, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 49, + 691, + 286, + 700 + ], + "type": "text", + "content": "vious studies [13, 24], we generate 500 shapes using our", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 703, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 703, + 286, + 712 + ], + "type": "text", + "content": "model. For each generated shape, we identify the top three", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "chart", + "bbox": [ + 305, + 68, + 545, + 319 + ], + "blocks": [ + { + "bbox": [ + 305, + 68, + 545, + 319 + ], + "type": "chart_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 68, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 68, + 545, + 319 + ], + "type": "chart", + "content": "| Chamfer Distance (x10^3) | Proportion of Generated Shapes |\n| --- | --- |\n| 0 | ~0.5 |\n| 1 | ~4.5 |\n| 2 | ~6.5 |\n| 3 | ~3.5 |\n| 4 | ~2.5 |\n| 5 | ~1.5 |\n| 6 | ~1.5 |\n| 7 | ~1.5 |\n| 8 | ~1.0 |\n| 9 | ~0.5 |\n| 10+ | ~4.5 |", + "image_path": "c529395af6d980051ddecada4916f283df5a930f3e3dfe3b5e19f6ee6a2f96a9.jpg" + } + ] + } + ], + "index": 8 + } + ], + "index": 8, + "sub_type": "bar" + }, + { + "type": "image", + "bbox": [ + 306, + 418, + 542, + 567 + ], + "blocks": [ + { + "bbox": [ + 305, + 326, + 547, + 415 + ], + "type": "image_caption", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 308, + 328, + 544, + 336 + ], + "spans": [ + { + "bbox": [ + 308, + 328, + 544, + 336 + ], + "type": "text", + "content": "Figure 8. Shape novelty analysis on ShapeNet [5] chair category.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 338, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 307, + 338, + 545, + 347 + ], + "type": "text", + "content": "We show the 3 nearest neighbors in terms of Chamfer Distance", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 350, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 308, + 350, + 545, + 358 + ], + "type": "text", + "content": "(CD) for a generated shape (top). We also plot the distribution of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 361, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 307, + 361, + 545, + 369 + ], + "type": "text", + "content": "500 generated chair samples from our method and their closeness", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 372, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 307, + 372, + 545, + 380 + ], + "type": "text", + "content": "to training distribution. Our method can generate shapes that are", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 383, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 307, + 383, + 545, + 392 + ], + "type": "text", + "content": "similar (low CD) as well as different (high CD) from the training", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 306, + 392, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 392, + 545, + 403 + ], + "type": "text", + "content": "distribution, with shapes at the 50th percentile looking different", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 405, + 395, + 413 + ], + "spans": [ + { + "bbox": [ + 308, + 405, + 395, + 413 + ], + "type": "text", + "content": "from closest train shape.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 306, + 418, + 542, + 567 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 418, + 542, + 567 + ], + "spans": [ + { + "bbox": [ + 306, + 418, + 542, + 567 + ], + "type": "image", + "content": "3D model of wooden furniture with various shapes and layouts, including chairs, tables, and blocks (no text or symbols)", + "image_path": "5b3a33b4221fb57854918e5b77130294ccf40f3adc775ccf038ce130eb125645.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 574, + 545, + 597 + ], + "type": "image_caption", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 308, + 575, + 545, + 584 + ], + "spans": [ + { + "bbox": [ + 308, + 575, + 545, + 584 + ], + "type": "text", + "content": "Figure 9. Given a partial mesh, our method can infer multiple", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 586, + 408, + 595 + ], + "spans": [ + { + "bbox": [ + 308, + 586, + 408, + 595 + ], + "type": "text", + "content": "possible shape completions.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 10, + "sub_type": "natural_image" + }, + { + "bbox": [ + 305, + 605, + 547, + 665 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 308, + 607, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 308, + 607, + 545, + 616 + ], + "type": "text", + "content": "nearest neighbors from the training set based on Chamfer", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 617, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 307, + 617, + 545, + 628 + ], + "type": "text", + "content": "Distance (CD). To ensure a fair distance computation, ac-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 630, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 307, + 630, + 545, + 639 + ], + "type": "text", + "content": "counting for potential discrepancies due to scale or shift in", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 642, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 308, + 642, + 545, + 651 + ], + "type": "text", + "content": "the augmented generations, we normalize all generated and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 654, + 471, + 664 + ], + "spans": [ + { + "bbox": [ + 307, + 654, + 471, + 664 + ], + "type": "text", + "content": "train shapes to be centered within [0, 1]3.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 305, + 666, + 547, + 714 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 319, + 666, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 319, + 666, + 545, + 677 + ], + "type": "text", + "content": "Fig. 8 displays the most similar shapes from the train", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 679, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 307, + 679, + 545, + 689 + ], + "type": "text", + "content": "set corresponding to a sample generated by our model. We", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 692, + 544, + 700 + ], + "spans": [ + { + "bbox": [ + 308, + 692, + 544, + 700 + ], + "type": "text", + "content": "conduct a detailed analysis of the shape similarity distri-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 703, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 307, + 703, + 545, + 712 + ], + "type": "text", + "content": "bution between the retrieved and generated shapes on the", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 300, + 742 + ], + "type": "page_number", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 293, + 733, + 301, + 743 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 301, + 743 + ], + "type": "text", + "content": "7", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6, + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 282, + 329 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 282, + 329 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 71, + 282, + 329 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 282, + 329 + ], + "type": "image", + "content": "GT Samples\nAtlasNet\tBSPNet\tPolygen\tOurs", + "image_path": "45b493818f6537a57fadcb2454130c2c50c5a184adc6d1ed712e535a4a05c269.jpg" + } + ] + } + ], + "index": 0 + } + ], + "index": 0, + "sub_type": "text_image" + }, + { + "type": "table", + "bbox": [ + 49, + 374, + 287, + 411 + ], + "blocks": [ + { + "bbox": [ + 47, + 337, + 287, + 370 + ], + "type": "table_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 49, + 338, + 286, + 347 + ], + "spans": [ + { + "bbox": [ + 49, + 338, + 286, + 347 + ], + "type": "text", + "content": "Figure 7. Qualitative comparison of Bench and Lamp meshes from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 350, + 286, + 358 + ], + "spans": [ + { + "bbox": [ + 49, + 350, + 286, + 358 + ], + "type": "text", + "content": "the ShapeNet [5] dataset. Compared to baselines, our method pro-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 361, + 222, + 369 + ], + "spans": [ + { + "bbox": [ + 49, + 361, + 222, + 369 + ], + "type": "text", + "content": "duces valid meshes with high geometric fidelity.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 49, + 374, + 287, + 411 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 374, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 49, + 374, + 287, + 411 + ], + "type": "table", + "html": "
PreferenceAtlasNet [18]BSPNet [7]Polygen [43]GET3D [14]
Our Shape82.65%78.57%85.71%68.37%
Our Triangulation84.69%71.43%84.69%73.47%
", + "image_path": "469b0707a1d0c24a76a461e6a0fbb95c58ce28348c8e9ee5a08dff8e39ee4713.jpg" + } + ] + } + ], + "index": 2 + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 49, + 460, + 287, + 538 + ], + "blocks": [ + { + "bbox": [ + 47, + 418, + 287, + 452 + ], + "type": "table_caption", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 49, + 420, + 286, + 428 + ], + "spans": [ + { + "bbox": [ + 49, + 420, + 286, + 428 + ], + "type": "text", + "content": "Table 2. Percentage of users who prefer our method over the base-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 431, + 286, + 440 + ], + "spans": [ + { + "bbox": [ + 49, + 431, + 286, + 440 + ], + "type": "text", + "content": "lines in terms of shape quality and the triangulation quality. Our", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 442, + 252, + 451 + ], + "spans": [ + { + "bbox": [ + 49, + 442, + 252, + 451 + ], + "type": "text", + "content": "generated meshes are preferred significantly more often.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 49, + 460, + 287, + 538 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 460, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 49, + 460, + 287, + 538 + ], + "type": "table", + "html": "
MethodCOV↑MMD↓1-NNAFID↓KID↓
w/o Learned Tokens27.504.5193.1540.200.024
w/o Encoder Features39.243.4384.4830.350.017
w/o Pretraining36.973.7384.6927.540.014
w/o Sequence Compression30.984.1588.9838.760.023
w/o per Vertex Quantization23.575.4998.3574.940.050
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", + "image_path": "0500b44c57dd1a58136123af0b3f1b93b7cfad5e8dead5b38ee8706f0c22e0c7.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 546, + 287, + 589 + ], + "type": "table_caption", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 48, + 547, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 48, + 547, + 287, + 556 + ], + "type": "text", + "content": "Table 3. Ablations of our design choices on the Chair category of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 559, + 286, + 567 + ], + "spans": [ + { + "bbox": [ + 49, + 559, + 286, + 567 + ], + "type": "text", + "content": "the ShapeNet [5] dataset. As highlighted by the drop in perfor-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 570, + 286, + 578 + ], + "spans": [ + { + "bbox": [ + 49, + 570, + 286, + 578 + ], + "type": "text", + "content": "mance by removing any of them, each of these contribute to the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 580, + 97, + 589 + ], + "spans": [ + { + "bbox": [ + 49, + 580, + 97, + 589 + ], + "type": "text", + "content": "final method.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 602, + 287, + 639 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 49, + 643, + 286, + 652 + ], + "spans": [ + { + "bbox": [ + 49, + 643, + 286, + 652 + ], + "type": "text", + "content": "Shape Novelty Analysis. We investigate whether our", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 655, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 49, + 655, + 286, + 664 + ], + "type": "text", + "content": "method can generate novel shapes that extend beyond the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 667, + 286, + 677 + ], + "spans": [ + { + "bbox": [ + 49, + 667, + 286, + 677 + ], + "type": "text", + "content": "training dataset, ensuring the model is not merely retriev-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 679, + 285, + 689 + ], + "spans": [ + { + "bbox": [ + 49, + 679, + 285, + 689 + ], + "type": "text", + "content": "ing existing shapes. Following the methodology in pre-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 691, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 49, + 691, + 286, + 700 + ], + "type": "text", + "content": "vious studies [13, 24], we generate 500 shapes using our", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 703, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 703, + 286, + 712 + ], + "type": "text", + "content": "model. For each generated shape, we identify the top three", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 607, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 308, + 607, + 545, + 616 + ], + "type": "text", + "content": "nearest neighbors from the training set based on Chamfer", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 617, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 307, + 617, + 545, + 628 + ], + "type": "text", + "content": "Distance (CD). To ensure a fair distance computation, ac-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 630, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 307, + 630, + 545, + 639 + ], + "type": "text", + "content": "counting for potential discrepancies due to scale or shift in", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 642, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 308, + 642, + 545, + 651 + ], + "type": "text", + "content": "the augmented generations, we normalize all generated and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 654, + 471, + 664 + ], + "spans": [ + { + "bbox": [ + 307, + 654, + 471, + 664 + ], + "type": "text", + "content": "train shapes to be centered within [0, 1]3.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "chart", + "bbox": [ + 305, + 68, + 545, + 319 + ], + "blocks": [ + { + "bbox": [ + 305, + 68, + 545, + 319 + ], + "type": "chart_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 68, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 68, + 545, + 319 + ], + "type": "chart", + "content": "| Chamfer Distance (x10^3) | Proportion of Generated Shapes |\n| --- | --- |\n| 0 | ~0.5 |\n| 1 | ~4.5 |\n| 2 | ~6.5 |\n| 3 | ~3.5 |\n| 4 | ~2.5 |\n| 5 | ~1.5 |\n| 6 | ~1.5 |\n| 7 | ~1.5 |\n| 8 | ~1.0 |\n| 9 | ~0.5 |\n| 10+ | ~4.5 |", + "image_path": "c529395af6d980051ddecada4916f283df5a930f3e3dfe3b5e19f6ee6a2f96a9.jpg" + } + ] + } + ], + "index": 8 + } + ], + "index": 8, + "sub_type": "bar" + }, + { + "type": "image", + "bbox": [ + 306, + 418, + 542, + 567 + ], + "blocks": [ + { + "bbox": [ + 305, + 326, + 547, + 415 + ], + "type": "image_caption", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 308, + 328, + 544, + 336 + ], + "spans": [ + { + "bbox": [ + 308, + 328, + 544, + 336 + ], + "type": "text", + "content": "Figure 8. Shape novelty analysis on ShapeNet [5] chair category.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 338, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 307, + 338, + 545, + 347 + ], + "type": "text", + "content": "We show the 3 nearest neighbors in terms of Chamfer Distance", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 350, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 308, + 350, + 545, + 358 + ], + "type": "text", + "content": "(CD) for a generated shape (top). We also plot the distribution of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 361, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 307, + 361, + 545, + 369 + ], + "type": "text", + "content": "500 generated chair samples from our method and their closeness", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 372, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 307, + 372, + 545, + 380 + ], + "type": "text", + "content": "to training distribution. Our method can generate shapes that are", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 383, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 307, + 383, + 545, + 392 + ], + "type": "text", + "content": "similar (low CD) as well as different (high CD) from the training", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 306, + 392, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 392, + 545, + 403 + ], + "type": "text", + "content": "distribution, with shapes at the 50th percentile looking different", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 405, + 395, + 413 + ], + "spans": [ + { + "bbox": [ + 308, + 405, + 395, + 413 + ], + "type": "text", + "content": "from closest train shape.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 306, + 418, + 542, + 567 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 418, + 542, + 567 + ], + "spans": [ + { + "bbox": [ + 306, + 418, + 542, + 567 + ], + "type": "image", + "content": "3D model of wooden furniture with various shapes and layouts, including chairs, tables, and blocks (no text or symbols)", + "image_path": "5b3a33b4221fb57854918e5b77130294ccf40f3adc775ccf038ce130eb125645.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 574, + 545, + 597 + ], + "type": "image_caption", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 308, + 575, + 545, + 584 + ], + "spans": [ + { + "bbox": [ + 308, + 575, + 545, + 584 + ], + "type": "text", + "content": "Figure 9. Given a partial mesh, our method can infer multiple", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 586, + 408, + 595 + ], + "spans": [ + { + "bbox": [ + 308, + 586, + 408, + 595 + ], + "type": "text", + "content": "possible shape completions.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 10, + "sub_type": "natural_image" + }, + { + "bbox": [ + 305, + 605, + 547, + 665 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 305, + 666, + 547, + 714 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 319, + 666, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 319, + 666, + 545, + 677 + ], + "type": "text", + "content": "Fig. 8 displays the most similar shapes from the train", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 679, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 307, + 679, + 545, + 689 + ], + "type": "text", + "content": "set corresponding to a sample generated by our model. We", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 692, + 544, + 700 + ], + "spans": [ + { + "bbox": [ + 308, + 692, + 544, + 700 + ], + "type": "text", + "content": "conduct a detailed analysis of the shape similarity distri-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 703, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 307, + 703, + 545, + 712 + ], + "type": "text", + "content": "bution between the retrieved and generated shapes on the", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 49, + 74, + 286, + 83 + ], + "spans": [ + { + "bbox": [ + 49, + 74, + 286, + 83 + ], + "type": "text", + "content": "Chair category in Fig. 8. The CD distribution reveals that", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 85, + 286, + 96 + ], + "spans": [ + { + "bbox": [ + 48, + 85, + 286, + 96 + ], + "type": "text", + "content": "our method not only covers shapes in the training set, in-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 98, + 286, + 108 + ], + "spans": [ + { + "bbox": [ + 48, + 98, + 286, + 108 + ], + "type": "text", + "content": "dicated by low CD values, but also successfully generates", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 110, + 285, + 119 + ], + "spans": [ + { + "bbox": [ + 49, + 110, + 285, + 119 + ], + "type": "text", + "content": "novel and realistic-looking shapes, indicated by high CD", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 122, + 286, + 131 + ], + "spans": [ + { + "bbox": [ + 49, + 122, + 286, + 131 + ], + "type": "text", + "content": "values. In the supplemental, we present further analysis of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 133, + 286, + 144 + ], + "spans": [ + { + "bbox": [ + 48, + 133, + 286, + 144 + ], + "type": "text", + "content": "the novelty of all meshes generated by our method, which", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 145, + 205, + 156 + ], + "spans": [ + { + "bbox": [ + 49, + 145, + 205, + 156 + ], + "type": "text", + "content": "are featured in the figures of this paper.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 46, + 159, + 288, + 208 + ], + "type": "text", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 48, + 160, + 286, + 171 + ], + "spans": [ + { + "bbox": [ + 48, + 160, + 286, + 171 + ], + "type": "text", + "content": "Shape Completion. Our model can infer multiple possible", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 173, + 285, + 182 + ], + "spans": [ + { + "bbox": [ + 49, + 173, + 285, + 182 + ], + "type": "text", + "content": "completions for a given partial shape, leveraging its proba-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 184, + 287, + 194 + ], + "spans": [ + { + "bbox": [ + 48, + 184, + 287, + 194 + ], + "type": "text", + "content": "bilistic nature to generate diverse shape hypotheses. Fig. 9", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 198, + 253, + 206 + ], + "spans": [ + { + "bbox": [ + 49, + 198, + 253, + 206 + ], + "type": "text", + "content": "illustrates examples of chair and table completions.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 47, + 223, + 122, + 233 + ], + "type": "title", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 48, + 223, + 121, + 234 + ], + "spans": [ + { + "bbox": [ + 48, + 223, + 121, + 234 + ], + "type": "text", + "content": "4.2.1 Ablations", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 46, + 242, + 288, + 278 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 49, + 243, + 286, + 253 + ], + "spans": [ + { + "bbox": [ + 49, + 243, + 286, + 253 + ], + "type": "text", + "content": "In Tab. 3, we show a set of ablations on the task of uncondi-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 256, + 286, + 265 + ], + "spans": [ + { + "bbox": [ + 49, + 256, + 286, + 265 + ], + "type": "text", + "content": "tional mesh generation on ShapeNet Chair category. 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We then choose, for each", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 323, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 49, + 323, + 287, + 332 + ], + "type": "text", + "content": "original shape, the decimated version with the Hausdorff", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 334, + 285, + 346 + ], + "spans": [ + { + "bbox": [ + 49, + 335, + 249, + 344 + ], + "type": "text", + "content": "distance closest to, but below, a pre-set threshold", + "score": 1.0 + }, + { + "bbox": [ + 251, + 334, + 285, + 346 + ], + "type": "inline_equation", + "content": "\\delta _ { \\mathrm { h a u s d o r f f } } .", + "score": 0.6928 + } + ] + }, + { + "bbox": [ + 48, + 346, + 286, + 356 + ], + "spans": [ + { + "bbox": [ + 48, + 346, + 286, + 356 + ], + "type": "text", + "content": "Shapes with more than 800 faces are excluded, resulting in a", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 358, + 285, + 368 + ], + "spans": [ + { + "bbox": [ + 49, + 358, + 285, + 368 + ], + "type": "text", + "content": "final count of 28980 shapes across all categories. The Chair,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 370, + 286, + 380 + ], + "spans": [ + { + "bbox": [ + 49, + 370, + 286, + 380 + ], + "type": "text", + "content": "Table, Bench, and Lamp categories are further divided into", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 382, + 286, + 392 + ], + "spans": [ + { + "bbox": [ + 48, + 382, + 286, + 392 + ], + "type": "text", + "content": "a 9:1 train-test split. All shapes from rest of the categories", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 396, + 286, + 403 + ], + "spans": [ + { + "bbox": [ + 49, + 396, + 286, + 403 + ], + "type": "text", + "content": "are used for pretraining phase, while only the training subset", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 407, + 285, + 415 + ], + "spans": [ + { + "bbox": [ + 49, + 407, + 285, + 415 + ], + "type": "text", + "content": "from specific categories is used for pretraining and finetun-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 418, + 286, + 428 + ], + "spans": [ + { + "bbox": [ + 49, + 418, + 286, + 428 + ], + "type": "text", + "content": "ing. 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Post-scaling, meshes are resized to keep", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 506, + 285, + 516 + ], + "spans": [ + { + "bbox": [ + 48, + 506, + 285, + 516 + ], + "type": "text", + "content": "the longest side at unit length. Additionally, jitter-shift aug-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 518, + 286, + 528 + ], + "spans": [ + { + "bbox": [ + 48, + 518, + 286, + 528 + ], + "type": "text", + "content": "mentation in the range of [−0.1, 0.1] is used, adjusted to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 530, + 285, + 539 + ], + "spans": [ + { + "bbox": [ + 49, + 530, + 285, + 539 + ], + "type": "text", + "content": "maintain the mesh within the unit bounding box around the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 542, + 286, + 552 + ], + "spans": [ + { + "bbox": [ + 49, + 542, + 286, + 552 + ], + "type": "text", + "content": "origin. 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The encoder comprises a series of SAGE-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 655, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 49, + 655, + 286, + 665 + ], + "type": "text", + "content": "Conv [20] graph convolution layers, processing the mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 666, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 48, + 666, + 287, + 677 + ], + "type": "text", + "content": "in the form of a face graph. 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Fur-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 322, + 367, + 331 + ], + "spans": [ + { + "bbox": [ + 308, + 322, + 367, + 331 + ], + "type": "text", + "content": "ther, we define", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 390, + 332, + 545, + 363 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 390, + 332, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 390, + 332, + 545, + 363 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {z}} ^ {(d)} = \\sum_ {1} ^ {d} \\mathbf {e} (t ^ {d}) \\tag {9}", + "image_path": "2211427a900f3cc85d32b0c0e542da3e1d541c41761a79d2b19bc6a2838d11a7.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 366, + 547, + 427 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 308, + 366, + 544, + 378 + ], + "spans": [ + { + "bbox": [ + 308, + 369, + 511, + 378 + ], + "type": "text", + "content": "as the partial sum of up to d code embeddings, and", + "score": 1.0 + }, + { + "bbox": [ + 512, + 366, + 544, + 377 + ], + "type": "inline_equation", + "content": "\\hat { \\mathbf { z } } = \\hat { \\mathbf { z } } ^ { D }", + "score": 0.9094 + } + ] + }, + { + "bbox": [ + 307, + 380, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 307, + 380, + 545, + 390 + ], + "type": "text", + "content": "is the quantized vector of z. 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To align its", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 643, + 286, + 653 + ], + "spans": [ + { + "bbox": [ + 48, + 643, + 286, + 653 + ], + "type": "text", + "content": "architecture with our method, we employ the same GPT2-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 654, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 48, + 654, + 286, + 665 + ], + "type": "text", + "content": "medium architecture for the vertex model in Polygen. Ad-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 667, + 286, + 677 + ], + "spans": [ + { + "bbox": [ + 49, + 667, + 286, + 677 + ], + "type": "text", + "content": "ditionally, mirroring our approach, Polygen undergoes pre-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 679, + 286, + 689 + ], + "spans": [ + { + "bbox": [ + 48, + 679, + 286, + 689 + ], + "type": "text", + "content": "training on all categories and is finetuned for each evalu-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 692, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 49, + 692, + 286, + 700 + ], + "type": "text", + "content": "ated category, applying the same train-time augmentations", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 704, + 139, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 704, + 139, + 712 + ], + "type": "text", + "content": "as used in our method.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 306, + 499, + 419, + 514 + ], + "type": "title", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 308, + 500, + 418, + 514 + ], + "spans": [ + { + "bbox": [ + 308, + 500, + 418, + 514 + ], + "type": "text", + "content": "C. 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After the samples are pre-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 632, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 307, + 632, + 545, + 641 + ], + "type": "text", + "content": "pared, we ask the users to pick the sample which they pre-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 644, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 307, + 644, + 545, + 652 + ], + "type": "text", + "content": "fer more based on the question. To avoid biases in this user", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 656, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 308, + 656, + 545, + 665 + ], + "type": "text", + "content": "study, we shuffle the pairs so that there is no positional hint", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 666, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 307, + 666, + 545, + 677 + ], + "type": "text", + "content": "to our method. We also show a collection of ground-truth", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 680, + 544, + 689 + ], + "spans": [ + { + "bbox": [ + 308, + 680, + 544, + 689 + ], + "type": "text", + "content": "meshes to the user for them to get an idea of the real distri-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 692, + 544, + 700 + ], + "spans": [ + { + "bbox": [ + 308, + 692, + 544, + 700 + ], + "type": "text", + "content": "bution. 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Shape novelty analysis on ShapeNet [5] bench and lamp category for shapes generated by our method shown in main paper. We", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 357, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 48, + 357, + 545, + 367 + ], + "type": "text", + "content": "show the 3 nearest neighbors in terms of Chamfer Distance (CD) for a generated shape. Shapes are scaled to a unit length along all axes to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 369, + 257, + 376 + ], + "spans": [ + { + "bbox": [ + 49, + 369, + 257, + 376 + ], + "type": "text", + "content": "account for augmented generations before computing CD.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 1, + "sub_type": "text_image" + }, + { + "type": "image", + "bbox": [ + 48, + 398, + 286, + 524 + ], + "blocks": [ + { + "bbox": [ + 48, + 398, + 286, + 524 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 398, + 286, + 524 + ], + "spans": [ + { + "bbox": [ + 48, + 398, + 286, + 524 + ], + "type": "image", + "content": "```mermaid\ngraph LR\n InputMesh[\"Input Mesh\"] -->|\"F| x196\"| GraphConvEncoder[\"Graph Conv Encoder\"]\n GraphConvEncoder -->|\"F| x576\"| ResidualQuantizationModule[\"Residual Face Quantization Module\"]\n SequenceOfFaces[\"Sequence Of Faces\"] -->|\"F| x576\"| ResNet34Decoder[\"ResNet34 Decoder\"]\n ResNet34Decoder --> ReconstructedMesh[\"Reconstructed Mesh\"]\n```", + "image_path": "4ec5ee7755bd6f8b5c1ddbe9d84366f8031e24b91ec1d239bef0eaaa83da18f7.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 533, + 287, + 601 + ], + "type": "image_caption", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 49, + 535, + 286, + 544 + ], + "spans": [ + { + "bbox": [ + 49, + 535, + 286, + 544 + ], + "type": "text", + "content": "Figure 14. Our encoder-decoder network features an encoder with", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 546, + 286, + 555 + ], + "spans": [ + { + "bbox": [ + 48, + 546, + 286, + 555 + ], + "type": "text", + "content": "SAGEConv [20] layers processing mesh faces as a graph. Each", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 557, + 286, + 566 + ], + "spans": [ + { + "bbox": [ + 49, + 557, + 286, + 566 + ], + "type": "text", + "content": "node inputs positionally encoded face triangle coordinates, area,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 568, + 286, + 577 + ], + "spans": [ + { + "bbox": [ + 49, + 568, + 286, + 577 + ], + "type": "text", + "content": "edge angles, and normal. 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Shape Novelty Analysis", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 49, + 643, + 286, + 653 + ], + "spans": [ + { + "bbox": [ + 49, + 643, + 286, + 653 + ], + "type": "text", + "content": "Fig. 12 and 13 displays the top-3 most similar shapes from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 655, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 49, + 655, + 286, + 665 + ], + "type": "text", + "content": "the train set corresponding to all samples used in the main", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 668, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 48, + 668, + 287, + 676 + ], + "type": "text", + "content": "paper that were generated by our model. These nearest", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 679, + 286, + 689 + ], + "spans": [ + { + "bbox": [ + 49, + 679, + 286, + 689 + ], + "type": "text", + "content": "neighbor shapes are identified based on Chamfer Distance", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 691, + 286, + 701 + ], + "spans": [ + { + "bbox": [ + 49, + 691, + 286, + 701 + ], + "type": "text", + "content": "(CD). 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Additional Results", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 306, + 473, + 545, + 508 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 307, + 474, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 307, + 474, + 545, + 484 + ], + "type": "text", + "content": "Metrics. 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Shape novelty analysis on ShapeNet [5] bench and lamp category for shapes generated by our method shown in main paper. We", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 357, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 48, + 357, + 545, + 367 + ], + "type": "text", + "content": "show the 3 nearest neighbors in terms of Chamfer Distance (CD) for a generated shape. Shapes are scaled to a unit length along all axes to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 369, + 257, + 376 + ], + "spans": [ + { + "bbox": [ + 49, + 369, + 257, + 376 + ], + "type": "text", + "content": "account for augmented generations before computing CD.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 1, + "sub_type": "text_image" + }, + { + "type": "image", + "bbox": [ + 48, + 398, + 286, + 524 + ], + "blocks": [ + { + "bbox": [ + 48, + 398, + 286, + 524 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 398, + 286, + 524 + ], + "spans": [ + { + "bbox": [ + 48, + 398, + 286, + 524 + ], + "type": "image", + "content": "```mermaid\ngraph LR\n InputMesh[\"Input Mesh\"] -->|\"F| x196\"| GraphConvEncoder[\"Graph Conv Encoder\"]\n GraphConvEncoder -->|\"F| x576\"| ResidualQuantizationModule[\"Residual Face Quantization Module\"]\n SequenceOfFaces[\"Sequence Of Faces\"] -->|\"F| x576\"| ResNet34Decoder[\"ResNet34 Decoder\"]\n ResNet34Decoder --> ReconstructedMesh[\"Reconstructed Mesh\"]\n```", + "image_path": "4ec5ee7755bd6f8b5c1ddbe9d84366f8031e24b91ec1d239bef0eaaa83da18f7.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 533, + 287, + 601 + ], + "type": "image_caption", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 49, + 535, + 286, + 544 + ], + "spans": [ + { + "bbox": [ + 49, + 535, + 286, + 544 + ], + "type": "text", + "content": "Figure 14. Our encoder-decoder network features an encoder with", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 546, + 286, + 555 + ], + "spans": [ + { + "bbox": [ + 48, + 546, + 286, + 555 + ], + "type": "text", + "content": "SAGEConv [20] layers processing mesh faces as a graph. Each", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 557, + 286, + 566 + ], + "spans": [ + { + "bbox": [ + 49, + 557, + 286, + 566 + ], + "type": "text", + "content": "node inputs positionally encoded face triangle coordinates, area,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 568, + 286, + 577 + ], + "spans": [ + { + "bbox": [ + 49, + 568, + 286, + 577 + ], + "type": "text", + "content": "edge angles, and normal. 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User study interface. We show users a set of random", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 336, + 286, + 345 + ], + "spans": [ + { + "bbox": [ + 49, + 336, + 286, + 345 + ], + "type": "text", + "content": "ground-truth shapes for a category and then ask users for shape", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 347, + 285, + 356 + ], + "spans": [ + { + "bbox": [ + 49, + 347, + 285, + 356 + ], + "type": "text", + "content": "quality and triangulation preference among meshed generated by", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 358, + 98, + 367 + ], + "spans": [ + { + "bbox": [ + 48, + 358, + 98, + 367 + ], + "type": "text", + "content": "two methods.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 1, + "sub_type": "text_image" + }, + { + "type": "table", + "bbox": [ + 50, + 380, + 287, + 495 + ], + "blocks": [ + { + "bbox": [ + 50, + 380, + 287, + 495 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 380, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 50, + 380, + 287, + 495 + ], + "type": "table", + "html": "
VariantTriangle Accuracy (%) ↑Cross-Entropy ↓
w/o Positional Encoding79.330.2484
w/o Output Discretization22.030.5705
w/o Residual Quantization1.294.6679
w/o per Vertex Quantization98.640.1413
w/ PointNet Encoder88.730.1896
w/ GAT [60] Encoder86.140.2015
w/ EdgeConv [61] Encoder91.230.1702
w/ ResNet19 Decoder96.290.1492
w/ PointNet Decoder95.470.1528
MeshGPT98.490.1473
", + "image_path": "49f0a0b67bf0922c8a8f7cf55a35efdf69ee6af7dd796a2f5d42c77189f570d4.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 504, + 287, + 526 + ], + "type": "table_caption", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 48, + 505, + 286, + 514 + ], + "spans": [ + { + "bbox": [ + 48, + 505, + 286, + 514 + ], + "type": "text", + "content": "Table 4. Ablations of our design choices for the encoder-decoder", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 517, + 260, + 525 + ], + "spans": [ + { + "bbox": [ + 49, + 517, + 260, + 525 + ], + "type": "text", + "content": "network on the Chair category of the ShapeNet [5] dataset.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 539, + 287, + 610 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 49, + 540, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 49, + 540, + 287, + 550 + ], + "type": "text", + "content": "We use a Chamfer Distance (CD) distance measure", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 550, + 286, + 563 + ], + "spans": [ + { + "bbox": [ + 48, + 550, + 86, + 563 + ], + "type": "inline_equation", + "content": "D ( X , Y )", + "score": 0.4963 + }, + { + "bbox": [ + 89, + 552, + 286, + 562 + ], + "type": "text", + "content": "for computing these metrics in 3D. To evaluate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 564, + 286, + 574 + ], + "spans": [ + { + "bbox": [ + 49, + 564, + 286, + 574 + ], + "type": "text", + "content": "these point-based measures, we sample 2048 points ran-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 577, + 285, + 586 + ], + "spans": [ + { + "bbox": [ + 49, + 577, + 285, + 586 + ], + "type": "text", + "content": "domly from all baseline outputs; and use 6000, 1200, 1000,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 588, + 285, + 597 + ], + "spans": [ + { + "bbox": [ + 49, + 588, + 285, + 597 + ], + "type": "text", + "content": "8000 generated shapes from chair, bench, lamp and table", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 601, + 93, + 609 + ], + "spans": [ + { + "bbox": [ + 49, + 601, + 93, + 609 + ], + "type": "text", + "content": "categories.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 47, + 614, + 287, + 651 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 50, + 616, + 286, + 625 + ], + "spans": [ + { + "bbox": [ + 50, + 616, + 286, + 625 + ], + "type": "text", + "content": "Qualitative Results. Fig. 11 shows more unconditional", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 628, + 286, + 638 + ], + "spans": [ + { + "bbox": [ + 49, + 628, + 286, + 638 + ], + "type": "text", + "content": "generations from our model across different ShapeNet cat-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 639, + 81, + 649 + ], + "spans": [ + { + "bbox": [ + 48, + 639, + 81, + 649 + ], + "type": "text", + "content": "egories.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 47, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 49, + 655, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 49, + 655, + 287, + 664 + ], + "type": "text", + "content": "Encoder-Decoder Ablations. In Tab. 4, we show a set of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 667, + 286, + 676 + ], + "spans": [ + { + "bbox": [ + 49, + 667, + 286, + 676 + ], + "type": "text", + "content": "ablations on the design choice for our encoder-decoder net-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 680, + 285, + 689 + ], + "spans": [ + { + "bbox": [ + 49, + 680, + 285, + 689 + ], + "type": "text", + "content": "work used for learning the triangle embeddings. We mea-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 692, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 49, + 692, + 286, + 700 + ], + "type": "text", + "content": "sure the performance in terms of triangle accuracy, which", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 704, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 704, + 287, + 712 + ], + "type": "text", + "content": "measures average accuracy with which all 9 coordinates of", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 307, + 73, + 545, + 84 + ], + "spans": [ + { + "bbox": [ + 307, + 73, + 545, + 84 + ], + "type": "text", + "content": "faces are correctly predicted, and the cross-entropy loss on", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 86, + 353, + 95 + ], + "spans": [ + { + "bbox": [ + 307, + 86, + 353, + 95 + ], + "type": "text", + "content": "the test set.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "image", + "bbox": [ + 306, + 102, + 547, + 220 + ], + "blocks": [ + { + "bbox": [ + 306, + 102, + 547, + 220 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 102, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 306, + 102, + 547, + 220 + ], + "type": "image", + "content": "Sequence of Faces = (F₁, F₂) = ((V₁, V₂, V₃), (V₂, V₄, V₃))\nIf 6 tokens are assigned per face:\nSequence: (t₁¹, t₁², t₁³, t₁⁴, t₁⁵, t₁⁶, t₂¹, t₂², t₂³, t₂⁴, t₂⁵, t₂⁶)\nIf 2 tokens are assigned per vertex:\nSequence: (t₁¹, t₁², t₁³, t₁⁴, t₁⁵, t₁⁶, t₂¹, t₂², t₂³, t₂⁴, t₂⁵, t₂⁶)\nRepetition of tokens", + "image_path": "93ed53b8c4f1a77bc0a632004090c5a0533351b6ab70863f6b98e63b4c7c521a.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 228, + 546, + 327 + ], + "type": "image_caption", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 307, + 229, + 545, + 237 + ], + "spans": [ + { + "bbox": [ + 307, + 229, + 545, + 237 + ], + "type": "text", + "content": "Figure 16. The effectiveness of per-vertex quantization over per-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 240, + 545, + 248 + ], + "spans": [ + { + "bbox": [ + 307, + 240, + 545, + 248 + ], + "type": "text", + "content": "face quantization can be understood through an example where", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 251, + 545, + 259 + ], + "spans": [ + { + "bbox": [ + 307, + 251, + 545, + 259 + ], + "type": "text", + "content": "two faces share an edge as shown above. With per-face tokeniza-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 262, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 308, + 262, + 545, + 270 + ], + "type": "text", + "content": "tion assigning 6 tokens per face, the sequence yields 12 unique", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 273, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 308, + 273, + 545, + 281 + ], + "type": "text", + "content": "tokens. In contrast, per-vertex tokenization leads to repeated to-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 284, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 307, + 284, + 545, + 292 + ], + "type": "text", + "content": "kens in the sequence due to shared vertices between faces. This", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 295, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 307, + 295, + 545, + 304 + ], + "type": "text", + "content": "repetition makes the sequence easier for the transformer to learn", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 306, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 308, + 306, + 545, + 314 + ], + "type": "text", + "content": "compared to a wholly unique sequence per face, especially when", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 316, + 434, + 325 + ], + "spans": [ + { + "bbox": [ + 307, + 316, + 434, + 325 + ], + "type": "text", + "content": "both sequences are of equal length.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 9, + "sub_type": "text_image" + }, + { + "bbox": [ + 305, + 341, + 546, + 497 + ], + "type": "text", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 320, + 343, + 545, + 351 + ], + "spans": [ + { + "bbox": [ + 320, + 343, + 545, + 351 + ], + "type": "text", + "content": "We evaluate the effect of various choices – how much", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 354, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 307, + 354, + 545, + 365 + ], + "type": "text", + "content": "does the positional encoding at input help, effect of using", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 366, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 307, + 366, + 545, + 376 + ], + "type": "text", + "content": "continuous predictions instead of discrete as outputs, us-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 379, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 307, + 379, + 545, + 388 + ], + "type": "text", + "content": "ing vector quantization (1 token per face) instead of resid-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 391, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 307, + 391, + 545, + 399 + ], + "type": "text", + "content": "ual quantization (D tokens per face), encoder architecture", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 403, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 307, + 403, + 545, + 412 + ], + "type": "text", + "content": "as a point encoder, or different graph convolution opera-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 415, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 307, + 415, + 545, + 423 + ], + "type": "text", + "content": "tors, and decoder architecture as either ResNet19 or Point-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 427, + 545, + 435 + ], + "spans": [ + { + "bbox": [ + 307, + 427, + 545, + 435 + ], + "type": "text", + "content": "Net decoder. Note that even though for encoder-decoder re-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 438, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 307, + 438, + 545, + 448 + ], + "type": "text", + "content": "construction, ‘w/o per Vertex Quantization’ performs best,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 451, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 308, + 451, + 545, + 459 + ], + "type": "text", + "content": "this variant works significantly worse than with per Vertex", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 463, + 544, + 472 + ], + "spans": [ + { + "bbox": [ + 308, + 463, + 544, + 472 + ], + "type": "text", + "content": "Quantization, as shown in the main paper. Fig. 16 describes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 475, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 308, + 475, + 545, + 483 + ], + "type": "text", + "content": "an intuition of why the embeddings from this variant are", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 487, + 413, + 495 + ], + "spans": [ + { + "bbox": [ + 308, + 487, + 413, + 495 + ], + "type": "text", + "content": "more transformer friendly.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 50, + 72, + 84, + 77 + ], + "type": "header", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 51, + 73, + 83, + 77 + ], + "spans": [ + { + "bbox": [ + 51, + 73, + 83, + 77 + ], + "type": "text", + "content": "MeshGPT User Study", + "score": 0.997 + } + ] + } + ] + }, + { + "bbox": [ + 291, + 732, + 303, + 742 + ], + "type": "page_number", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 291, + 732, + 303, + 743 + ], + "spans": [ + { + "bbox": [ + 291, + 732, + 303, + 743 + ], + "type": "text", + "content": "16", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 15, + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 79, + 286, + 314 + ], + "blocks": [ + { + "bbox": [ + 50, + 79, + 286, + 314 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 79, + 286, + 314 + ], + "spans": [ + { + "bbox": [ + 50, + 79, + 286, + 314 + ], + "type": "image", + "content": "I filter your name\nwere are some artist designed mesh of the category chair:\nPlease answer the following questions keeping these in mind.\n• which of the objects is a better quality mesh for this category?\n• which of the objects better matches the quality of artist meshes in this category!", + "image_path": "9c8f17f2ed164e56329aa2345718e115db7f4d94e1cb5a94b39d1e155c6a929e.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 323, + 287, + 367 + ], + "type": "image_caption", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 49, + 325, + 286, + 334 + ], + "spans": [ + { + "bbox": [ + 49, + 325, + 286, + 334 + ], + "type": "text", + "content": "Figure 15. User study interface. We show users a set of random", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 336, + 286, + 345 + ], + "spans": [ + { + "bbox": [ + 49, + 336, + 286, + 345 + ], + "type": "text", + "content": "ground-truth shapes for a category and then ask users for shape", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 347, + 285, + 356 + ], + "spans": [ + { + "bbox": [ + 49, + 347, + 285, + 356 + ], + "type": "text", + "content": "quality and triangulation preference among meshed generated by", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 358, + 98, + 367 + ], + "spans": [ + { + "bbox": [ + 48, + 358, + 98, + 367 + ], + "type": "text", + "content": "two methods.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 1, + "sub_type": "text_image" + }, + { + "type": "table", + "bbox": [ + 50, + 380, + 287, + 495 + ], + "blocks": [ + { + "bbox": [ + 50, + 380, + 287, + 495 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 380, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 50, + 380, + 287, + 495 + ], + "type": "table", + "html": "
VariantTriangle Accuracy (%) ↑Cross-Entropy ↓
w/o Positional Encoding79.330.2484
w/o Output Discretization22.030.5705
w/o Residual Quantization1.294.6679
w/o per Vertex Quantization98.640.1413
w/ PointNet Encoder88.730.1896
w/ GAT [60] Encoder86.140.2015
w/ EdgeConv [61] Encoder91.230.1702
w/ ResNet19 Decoder96.290.1492
w/ PointNet Decoder95.470.1528
MeshGPT98.490.1473
", + "image_path": "49f0a0b67bf0922c8a8f7cf55a35efdf69ee6af7dd796a2f5d42c77189f570d4.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 504, + 287, + 526 + ], + "type": "table_caption", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 48, + 505, + 286, + 514 + ], + "spans": [ + { + "bbox": [ + 48, + 505, + 286, + 514 + ], + "type": "text", + "content": "Table 4. Ablations of our design choices for the encoder-decoder", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 517, + 260, + 525 + ], + "spans": [ + { + "bbox": [ + 49, + 517, + 260, + 525 + ], + "type": "text", + "content": "network on the Chair category of the ShapeNet [5] dataset.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 539, + 287, + 610 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 49, + 540, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 49, + 540, + 287, + 550 + ], + "type": "text", + "content": "We use a Chamfer Distance (CD) distance measure", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 550, + 286, + 563 + ], + "spans": [ + { + "bbox": [ + 48, + 550, + 86, + 563 + ], + "type": "inline_equation", + "content": "D ( X , Y )", + "score": 0.4963 + }, + { + "bbox": [ + 89, + 552, + 286, + 562 + ], + "type": "text", + "content": "for computing these metrics in 3D. To evaluate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 564, + 286, + 574 + ], + "spans": [ + { + "bbox": [ + 49, + 564, + 286, + 574 + ], + "type": "text", + "content": "these point-based measures, we sample 2048 points ran-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 577, + 285, + 586 + ], + "spans": [ + { + "bbox": [ + 49, + 577, + 285, + 586 + ], + "type": "text", + "content": "domly from all baseline outputs; and use 6000, 1200, 1000,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 588, + 285, + 597 + ], + "spans": [ + { + "bbox": [ + 49, + 588, + 285, + 597 + ], + "type": "text", + "content": "8000 generated shapes from chair, bench, lamp and table", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 601, + 93, + 609 + ], + "spans": [ + { + "bbox": [ + 49, + 601, + 93, + 609 + ], + "type": "text", + "content": "categories.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 47, + 614, + 287, + 651 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 50, + 616, + 286, + 625 + ], + "spans": [ + { + "bbox": [ + 50, + 616, + 286, + 625 + ], + "type": "text", + "content": "Qualitative Results. Fig. 11 shows more unconditional", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 628, + 286, + 638 + ], + "spans": [ + { + "bbox": [ + 49, + 628, + 286, + 638 + ], + "type": "text", + "content": "generations from our model across different ShapeNet cat-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 639, + 81, + 649 + ], + "spans": [ + { + "bbox": [ + 48, + 639, + 81, + 649 + ], + "type": "text", + "content": "egories.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 47, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 49, + 655, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 49, + 655, + 287, + 664 + ], + "type": "text", + "content": "Encoder-Decoder Ablations. In Tab. 4, we show a set of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 667, + 286, + 676 + ], + "spans": [ + { + "bbox": [ + 49, + 667, + 286, + 676 + ], + "type": "text", + "content": "ablations on the design choice for our encoder-decoder net-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 680, + 285, + 689 + ], + "spans": [ + { + "bbox": [ + 49, + 680, + 285, + 689 + ], + "type": "text", + "content": "work used for learning the triangle embeddings. We mea-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 49, + 692, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 49, + 692, + 286, + 700 + ], + "type": "text", + "content": "sure the performance in terms of triangle accuracy, which", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 48, + 704, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 704, + 287, + 712 + ], + "type": "text", + "content": "measures average accuracy with which all 9 coordinates of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 73, + 545, + 84 + ], + "spans": [ + { + "bbox": [ + 307, + 73, + 545, + 84 + ], + "type": "text", + "content": "faces are correctly predicted, and the cross-entropy loss on", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 86, + 353, + 95 + ], + "spans": [ + { + "bbox": [ + 307, + 86, + 353, + 95 + ], + "type": "text", + "content": "the test set.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "type": "image", + "bbox": [ + 306, + 102, + 547, + 220 + ], + "blocks": [ + { + "bbox": [ + 306, + 102, + 547, + 220 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 102, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 306, + 102, + 547, + 220 + ], + "type": "image", + "content": "Sequence of Faces = (F₁, F₂) = ((V₁, V₂, V₃), (V₂, V₄, V₃))\nIf 6 tokens are assigned per face:\nSequence: (t₁¹, t₁², t₁³, t₁⁴, t₁⁵, t₁⁶, t₂¹, t₂², t₂³, t₂⁴, t₂⁵, t₂⁶)\nIf 2 tokens are assigned per vertex:\nSequence: (t₁¹, t₁², t₁³, t₁⁴, t₁⁵, t₁⁶, t₂¹, t₂², t₂³, t₂⁴, t₂⁵, t₂⁶)\nRepetition of tokens", + "image_path": "93ed53b8c4f1a77bc0a632004090c5a0533351b6ab70863f6b98e63b4c7c521a.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 228, + 546, + 327 + ], + "type": "image_caption", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 307, + 229, + 545, + 237 + ], + "spans": [ + { + "bbox": [ + 307, + 229, + 545, + 237 + ], + "type": "text", + "content": "Figure 16. The effectiveness of per-vertex quantization over per-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 240, + 545, + 248 + ], + "spans": [ + { + "bbox": [ + 307, + 240, + 545, + 248 + ], + "type": "text", + "content": "face quantization can be understood through an example where", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 251, + 545, + 259 + ], + "spans": [ + { + "bbox": [ + 307, + 251, + 545, + 259 + ], + "type": "text", + "content": "two faces share an edge as shown above. With per-face tokeniza-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 262, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 308, + 262, + 545, + 270 + ], + "type": "text", + "content": "tion assigning 6 tokens per face, the sequence yields 12 unique", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 273, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 308, + 273, + 545, + 281 + ], + "type": "text", + "content": "tokens. In contrast, per-vertex tokenization leads to repeated to-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 284, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 307, + 284, + 545, + 292 + ], + "type": "text", + "content": "kens in the sequence due to shared vertices between faces. This", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 295, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 307, + 295, + 545, + 304 + ], + "type": "text", + "content": "repetition makes the sequence easier for the transformer to learn", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 306, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 308, + 306, + 545, + 314 + ], + "type": "text", + "content": "compared to a wholly unique sequence per face, especially when", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 316, + 434, + 325 + ], + "spans": [ + { + "bbox": [ + 307, + 316, + 434, + 325 + ], + "type": "text", + "content": "both sequences are of equal length.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 9, + "sub_type": "text_image" + }, + { + "bbox": [ + 305, + 341, + 546, + 497 + ], + "type": "text", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 320, + 343, + 545, + 351 + ], + "spans": [ + { + "bbox": [ + 320, + 343, + 545, + 351 + ], + "type": "text", + "content": "We evaluate the effect of various choices – how much", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 354, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 307, + 354, + 545, + 365 + ], + "type": "text", + "content": "does the positional encoding at input help, effect of using", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 366, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 307, + 366, + 545, + 376 + ], + "type": "text", + "content": "continuous predictions instead of discrete as outputs, us-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 379, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 307, + 379, + 545, + 388 + ], + "type": "text", + "content": "ing vector quantization (1 token per face) instead of resid-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 391, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 307, + 391, + 545, + 399 + ], + "type": "text", + "content": "ual quantization (D tokens per face), encoder architecture", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 403, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 307, + 403, + 545, + 412 + ], + "type": "text", + "content": "as a point encoder, or different graph convolution opera-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 415, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 307, + 415, + 545, + 423 + ], + "type": "text", + "content": "tors, and decoder architecture as either ResNet19 or Point-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 427, + 545, + 435 + ], + "spans": [ + { + "bbox": [ + 307, + 427, + 545, + 435 + ], + "type": "text", + "content": "Net decoder. Note that even though for encoder-decoder re-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 307, + 438, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 307, + 438, + 545, + 448 + ], + "type": "text", + "content": "construction, ‘w/o per Vertex Quantization’ performs best,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 451, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 308, + 451, + 545, + 459 + ], + "type": "text", + "content": "this variant works significantly worse than with per Vertex", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 308, + 463, + 544, + 472 + ], + "spans": [ + { + "bbox": [ + 308, + 463, + 544, + 472 + ], + "type": "text", + "content": "Quantization, as shown in the main paper. 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b/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_model.json new file mode 100644 index 0000000000000000000000000000000000000000..241a159bf5602140a6369bf9bd9a603ae07c963b --- /dev/null +++ b/papers/markdown/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers/hybrid_auto/2311.15475_MeshGPT_Generating_Triangle_Meshes_with_Decoder-Only_Transformers_model.json @@ -0,0 +1,16121 @@ +[ + [ + { + "type": "aside_text", + "bbox": [ + 0.023, + 0.259, + 0.058, + 0.708 + ], + "angle": 270, + "content": "arXiv:2311.15475v1 [cs.CV] 27 Nov 2023" + }, + { + "type": "doc_title", + "bbox": [ + 0.114, + 0.093, + 0.856, + 0.114 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.143, + 0.704, + 0.161 + ], + "angle": 0, + "content": null, + "merge_prev": false + }, + { + "type": "text", + "bbox": [ + 0.107, + 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ClassMethodCOV↑MMD↓1-NNAFID↓KID↓|V||F|
ChairAtlasNet [18]9.034.0595.13170.710.16925004050
BSPNet [7]16.483.6291.7546.730.0306731165
Polygen [43]31.224.4193.5661.100.043248603
GET3D [14]40.853.5683.0481.450.0541372527457
GET3D*38.753.5784.0778.290.065199399
MeshGPT43.283.2975.5118.460.010125228
TableAtlasNet [18]7.163.8596.30161.380.15025004050
BSPNet [7]16.833.1493.5830.780.017420699
Polygen [43]32.993.0088.6538.530.029147454
GET3D [14]41.702.7885.5493.930.0761376727537
GET3D*37.952.8581.9350.460.037199399
MeshGPT45.682.3672.886.240.00299187
BenchAtlasNet [18]20.532.4790.58189.390.16325004050
BSPNet [7]28.742.0588.4459.110.030457756
Polygen [43]51.921.9776.9849.340.031172430
MeshGPT55.231.4468.248.720.001159291
LampAtlasNet [18]19.974.6891.85177.910.13925004050
BSPNet [7]18.385.3293.13112.650.0775871011
Polygen [43]47.864.1881.4252.480.025185558
MeshGPT53.883.9465.7319.910.004150288
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PreferenceAtlasNet [18]BSPNet [7]Polygen [43]GET3D [14]
Our Shape82.65%78.57%85.71%68.37%
Our Triangulation84.69%71.43%84.69%73.47%
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MethodCOV↑MMD↓1-NNAFID↓KID↓
w/o Learned Tokens27.504.5193.1540.200.024
w/o Encoder Features39.243.4384.4830.350.017
w/o Pretraining36.973.7384.6927.540.014
w/o Sequence Compression30.984.1588.9838.760.023
w/o per Vertex Quantization23.575.4998.3574.940.050
MeshGPT43.283.2975.5118.460.010
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{ + "type": "ocr_text", + "bbox": [ + 0.504, + 0.835, + 0.89, + 0.846 + ], + "text": "", + "score": 1.0 + }, + { + "type": "ocr_text", + "bbox": [ + 0.502, + 0.849, + 0.849, + 0.862 + ], + "text": "", + "score": 1.0 + }, + { + "type": "ocr_text", + "bbox": [ + 0.476, + 0.925, + 0.496, + 0.939 + ], + "text": "", + "score": 1.0 + } + ], + [ + { + "type": "header", + "bbox": [ + 0.082, + 0.091, + 0.138, + 0.098 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.1, + 0.468, + 0.397 + ], + "angle": 0, + "content": "I filter your name\nwere are some artist designed mesh of the category chair:\nPlease answer the following questions keeping these in mind.\n• which of the objects is a better quality mesh for this category?\n• which of the objects better matches the quality of artist meshes in this category!", + "sub_type": "text_image" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.409, + 0.47, + 0.464 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.481, + 0.469, + 0.626 + ], + "angle": 0, + "content": "
VariantTriangle Accuracy (%) ↑Cross-Entropy ↓
w/o Positional Encoding79.330.2484
w/o Output Discretization22.030.5705
w/o Residual Quantization1.294.6679
w/o per Vertex Quantization98.640.1413
w/ PointNet Encoder88.730.1896
w/ GAT [60] Encoder86.140.2015
w/ EdgeConv [61] Encoder91.230.1702
w/ ResNet19 Decoder96.290.1492
w/ PointNet Decoder95.470.1528
MeshGPT98.490.1473
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b/papers/markdown/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation/hybrid_auto/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation.md new file mode 100644 index 0000000000000000000000000000000000000000..9e0dbb48539b3303e67f1d10b43692ea5b6d4807 --- /dev/null +++ b/papers/markdown/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation/hybrid_auto/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation.md @@ -0,0 +1,844 @@ +# NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation + +QIUJIE DONG, Shandong University, China, The University of Hong Kong, China, and TransGP, China + +HUIBIAO WEN, Shandong University, China + +RUI XU, The University of Hong Kong, China + +SHUANGMIN CHEN, Qingdao University of Science and Technology, China + +JIARAN ZHOU, Ocean University of China, China + +SHIQING XIN∗, Shandong University, China + +CHANGHE TU, Shandong University, China + +TAKU KOMURA, The University of Hong Kong, China + +WENPING WANG, Texas A&M University, United States of America + +![](images/ec5c189df3d8309359b7cb1e9ef73d98ec4ded9f2d1c1f1a4a5200bff5643d0d.jpg) + +
+natural_image + +3D wireframe models of various 3D geometric structures, including human figures and torus-like forms (no text or symbols) +
+ +Fig. 1. Gallery of quad meshes generated with our NeurCros method. NeurCross excels in computing cross field for generating high-quality quad meshes. Its advantages include optimized singular point placement, insensitivity to surface noise and minor surface undulations, and faithful alignment with principa curvature directions and sharp feature curves. + +Quadrilateral mesh generation plays a crucial role in numerical simulations within Computer-Aided Design and Engineering (CAD/E). Producing high quality quadrangulation typically requires satisfying four key criteria. First, the quadrilateral mesh should closely align with principal curvature direc tions. Second, singular points should be strategically placed and efectively minimized. Third, the mesh should accurately conform to sharp feature edges. Lastly, quadrangulation results should exhibit robustness against noise and minor geometric variations. Existing methods generally involve first computing a regular cross field to represent quad element orientations across the surface, followed by extracting a quadrilateral mesh aligned closely with this cross field. A primary challenge with this approach is balancing the smoothness of the cross field with its alignment to pre-computed principal curvature directions, which are sensitive to small surface perturbations and often ill-defined in spherical or planar regions. + +To tackle this challenge, we propose NeurCross, a novel framework that simultaneously optimizes a cross field and a neural signed distance function (SDF), whose zero-level set serves as a proxy of the input shape. Our joint optimization is guided by three factors: faithful approximation of the optimized SDF surface to the input surface, alignment between the cross field and the principal curvature field derived from the SDF surface, and smoothness of the cross field. Acting as an intermediary, the neural SDF contributes in two essential ways. First, it provides an alternative, optimizable base surface exhibiting more regular principal curvature directions for guiding the cross field. Second, we leverage the Hessian matrix of the neural SDF to implicitly enforce cross field alignment with principal curvature directions, thus eliminating the need for explicit curvature extraction. Extensive experiments demonstrate that NeurCross outperforms the state-of-the-art methods in terms of singular point placement, robustness against surface noise and surface undulations, and alignment with principal curvature directions and sharp feature curves. + +## CCS Concepts: • Computing methodologies → Shape analysis; Mesh geometry models. + +Additional Key Words and Phrases: quadrangulation, neural network, cross field, signed distance function, principal curvature + +## 1 INTRODUCTION + +Quadrangulation is fundamental in both Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) [Bommes et al. 2013b; Vaxman et al. 2016], with significant applications in finite element analysis, isogeometric analysis, character animation, and physics simulations [Bommes et al. 2013a, 2009; Campen et al. 2015a; Jakob et al. 2015; Mu et al. 2023]. + +Existing approaches typically first compute a reliable cross field to represent quad element orientations across the surface, followed by extracting quad meshes aligned closely with the computed field [Bommes et al. 2013a, 2009; Huang et al. 2018; Jakob et al. 2015; Zhang et al. 2020]. Most methods require principal curvature di rections as input. However, computing a desired cross field from principal curvature directions entails meeting four key requirements: First, the quadrilateral mesh should align closely with principal cur vature directions. Second, singular points should be strategically placed and minimized. Third, the mesh should conform accurately to sharp feature edges. Lastly, quadrangulation results should be robust against noise and minor surface variations. These challenges are particularly pronounced in geometrically or topologically complex shapes. + +Fig. 2 shows quadrangulation results of some existing methods. As shown, for instance, QuadWild [Pietroni et al. 2021] fails to align properly with principal curvature directions due to an overemphasis on the smoothness of the cross field. Although principal curvature directions provide useful geometric clues, precisely controlling their influence on the inferred cross field is dificult, especially in nearly spherical or planar regions, or on a surface with small undulations, where principal curvature directions become unstable. + +We introduce an optimizable neural signed distance function (SDF) as the underlying shape representation to infer the desired cross field. The neural SDF serves as a proxy for the input shape, which often exhibits unstable principal curvature directions. Opti mizing this SDF alongside the cross field provides a smooth approximation to the input shape, generating a regular principal curvature field to guide cross field generation. More specifically, our joint optimization is guided by three factors: faithful approximation of the optimized SDF surface to the input surface, alignment between the cross field and the principal curvature field derived from the SDF surface, and smoothness of the cross field. We integrate these requirements into a unified neural optimization framework, called NeurCross, that enables simultaneous optimization of the SDF and cross field. Fig. 3 illustrates our method’s success on a dimpled el lipsoid with irregular curvature directions, compared to a naïve two-stage approach that first optimizes an SDF to properly fit the input shape and then uses the curvature field of this fixed SDF to guide the generation of the cross field. The key to the success of our method is its simultaneous optimization strategy that allows the cross field smoothness term to inform the optimal shape of the neural SDF as a proxy surface. + +Additionally, a key advantage is that the SDF-based shape operator implicitly encodes principal curvature directions, enabling enforcement of alignment between principal curvature directions and the cross field by evaluating whether the cross at each point match well with the eigenvectors of the shape operator, bypassing the need for explicit extraction of principal curvature direction, a step susciptable to unstability in nearly spherical or planar regions. + +We implement NeurCross using a SIREN-based [Sitzmann et al. 2020] module for SDF fitting and a U-Net-based [Ronneberger et al. 2015] module for cross field prediction. Over 10,000 iterations, both components are optimized simultaneously to satisfy quadrangulation criteria. Finally, we employ global-seamless parametrization from libigl [Jacobson et al. 2017] aligned with our cross field, followed by quad mesh extraction using libQEx [Ebke et al. 2013]. Fig. 4 illustrates this process. Extensive experiments validate Neur-Cross’s efectiveness, demonstrating improvements in singular point placement, robustness to noise and geometric variations, and approximation accuracy, as shown in the teaser figure. + +Our contributions are summarized as follows: + +- We propose NeurCross, the first self-supervised neural network for learning cross fields. +- We implicitly enforce cross field alignment with principal curvature directions via an SDF-based shape operator, naturally addressing potential ambiguity. +- We leverage an optimizable neural SDF as an underlying representation to coordinate requirements, dynamically adjusting to minor surface variations. + +## 2 RELATED WORK + +This paper focuses on developing a neural representation of the cross field for quadrilateral mesh generation. In this section, we review two main categories of related work: quad mesh generation techniques and neural SDF representations. + +## 2.1 Quad Mesh Generation + +Quadrilateral mesh generation has attracted significant attention in recent years. While some methods, such as Dual Marching Cubes (DMC) [Nielson 2004], can directly extract quad facets without relying on direction fields, the resulting meshes often lack quality, particularly in aligning with principal directions. Most state-of-theart approaches rely on a cross field [Lai et al. 2010; Palmer et al. 2021; Ray et al. 2008] to guide the generation of high-quality quad meshes, as it ensures edge alignment and proper placement of irregular vertices. Typically, after computing a cross field, a parameterization step [Bommes et al. 2009; Chien et al. 2016; Levi and Zorin 2014; Myles et al. 2014] aligns gradients with the direction field and traces integer iso-lines across multiple charts [Ebke et al. 2013]. Although several robust quadrangulation methods [Dong et al. 2006; Gurung et al. 2011; Ling et al. 2014; Owen et al. 1999; Remacle et al. 2012; Velho and Zorin 2001; Zhang et al. 2010] operate independently of direction fields, they often fail to achieve global smoothness. Below, we review related works on direction fields. + +![](images/5d8ee6e01f2c6e28b5a490858bdcb70619707e26fa8b94cabb71038b3f0d069c.jpg) +Fig. 2. Existing approaches typically rely on principal curvature directions as input. However, due to the inherent instability of these directions, current methods often prioritize the smoothness of the cross field at the cost of alignment with the principal curvature directions. To address this limitation, our approach avoids explicitly extracting principal curvature directions. Instead, we assess whether the cross field at each point can function as eigenvectors of the shape operator. + +(a) Input +![](images/cdb36e7fe472f41c69f30ff6a0555ba38ab7aa8254e2b54bd9e90c9af04cad82.jpg) +GT surface + +![](images/97e0129853317a23ac177a004919fd97745a6927c1b4bcc99af1367275860590.jpg) +GT curvature field + +(b) Two-step method +![](images/ba2b9b52fbc1a845e1dd3debada5c6166729808cd3ff86628d05c3a77670a3d0.jpg) + +(c) Our joint optimization +![](images/b1ad9d112050fb0ab658a4817c97689f3676163fee1383eacd237491e3415cad.jpg) +SDF shape + +![](images/26a08368b289a1788bb03735a0dbb19ce78b304a4380a537bc2354705f053799.jpg) + +![](images/f215ec0df7daddca2a9cbcb63a92ef184379279979a0b34084925a13d085f291.jpg) +Fitting error + +![](images/e06b190c46ba89f80afa3b86bc90c7866478bd6defd38ff2ecf558186e498f1d.jpg) + +![](images/70a65601f6b87a407bbc69bc05ee6bf378c6053b9a1f8a8a3af9085cba2bc355.jpg) + +![](images/e5f2577ea0ad09c7aad4dd4e85230f871971d3b796c7ac542479d950cf690ff8.jpg) +Cross field + +![](images/add7ac0fb6932a9607a7892ad64969086c64df63b898c7c5eeae7584d59a08d2.jpg) + +![](images/e58c62b09e94b1ebce6a4df5d8754660e1d45e4093ae0eb1c3532ee74f8076a7.jpg) +Quad mesh +Fig. 3. (a) The input mesh and its ground-truth principal curvature directions. (b) Two-step optimization: by first precomputing an SDF that precisely fits the input shape, the subsequent optimization step still sufers from sensitivity to minor geometric variations, failing to yield the desired cross field. (c) Joint optimization: by treating the SDF as a proxy for the input shape, simultaneous optimization of the SDF and the cross field allows the SDF to approximate the input shape while remaining robust to minor geometric variations, resulting in the desired cross field. We visualize the fiting errors between the SDF surface and the original surface using a color-coded scheme + +A fundamental requirement for direction fields is to align edge directions with principal curvature directions [Bommes et al. 2013a, 2009; Fang et al. 2018; Hertzmann and Zorin 2000; Huang et al. 2018; Jakob et al. 2015; Kälberer et al. 2007; Lyon et al. 2019; Vaxman et al. 2016]. Lai et al. [2008] proposed an iterative relaxation scheme that incrementally aligns mesh edges with principal directions, though it requires additional post-processing to refine results. Jakob et al. [2015] introduced a unified local smoothing operator that optimizes both edge orientations and vertex positions in the output quad mesh. QuadriFlow [Huang et al. 2018] improved upon In stant Meshes [Jakob et al. 2015] by introducing linear and quadratic constraints, reducing singularities but struggling to preserve the original shape. Several methods [Bommes et al. 2013a; Huang et al. 2018; Jakob et al. 2015] optimize parametrization while incorporating integer constraints, a challenging mixed-integer programming (MIP) problem [Bommes et al. 2009] that is computationally inten sive. These methods typically aim to minimize distortion and reduce singularities [Bommes et al. 2013a; Levi and Zorin 2014; Myles et al. + +2014; Myles and Zorin 2013]. To address the computational complexity of IGM [Bommes et al. 2013a] on complex meshes, Ebke et al. [2016] proposed a framework using eficient decimation and coarse-to-fine mapping to improve interactive performance. Dielen et al. [2021] introduced a learning-based approach for predicting di rection fields, demonstrating its potential for quad mesh generation. However, its reliance on domain-specific networks and canonical alignment limits its generalizability and robustness to non-rigid changes. + +## 2.2 Neural SDF + +The Signed Distance Function (SDF) is a widely used geometric representation in computer graphics, particularly for surface reconstruction. For example, radial basis functions (RBF) [Carr et al. 2001] approximate the SDF, enabling the extraction of the target surface as the zero-isosurface of the SDF. + +SDFs have also been extensively employed in deep learning-based surface reconstruction, including supervised implicit surface reconstruction methods [Erler et al. 2020; Huang et al. 2022; Park et al. + +![](images/989c51839f42396f1b4f800d0b8e5c888127938bec1e4096e97283a8a61ea47d.jpg) + +
+natural_image + +3D wireframe model of a complex, irregularly shaped mechanical structure (no text or symbols) +
+ +(a) Triangle mesh + +![](images/cbfe4482b9c604d09b696ba6e241b1c391ca9ae535ef812e26dc8b6b3af93bfb.jpg) + +
+natural_image + +Abstract 3D sculpture of intertwined human figures in a dynamic pose (no text or symbols) +
+ +(b) Random initialization + +![](images/c1adaa84e307303f5b901506152925de880749120dbe40b2415f36a68a3cd74c.jpg) + +
+natural_image + +3D rendered abstract mechanical structure with colorful grid pattern (no text or symbols) +
+ +(c) Resultant cross field + +![](images/c877d31cacdb7415b6f448daea08ff7ec3c46527ddb57f1699d7a88ed5571823.jpg) + +
+natural_image + +3D wireframe model of a complex geometric structure with no visible text or symbols +
+ +(d) Quad mesh +Fig. 4. Given the input triangular surface in (a), starting with a randomly initialized cross field in (b), our NeurCross method produces a smooth cross field in (c) that is well aligned with the principal curvature directions of the input surface. We use the global-seamless parametrization from libigl to obtain a parametrization aligned with the computed cross field, and then use libQEx to extract the final quad mesh in (d). + +2019] and self-supervised approaches [Ma et al. 2021, 2022; Wang et al. 2021]. For instance, IGR [Gropp et al. 2020] incorporates the Eikonal term to enforce implicit geometric regularization, providing an efective mechanism for surface reconstruction. SIREN [Sitz mann et al. 2020] demonstrates that periodic activation functions are well-suited for representing complex natural signals and their derivatives using implicit neural representations. DiGS [Ben-Shabat et al. 2022] integrates Laplacian energy as a soft constraint for the SDF, proving efective for reconstructing surfaces from unoriented point clouds. Neural-Singular-Hessian [Wang et al. 2023] ensures that the Hessian of the neural implicit function has a zero determinant for points near the surface, which is particularly useful for recovering details from unoriented point clouds. Additionally, Dong et al. [2024] proposed a zero Gaussian curvature constraint for re constructing CAD-type surfaces from low-quality unoriented point clouds. All these methods leverage neural networks to approximate the SDF. + +In this paper, SDFs play a central role in quad mesh generation, as the Hessian of the SDF fully encodes principal curvatures and their directions [Dong et al. 2024; Wang et al. 2023]. + +## 3 OUR APPROACH + +## 3.1 Overview + +The core idea of NeurCross is to leverage the optimizable neural Signed Distance Function (SDF) as an underlying representation to coordinate various requirements. On one hand, the adjustable SDF can efectively reduce sensitivity to minor surface variations. On the other hand, the SDF-based shape operator enables us to implicitly evaluate the diference between the principal curvature directions and the cross field. NeurCross consists of two core modules: a surface fitting module and an orientation prediction module, both centered around the SDF. + +(1) Surface Fitting Module: This module aims to represent the input triangular surface using a neural SDF. Its loss incorporates the Dirichlet condition [Lipman 2021], the Eikonal condition [Gropp et al. 2020], and the singular Hessian con dition [Wang et al. 2024] to ensure high fidelity to the input surface geometry. Together, these constraints guarantee an accurate surface representation. +(2) Cross Field Prediction Module: This module is designed to represent the cross field while implicitly enforcing alignment + +with principal curvature directions and spatial smoothness. It employs a U-Net architecture [Ronneberger et al. 2015] to predict a rotation angle for each triangular facet, yielding a geometry-aware cross field. Additionally, this module supports explicit alignment with geometric features. + +These two modules are coordinated through a total loss function, which ensures simultaneous optimization of the SDF and the cross field during the training process. The interaction between the modules allows for dynamic updates to both the surface representation and the cross field, leading to improved accuracy and robustness. The overall network architecture is illustrated in Fig. 5. + +Total Loss. Our total loss is defined as follows. + +$$ +\mathcal {L} = \underbrace {\lambda_ {\mathrm{E}} \mathcal {L} _ {\mathrm{E}} + \lambda_ {\mathrm{DM}} \mathcal {L} _ {\mathrm{DM}} + \lambda_ {\mathrm{DNM}} \mathcal {L} _ {\mathrm{DNM}} + \tau \lambda_ {\mathrm{AN}} \mathcal {L} _ {\mathrm{AN}}} _ {\text {SDF}} + \underbrace {\lambda_ {\mathrm{AP}} \mathcal {L} _ {\mathrm{AP}} + \lambda_ {\mathrm{S}} \mathcal {L} _ {\mathrm{S}}} _ {\text {Cross Field}}, \tag {1} +$$ + +where � is the annealing factor [Dong et al. 2024; Wang et al. 2024, 2023]. The individual terms, along with their corresponding weights, will be detailed in the following subsections. + +## 3.2 SDF Fiting + +Let Θ denote the parameters of a neural SDF $f ( \boldsymbol { x } ; \Theta ) : \mathbb { R } ^ { 3 } \to \mathbb { R } ,$ where � = 0 approximates the input triangular surface. We begin by sampling the centroid of each triangle, forming a point set P, where each point is associated with a normal vector. In the following, we define a loss term to enforce alignment with the predefined surface normals, while leaving further details to Sec. 3.5. + +SDF Based Shape Operator. The shape operator of a surface measures the rate of change of the unit normal in any direction, thereby describing how the shape changes in that direction. In diferential geometry, it is very common to assume the surface has a parametric form, such that the shape operator defines a quadratic form on the tangent space, and the eigenvectors of the shape operator correspond exactly to the principal directions. In fact, the Hessian matrix of the SDF is closely related to the shape operator. For a point � on the base surface, the Hessian matrix $H _ { P }$ of the SDF has an eigenvalue of 0, with its corresponding eigenvector being the normal vector $\mathbf { \Delta } _ { n _ { P } }$ [Dong et al. 2024; Wang et al. 2024, 2023]. Simultaneously, the other two eigenvectors of $H _ { p }$ correspond to the two principal curvature directions. + +Alignment with Predefined Surface Normals. Since for a point � suficiently close to the base surface, the eigenvector corresponding to the zero eigenvalue of the Hessian matrix $H _ { p }$ of the SDF aligns with the normal vector $\scriptstyle n _ { p }$ at ${ \pmb \rho } .$ Given that the normal direction of $\pmb { p } \in \mathcal { S }$ can be directly obtained from the input triangle mesh, we require the neural SDF to align with the predefined surface normal $\mathbf { \Delta } _ { n _ { P } }$ as follows: + +![](images/de77e6dbc3e8b40ddf3fe821e9c18bcdc2eb8f2daed28bf5505c5cbc863228c1.jpg) + +
+flowchart + +```mermaid +graph LR + A["Input Image"] --> B["Image with Scatter Plot"] + B --> C["P"] + C --> D["SDF fitting module"] + D --> E["Feature Output"] + F["MLP"] --> G["θ"] + G --> H["μ, ν"] + H --> I["⊕"] + J["L_SDF"] --> K["min L"] + K --> L["L_CrossField"] + L --> M["Output Image"] + N["α = μcosθ + vsinθ\nβ = vcosθ - μsinθ"] --> I + E --> O["H"] + O --> P["⊕"] + P --> Q["Output Image"] +``` +
+ +Fig. 5. Our self-supervised network pipeline for representing cross fields in quad mesh generation. All layers in the network are implemented as multi-layer perceptrons (MLPs), with the SDF fiting module utilizing the SIREN [Sitzmann et al. 2020] architecture. The circled $^ { 6 } + \prime$ symbol denotes a data-combining operation. + +$$ +H _ {p} \cdot n _ {p} = 0. \tag {2} +$$ + +The overall alignment with predefined surface normals can be quantified as: + +$$ +\mathcal {L} _ {\mathrm{AN}} = \frac {1}{| \mathcal {P} |} \int_ {\mathcal {P}} \left| H _ {\boldsymbol {p}} \cdot \boldsymbol {n} _ {\boldsymbol {p}} \right| \mathrm{d} \boldsymbol {p}. \tag {3} +$$ + +## 3.3 Cross Field Prediction + +Local Coordinate System. Recall that each point $\pmb { p } \in \mathcal { P }$ corresponds to the centroid of a triangular face. The task of computing the cross field involves inferring a pair of orthogonal vectors, $( \alpha _ { p } , \beta _ { p } )$ , that align as closely as possible with the principal curvature directions. To achieve this, we assume that each triangle has a pre-defined coordinate system + +with two axes, $\mu _ { p }$ and $\nu _ { p } ,$ , which are mutually orthogonal unit vectors satisfying $\mu _ { \pmb { p } } \times \nu _ { \pmb { p } } = n _ { p }$ . We introduce a rotation angle $\theta _ { P }$ to represent $\alpha _ { p }$ and $\beta _ { p }$ as follows: + +$$ +\left\{ \begin{array}{l} \boldsymbol {\alpha} _ {p} = \boldsymbol {\mu} _ {p} \cos \theta_ {p} + \nu_ {p} \sin \theta_ {p}, \\ \boldsymbol {\beta} _ {p} = \nu_ {p} \cos \theta_ {p} - \boldsymbol {\mu} _ {p} \sin \theta_ {p}. \end{array} \right. \tag {4} +$$ + +See the inset figure for an illustration. Notably, $\alpha _ { p }$ and $\beta _ { p }$ are natu rally mutually orthogonal unit vectors. As a result, the optimization of the cross field reduces to computing the rotation angle $\theta _ { P }$ for each triangle. + +Implicit Alignment with Principal Directions. An explicit approach to implementing alignment with principal directions involves comparing the cross field with pre-extracted principal directions. However, most existing methods for extracting principal directions heavily rely on local shape variations, which can lead to instability, particularly when the local geometry is approximately planar or spherical. To address this limitation, we adopt an implicit alignment strategy by evaluating the compatibility between the cross field and the shape operator. + +To align the cross field with the principal directions, we encourage $\alpha _ { p }$ and $\beta _ { p }$ to coincide with two of the eigenvectors of $H _ { p } .$ . To enforce collinearity between $H _ { P } \alpha _ { P }$ and $\alpha _ { p }$ , we impose the following condition: + +$$ +H _ {p} \alpha_ {p} \times \alpha_ {p} = 0. \tag {5} +$$ + +Similarly, we require: + +$$ +H _ {p} \boldsymbol {\beta} _ {p} \times \boldsymbol {\beta} _ {p} = 0. \tag {6} +$$ + +We define the loss term to measure alignment with the principal directions as follows: + +$$ +\mathcal {L} _ {\mathrm{AP}} ^ {(1)} = \frac {1}{| \mathcal {P} |} \int_ {\mathcal {P}} \left| H _ {p} \boldsymbol {\alpha} _ {p} \times \boldsymbol {\alpha} _ {p} \right| + \left| H _ {p} \boldsymbol {\beta} _ {p} \times \boldsymbol {\beta} _ {p} \right| \mathrm{d} p. \tag {7} +$$ + +Smoothness ofthe Cross Field. Consider two pairs of orthogonal unit vectors in a plane, denoted as $( \pmb { \alpha } _ { 1 } , \pmb { \beta } _ { 1 } )$ and $( \alpha _ { 2 } , \beta _ { 2 } )$ . We say that the pair $( \alpha _ { 1 } , \beta _ { 1 } )$ aligns with $( \alpha _ { 2 } , \beta _ { 2 } )$ if either $\pmb { \alpha } _ { 1 }$ and $\pmb { \alpha } _ { 2 }$ are colinear, or $\pmb { \alpha } _ { 1 }$ and $\beta _ { 2 }$ are colinear. + +Based on the above definition, it can be proved that $( \alpha _ { 1 } , \beta _ { 1 } )$ aligns with $( \alpha _ { 2 } , \beta _ { 2 } )$ if and only if + +$$ +\left| \boldsymbol {\alpha} _ {1} \cdot \boldsymbol {\alpha} _ {2} \right| + \left| \boldsymbol {\alpha} _ {1} \cdot \boldsymbol {\beta} _ {2} \right| + \left| \boldsymbol {\beta} _ {1} \cdot \boldsymbol {\alpha} _ {2} \right| + \left| \boldsymbol {\beta} _ {1} \cdot \boldsymbol {\beta} _ {2} \right| \tag {8} +$$ + +achieves the minimum. We explain the correctness as follows. Without loss of generality, we assume that $\pmb { \alpha } _ { 1 } = ( 1 , 0 )$ and $\beta _ { 1 } = ( 0 , 1 )$ . By denoting $\alpha _ { 2 }$ as (cos �, sin �), the above sum simplifies to + +$$ +2 (| \cos \theta | + | \sin \theta |). \tag {9} +$$ + +![](images/e25e014b81e442d4ef1e4de0a12ae3b00366cc55c89de021c24e1ab966faba24.jpg) +(a) Input mesh + +![](images/abd18d26b8968f9383ada7d35e09811fa1e6a1fce34a88de24b2504a8e51d81a.jpg) +(b) Cross field + +![](images/43e9470e0ad9c0142f03591ec741c2d53247c12dbe072ad34cc88a813ba93a5a.jpg) +(c) Quad mesh +Fig. 6. The smoothness constraint of the cross field beter controls the distribution of singularity points. From left to right: (a) an input triangular mesh; (b) a cross field computed with NeurCross; (c) the quad mesh extracted from the cross field. + +In the inset figure, we illustrate how the function value of 2(| cos �| + | sin �|) varies with �. It can be observed that the minimum is achieved at $\begin{array} { r } { \theta = k \frac { \pi } { 2 } } \end{array}$ , while the maximum occurs at $\begin{array} { r } { \theta = k \frac { \pi } { 2 } + \frac { \pi } { 4 } } \end{array}$ . Therefore, it can be concluded that + +![](images/19ff735f8956b3472f74ba727fe052b3bf43920b06e2e28ae05534b0b4d5d9c7.jpg) + +
+contour + +| X | Y | +| --- | --- | +| 0 | 2 | +| \(\pi/4\) | \(2\sqrt{2}\) | +| \(\pi/2\) | 2 | +
+ +only when the sum reaches the minimum value of 2, one cross aligns with another $\begin{array} { r } { ( \theta = k \frac { \pi } { 2 } ) } \end{array}$ + +We denote the three neighboring points of $\pmb { p }$ as ${ \pmb q } _ { 1 } , { \pmb q } _ { 2 } , { \pmb q } _ { 3 }$ . Since each $\pmb { q } _ { i }$ lies on a neighboring face, a rotation around the common edge is necessary before aligning the directions between � and $\mathbf { \nabla } _ { q _ { i } . }$ We define $\{ R _ { i } \mid i = 1 , 2 , 3 \}$ as the rotation matrices associated with dihedral angles $\{ \varphi _ { i } \mid i = 1 , 2 , 3 \}$ + +![](images/37cfd3e08b4e7dde5c6d984906df26a34bccb69c180b9a4d42ab63954739dd03.jpg) + +
+text_image + +q₂ +φ₂ +p +φ₁ +φ₃ +q₃ +
+ +and shared edges, which can be precomputed. To this end, the smoothness loss can be written as + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm{S}} = \frac {1}{3 | \mathcal {P} |} \int_ {\mathcal {P}} \sum_ {i = 1} ^ {3} \left(\left| \boldsymbol {\alpha} _ {\boldsymbol {p}} \cdot R _ {i} \boldsymbol {\alpha} _ {\boldsymbol {q} _ {i}} \right| + \left| \boldsymbol {\alpha} _ {\boldsymbol {p}} \cdot R _ {i} \boldsymbol {\beta} _ {\boldsymbol {q} _ {i}} \right| \right. \tag {10} \\ \left. + \left| \boldsymbol {\beta} _ {\boldsymbol {p}} \cdot R _ {i} \boldsymbol {\alpha} _ {\boldsymbol {q} _ {i}} \right| + \left| \boldsymbol {\beta} _ {\boldsymbol {p}} \cdot R _ {i} \boldsymbol {\beta} _ {\boldsymbol {q} _ {i}} \right| - 2\right) \mathrm{d} \boldsymbol {p}. \\ \end{array} +$$ + +Remark: Consider a spherical surface, as shown in Fig. 6. At each point on such a surface, the principal curvature directions are not unique. In this case, the smoothness constraint of the cross field plays a crucial role in better controlling the distribution of singular ity points. It is worth noting that our implicit principal curvature alignment is simultaneously satisfied. Moreover, Fig. 6 highlights the importance of efective cross field smoothing, which has also been addressed in prior work. Knöppel et al. [2013] and Diamanti et al. [2014] introduced convex smoothness energies to smooth N-RoSy fields. Knöppel et al. [2013]’s method achieves global optimality but requires a nonlinear transformation, which can cause extra singu larities and distortion. Jakob et al. [2015] uses an extrinsic energy to align with surface features, but its strong reliance on local information often leads to suboptimal results and unwanted singularities. In contrast, our NeurCross smooths the cross field using Equ. 10, introducing singularities only in areas with high curvature variation. A detailed comparison is provided in Section 4.2. + +![](images/cbc7bee6d39bd37e82e8ad9181a3ffcf185ff11033690bf3ce6022d134d764c5.jpg) + +
+natural_image + +3D wireframe model of a mechanical part with colored grid lines and highlighted regions (no text or symbols) +
+ +(a) w/o feature line const. + +![](images/5bec5fdbbdbfbb4955d8bbd9684803dea4ea2565e0e233ea4449ecb69823c87a.jpg) + +
+natural_image + +3D wireframe model of a furniture or chair with colorful mesh patterns, no visible text or symbols +
+ +(b) w/ feature line const. +Fig. 7. NeurCross supports feature line constraints. (a) The results without (w/o) the feature line constraint (const.); and (b) The result with (w/) the feature line constraint. + +Sharp Feature Alignment. As pointed out in [Pietroni et al. 2021], in the context of quad-meshing, it is important to incorporate feature lines of the input shape, such as crease angles in CAD models, when generating quadrangulation outcomes. However, reconciling this + +requirement with all other objectives is challenging. Generally, the influence of feature lines diminishes with increasing distance. + +As illustrated in the inset figure, let �� be the feature lines, where the cross field at each point of �� has been specified. We use $d _ { g } ( \pmb { p } , \pmb { F } \pmb { L } )$ to denote the geodesic distance between a surface point � and ��. We introduce + +![](images/417855208b3a5d7940999284be14d590e6abcf29bca0b43d7c1d240b592ec281.jpg) + +
+text_image + ++FL +dg(p,FL) +p +
+ +$$ +D _ {\boldsymbol {p}} = 1 - \exp \left(- \rho_ {\text {feature}} d _ {g} (\boldsymbol {p}, F L)\right), \tag {11} +$$ + +and redefine the principal curvature direction alignment as follows: + +$$ +\mathcal {L} _ {\mathrm{AP}} = \frac {1}{| \mathcal {P} |} \int_ {\mathcal {P}} D _ {p} \left(\left| H _ {p} \boldsymbol {\alpha} _ {p} \times \boldsymbol {\alpha} _ {p} \right| + \left| H _ {p} \boldsymbol {\beta} _ {p} \times \boldsymbol {\beta} _ {p} \right|\right) \mathrm{d} p, \tag {12} +$$ + +where $\rho _ { \mathrm { f e a t u r e } }$ (10 by default) in $D _ { P }$ serves as a suficiently large constant to regulate the influence of the feature line. The color gradient in the insert figure represents the value of $D _ { P }$ , which increases with distance from the feature line, reflecting the gradual reduction in � � influence on the surface point. For ease of implementation, we approximate $d _ { g } ( \pmb { p } , F L )$ using straight-line distances. As shown in Fig. 7, the crease line of the model is faithfully preserved in the neighborhood of $F L .$ , while its influence diminishes as the distance increases. Moreover, in regions where sharp features conflict with principal curvature directions, our NeurCross prioritizes feature alignment (see Fig. 8). + +Rotation Angle Prediction. Drawing inspiration from various object segmentation works [Hu et al. 2021; Milano et al. 2020], we employ the U-Net architecture [Ronneberger et al. 2015] to construct our rotation angle prediction network. The input to our U-Net-based network includes the point cloud P, along with the normal direction for each point, and the direction vectors � and � that represent the local coordinate system. The network outputs a scalar value $\omega _ { p } \in \left[ 0 , 1 \right]$ for each point �, allowing the rotation angle $\theta _ { P }$ to be represented as $\theta _ { P } = 2 \pi \omega _ { P }$ . For this module, we initialize the orien tation at a point � using a normal distribution with a mean of 0 and a standard deviation of 0.2. + +![](images/d91125ee830bc8f885f8ace60176c3868c7c77d54794a043ade2401aab73bb22.jpg) + +
+natural_image + +3D diagram of a cube with blue curved lines on top face (no text or symbols) +
+ +(a) Input mesh + +![](images/859f91eabda563b682bdeb999b37d405ed7f8ecd026d2a5078e9a65077eee540.jpg) + +
+natural_image + +3D wireframe cube with colorful grid pattern, no text or symbols visible +
+ +(b) Principal curvature field + +![](images/51aee388513df485afe536825e604692a93b5b7c5ac94aafd31208edc95a93ac.jpg) + +
+natural_image + +3D wireframe cube with multicolored grid pattern, no text or symbols visible +
+ +(c) Our cross field + +![](images/73b576dd4e229a7b5bc0d1d913f80e40d1b3b29bc77c36e418c0f17cf93589d3.jpg) + +
+natural_image + +3D wireframe cube with grid pattern, no text or symbols present +
+ +(d) Our quad mesh +Fig. 8. NeurCross enforces alignment with sharp features even when they diverge from principal curvature directions. (a) An input mesh with conflict ing principal curvature directions (blue) and feature curves (red); (b) The principal curvature field of the input surface; (c) The cross field computed by NeurCross; (d) The resulting quad mesh generated using NeurCross. + +## 3.4 SDF and Cross Field Joint Optimization + +One challenge in quad meshing is balancing the overall simplicity of the cross field with alignment to the principal directions, a dificulty that becomes more pronounced for geometrically or topologically complex shapes. In this paper, we address this challenge by using an optimizable neural SDF as a bridge to achieve this balance. Notably, the neural SDF and the cross field are optimized simultaneously. + +An alternative approach is to first fully optimize the SDF to accu rately represent the input shape and then keep it fixed. However, in this case, the cross field may become severely constrained, as it must align with potentially irregular curvature lines of the pre-fixed SDF. As shown in Fig. 9, the fixed SDF, while providing an accurate representation, may introduce overly complex curvature lines, leading to an excessive number of singular points in the final cross field. + +![](images/08575997b0e24ff7c2d0e51a07d30705fcf0f1763876fb57050444dad618e6c4.jpg) + +
+natural_image + +3D modeling visualization of two humanoid figures with meshed surfaces and color-coded heatmaps (no text or symbols) +
+ +(a) Cross field +(b) Quad mesh +(c) SDF fitting +(d) Fitting error +Fig. 9. Comparison between the two-step method (top row) and our joint optimization strategy (botom row). (a) Cross field; (b) Quad mesh; (c) The underlying SDF surface; (d) Fiting error between the SDF and the input triangular mesh. The final quad mesh is extracted based on the computed cross field and the input triangular mesh. As shown, our joint optimization strategy balances the overall smoothness of the cross field with alignment to the principal curvature directions. + +## 3.5 Implementation Details + +SDF Loss Terms. The loss terms used to regularize the SDF include the Eikonal condition [Gropp et al. 2020], the Dirichlet condition [Lipman 2021], and the alignment condition [Wang et al. 2024, 2023]. For further details on these loss terms, we refer readers to the existing literature [Dong et al. 2024; Wang et al. 2024, 2023]. + +Sampling Strategy. A neural SDF is employed to approximate the base surface, with regularization at sample points, as detailed in previous works [Ben-Shabat et al. 2022; Boulch and Marlet 2022; Dong et al. 2024; Gropp et al. 2020; Hou et al. 2022; Huang et al. 2022; Kazhdan and Hoppe 2013; Ma et al. 2021; Sitzmann et al. 2020; Wang et al. 2024, 2023; Xu et al. 2022]. We extract centroids from all triangles in the mesh to define the sample set P, chosen for their representative nature of the surface. For each point $\pmb { \mathscr { p } } \in \mathscr { P }$ the normal vector $\scriptstyle n _ { p }$ is derived from the corresponding triangular face’s normal. + +Given that each triangular face has three neighboring faces, neighboring relationships between points in $\mathcal { P }$ can be thus established. The SDF is assumed diferentiable within a narrow, thin-shell space Ω, which closely encloses the base surface. Following previous studies [Dong et al. 2024; Gropp et al. 2020; Ma et al. 2021; Wang et al. 2024, 2023], Ω is sampled using random displacements around each point $\pmb { \mathscr { p } } \in \mathscr { P }$ . A Gaussian distribution centered at each �, with a standard deviation based on the distance to its �-th nearest neighbor (typically $k = 5 0 )$ , is used for this purpose. A one-point sampling technique is then applied to generate the sample set Ω, which is the same size as $\mathcal { P }$ + +![](images/180acd3c13b491fd98c00e77c891d82db3583462811d747d1ca344de205641c3.jpg) + +
+flowchart + +This diagram illustrates a neural network architecture for ResNet activation, showing the flow of data through FC (Functional Component) and Concatenation layers to generate output. +
+ +Fig. 10. An overview of our U-Net-based module designed for predicting the rotation angle �. The network architecture incorporates the ResNet struc ture, with all layers being Multi-Layer Perceptrons (MLPs). The “ResNets” represents a combination of multiple ResNet blocks, the “FC” denotes the Fully Connected Layer, and the circled $^ { * } C ^ { * }$ symbol indicates the concatena tion operation. + +To prevent outlier zero iso-surfaces far from ${ \mathcal { P } } ,$ we uniformly sample the bounding box (assuming input points are normalized within $[ - 0 . 5 , 0 . 5 ] ^ { 3 } )$ , generating a sample set Q. + +Eikonal Condition. The Eikonal condition is crucial for ensuring that the SDF $f ( \boldsymbol { x } ; \Theta )$ maintains a unit gradient at every point, i.e., $\| \nabla f \| = 1$ , particularly in the vicinity of the surface. The corresponding loss term is defined as: + +$$ +\mathcal {L} _ {E} = \frac {1}{| \mathcal {P} | + | \Omega |} \int_ {\mathcal {P} \cup \Omega} \left| 1 - \| \nabla f (\boldsymbol {x}; \Theta) \| \right| \mathrm{d} \boldsymbol {x}, \tag {13} +$$ + +where $\mathcal { P }$ represents the sample points $( \mathrm { e . g . }$ , centroids of mesh triangles), and Ω encodes a narrow band around the surface where the SDF is diferentiable. Notably, the point set $\scriptstyle Q ,$ which represents regions far from the base surface, is excluded from this loss term and serves to prevent outlier zero isosurfaces in distant regions. + +Dirichlet Condition. For every point $\pmb { p } \in \mathcal { P }$ , it is essential that they lie as close as possible to the underlying surface, ideally satisfying $f ( \pmb { \mathscr { p } } ; \Theta ) = 0 .$ . Conversely, for points $q \in { \cal Q }$ , which lie away from the underlying surface, we aim to partition Q into interior and exterior regions, preventing � from degenerating. These conditions are formalized as the following loss terms: + +$$ +\mathcal {L} _ {\mathrm{DM}} = \frac {1}{| \mathcal {P} |} \int_ {\mathcal {P}} \left| f (\boldsymbol {p}; \Theta) \right| \mathrm{d} \boldsymbol {p}, \tag {14} +$$ + +and + +$$ +\mathcal {L} _ {\mathrm{DNM}} = \frac {1}{| Q |} \int_ {Q} \exp \left(- \rho_ {\mathrm{DNM}} \big | f (\boldsymbol {q}; \Theta) \big |\right) \mathrm{d} \boldsymbol {q}, \tag {15} +$$ + +where $\rho _ { \mathrm { D N M } }$ (defaulting to 100) is the exponential weight controlling the penalty for deviations from the surface. + +SIREN-based Module. Similar to various implicit surface reconstruction methods [Ben-Shabat et al. 2022; Lipman 2021; Wang et al. 2024, 2022b, 2023], our NeurCross employs the SIREN [Sitzmann et al. 2020] network architecture, which consists of four hidden layers with 256 units each. The SIREN architecture is based on multi-layer perceptrons (MLPs), where inputs are first normalized to the range $[ - 1 , 1 ] ^ { 3 }$ before being processed by the network. The activation function used in this architecture is the sine periodic function, which operates on the input point cloud $\mathcal { P }$ to produce the SDF field required for computing the Hessian matrix. For initializing this SIREN-based module, we follow SIREN’s initialization strategy [Sitzmann et al. 2020], which ensures that the distribution of activations remains consistent across all layers of the network. + +Table 1. The sizes of the building blocks within our U-Net-based module. �b l k denotes the number of botleneck layers within each ResNet block. From the 1st to the 7th block, the values of �b l k are set to 3, 4, 6, 3, 3, 4, and 6, respectively. + +
Layer NameLayer ArchitectureOutput Size
$1 \times 1, input\_size=12$ 256
ResNets #1, #2, #3 $\begin{bmatrix} 1 \times 1, 256 \\ 1 \times 1, 64 \\ 1 \times 1, 64 \end{bmatrix} \times n_{bottleneck}$ 256
ResNets #4, #5, #6, #7 $\begin{bmatrix} 1 \times 1, 512 \\ 1 \times 1, 128 \\ 1 \times 1, 128 \end{bmatrix} \times n_{bottleneck}$ 512
$1 \times 1, 512$ 32
$1 \times 1, 32$ 1
+ +U-Net-based Module. We adopt a U-Net architecture [Ronneberger et al. 2015] as the backbone for predicting rotation angles. To address the vanishing gradient issue in deep networks, we incorporate ResNet blocks [He et al. 2016] as the core components of the U-Net. As shown in Fig. 10, our network consists of ResNet blocks (ResNets) and fully connected layers (FC), with all layers implemented using MLPs. A detailed configuration of each ResNet block is provided in Tab. 1. + +Parameter Setting. In this paper, we set the weights as follows based on our tailored configurations: $\lambda _ { \mathrm { E } } = 5 0 , \lambda _ { \mathrm { D M } } = 7 0 0 0 , \lambda _ { \mathrm { D N M } } =$ 600, $\lambda _ { \mathrm { A N } } = 3 , \lambda _ { \mathrm { A P } } = 1 0 .$ , and $\lambda _ { S } = 3 0$ . The annealing factor � remains 1 during the initial 20% of iterations, then linearly decreases to $3 \times 1 0 ^ { - 4 }$ from 20% to 40% of the iteration span, and finally drops to 0 towards the end. Throughout the training phase, we apply the Adam optimizer [Kingma and Ba 2014] with a default learning rate of $5 \times 1 0 ^ { - 5 }$ and complete 10,000 iterations. + +Quad Mesh Extraction. The extraction of the quad mesh from our cross field follows a two-step scheme, as detailed in references Bommes et al. [2009], Ebke et al. [2013], and Dielen et al. [2021], to achieve a high-quality outcome. This process begins with a step of parametrization based on our cross field. In implementation, we utilize the global-seamless parametrization technique from libigl [Jacobson et al. 2017] to align the parametrization with our cross field. Subsequently, we employ libQEx [Ebke et al. 2013] to extract the quad mesh from this parameterization. + +## 4 EXPERIMENTS + +Evaluation Metrics and Platform. To evaluate the accuracy of the quad mesh, we utilize four primary metrics [Huang et al. 2018; Wang et al. 2023]: area distortion (Area), angle distortion (Angle), the number of singularities (# of Sings), chamfer distance (CD), and Jacobian Ratio (JR). The area distortion metric, scaled by 10,000, represents the standard deviation of the areas of the quadrilateral faces within a mesh. The angle distortion is quantified using the formula $\begin{array} { r } { \sqrt { \frac { 1 } { N } \sum _ { i } ( \phi _ { i } - \frac { \pi } { 2 } ) ^ { 2 } } } \end{array}$ , where the summation extends over all angles $\phi$ in the quad mesh, and � denotes their count. Chamfer distance, scaled by 10,000 and calculated using the �1-norm, quantifies the similarity between two surfaces. The Jacobian Ratio quantifies the uniformity of local deformation in quadrilateral elements. It is defined as the ratio of the smallest to the largest determinant of the Jacobian matrices at element corners, providing a dimensionless measure from 0 (degenerate element) to 1 (perfect parallelogram). The experiments detailed in this paper were executed on an NVIDIA GeForce RTX 3090 graphics card equipped with 24GB of video mem ory and powered by an AMD EPYC 7642 processor. + +![](images/d3234236f683909e2ffd9df3f83a583e3333e2acd52920c683db8773aa05bf28.jpg) +Fig. 11. Quad meshes generated by NeurCross and four other methods on the table model in the ShapeNet dataset [Chang et al. 2015]. + +Datasets. We carry out quad mesh generation experiments on two popular datasets: ShapeNet [Chang et al. 2015] and Thingi10K [Zhou and Jacobson 2016]. To maintain uniformity in evaluation, all input meshes are scaled to fit within the range of $[ - 0 . 5 , 0 . 5 ] ^ { 3 }$ ensuring a consistent and fair basis for comparison across all datasets. + +## 4.1 Comparison on Open Datasets + +We assess the eficacy of our proposed method, NeurCross, by con ducting evaluations on two distinct datasets and comparing its performance against four contemporary state-of-the-art quadrilateral mesh generation methods. For the three methods, namely Instant Meshes (IM) [Jakob et al. 2015], QuadriFlow [Huang et al. 2018], and QuadWild [Pietroni et al. 2021], we employed the open-source imple mentations that are readily available. It is worth noting that Quad Wild [Pietroni et al. 2021] is primarily a quadrangulation method rather than a cross field generation approach. The Mixed-Integer Quadrangulation (MIQ) method [Bommes et al. 2009] does not re lease its source code; therefore, we use the implementation provided by libigl [Jacobson et al. 2017]. However, the available implementation does not support the feature alignment constraint. For a fair comparison with MIQ, we employ the same parameterization and extraction techniques, namely global-seamless parameterization and libQEx [Ebke et al. 2013]. + +ShapeNet Dataset. The ShapeNet dataset [Chang et al. 2015] con sists of a diverse range of human-made models. As the global seamless parametrization from libigl [Jacobson et al. 2017] cannot handle non-manifold meshes, we use manifold ShapeNet meshes repaired with DualOctreeGNN [Wang et al. 2022a]. We apply our + +Table 2. Quantitative comparison on the ShapeNet dataset [Chang et al. 2015]. Within each column, the best scores are emphasized with bold and underlining (best), whereas the second-best scores are highlighted in bold (second best). The quad mesh generated by all the methods comprises an average of 6,000 vertices and 12,000 faces. + +
Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
IM [Jakob et al. 2015]1.5711.78200.528.970.70
QuadriFlow [Huang et al. 2018]2.2813.2491.5850.180.65
QuadWild [Pietroni et al. 2021]1.5211.0593.0410.340.73
MIQ [Bommes et al. 2009]5.2312.89 $\underline{82.12}$ 8.250.58
NeurCross (Ours) $\underline{1.48}$ $\underline{9.85}$ 85.32 $\underline{8.03}$ $\underline{0.78}$
+ +Table 3. Quantitative comparison on the Thingi10K dataset [Zhou and Jacobson 2016]. The quad mesh generated by all methods comprises an average of 10,000 vertices and 20,000 faces. Within each column, the best scores are emphasized with bold and underlining (best), whereas the secondbest scores are simply highlighted in bold (second best). + +
Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
IM [Jakob et al. 2015]1.4510.57397.189.830.75
QuadriFlow [Huang et al. 2018]1.5812.3978.3226.890.72
QuadWild [Pietroni et al. 2021]1.4010.1685.1128.120.77
MIQ [Bommes et al. 2009]1.389.8566.548.570.67
NeurCross (Ours)1.339.6868.968.220.81
+ +NeurCross to three randomly selected categories—airplane, bench, and cabinet—which together contain 7433 models. For a fair comparison, all generated quad meshes are standardized to contain an average of 6,000 vertices and 12,000 faces. + +In Fig. 11, we display the quad meshes generated by our Neur-Cross alongside four other methods. For this example, although IM [Jakob et al. 2015] produces a regular quadrilateral mesh, the outcome includes some triangular elements. More comparisons between IM and our method will be provided in Sec. 4.2. Quadri-Flow [Huang et al. 2018], MIQ [Bommes et al. 2009], and Quad-Wild [Pietroni et al. 2021] generate some misaligned quadrilateral elements, as seen in the highlighted windows. In contrast, our method yields a better quadrilateral mesh. Tab. 2 shows the quantitative comparison of our method against the four approaches. + +Thingi10K Dataset. The Thingi10K dataset [Zhou and Jacobson 2016] features a variety of shapes with intricate geometric details. For our analysis based on Thingi10K, we tested 1,000 randomly selected triangle meshes from the dataset, which were also used as inputs for all comparative methods. The quad meshes generated by all methods contain, on average, 10,000 vertices and 20,000 faces to maintain fidelity to the original models. + +![](images/4bd962ed3e1ea479a69cd57aaa89aea978fc3daa34396d7fca61a84b739dc821.jpg) +Fig. 12. Quad meshes generated by NeurCross and four other methods on a cup model in the Thingi10K dataset [Zhou and Jacobson 2016]. + +![](images/b6825fb9918d39e8f312f63ebde7015297c773d90604b0c047d02e8edfaa2917.jpg) + +
+natural_image + +Three 3D wireframe models of a vase-like object with mesh surfaces and bounding boxes, no text or symbols present. +
+ +IGM + +![](images/cbbcd70cf0c8a4de657d5efa22dead0fda074d25d931b0c002ea85bc1e994a9f.jpg) + +
+natural_image + +3D wireframe model of a vase-like object with geometric cutouts, no visible text or symbols +
+ +IM + +![](images/baf456f6bdcd214dad0d890be2800e3964714f633be8628e3770db97cb1055e1.jpg) + +
+natural_image + +3D wireframe model of a jug with mesh structure and inset showing cross-section (no text or symbols) +
+ +QuadriFlow + +![](images/28db9c04fb0fcf8702bba759d2eb75cdcf657149cc0078f6ce4d7a8f2e881c33.jpg) + +
+natural_image + +3D wireframe model of a vase with a square inset showing internal mesh structure (no text or symbols) +
+ +QuadWild + +![](images/420ade657de8989f3176bc463fc7bd07e12456c84a98fe49420edf0c949fd573.jpg) + +
+natural_image + +3D wireframe model of a knitted object with mesh grid and inset showing circular pattern (no text or symbols) +
+ +MIQ + +![](images/a49940b47cae5d6b5f8214fcb31435795d190291761b2e30327d7f4e52b661b8.jpg) + +
+natural_image + +3D wireframe model of a jug with mesh structure and inset showing mesh grid (no text or symbols) +
+ +NeurCross (Ours) +Fig. 13. Comparison with five state-of-the-art methods using data provided in IGM [Bommes et al. 2013a]. + +Quantitative comparison statistics are presented in Tab. 3. Our method consistently outperforms others on average across this dataset. Interestingly, MIQ [Bommes et al. 2009] shows commend able performance on this dataset. However, it is important to note that despite this improvement, the issue of producing distorted quadrilaterals in the resulting quad mesh remains (see Fig. 12 and the JR metric in Tab. 3). Quadwild [Pietroni et al. 2021] requires smoothing of the generated quad mesh, which compromises geo metric details and increases the Chamfer Distance (CD). In contrast, our method produces a more intuitive cross field without needing to introduce excessive singular points (see zoom-in windows in Fig. 12). + +![](images/47770f35d9ed1106c7301a54173f218e014bca3011454c5bc1bee39658e9a82d.jpg) +Fig. 14. Comparison with five methods on Human Body data. Dielen et al. [2021] proposed a supervised learning-based approach designed to generate quad meshes on human body data from the FAUST dataset [Bogo et al. 2014]. Due to the absence of available open-source data, the comparison result in the upper left is taken from Dielen et al. [2021]’s paper. + +## 4.2 Further Comparison + +Comparison with IGM. IGM [Bommes et al. 2013a] is characterized as a global approach, primarily focused on the joint optimization of parametrization with integer constraints. Like our method, it also utilizes libQEx [Ebke et al. 2013] for extracting quad meshes from the parametrization. Although IGM provides full control over edge alignment and singularity placement, yielding high-quality quad meshes, its lack of scalability can lead to severely distorted quadrilaterals (see Fig. 13). + +Comparison with Learning Methods. Dielen et al. [2021] represents a pioneering efort in quad mesh generation through deep learning methodologies. Their method uses a supervised network architecture to predict the frame field, comprising both a global network and a local network for field prediction. Subsequently, the parametrization-based quadrangulation method proposed in Campen et al. [2015b] is employed to generate the quad meshes. + +![](images/9a2a08412c7f36afe57072ddff0fe3f9e94217d7e42405da1bd0a41660d5d2e9.jpg) + +
+text_image + +Power Fields +PolyVectors +NeurCross (Ours) +
+ +Fig. 15. Comparison of quad meshes generated by Power Fields [Knöppel et al. 2013], PolyVectors [Diamanti et al. 2014], and NeurCross. + +![](images/d50c48406bee2d709601f7f465d5f6fa5f4213fde40647fff6c37e264cb82ed2.jpg) + +
+natural_image + +3D wireframe models of mechanical components with grid patterns, comparing IM and NeurCross (Ours) methods (no text or symbols on models) +
+ +Fig. 16. Comparison with IM. Here, the same approach—applying globa seamless parameterization [Jacobson et al. 2017] and libQEx [Ebke et al. 2013]— is used to extract quadrilateral meshes from the respective cross fields of IM and our NeurCross. +![](images/126bc8f58e5f3485846f850a50b2649ddfb2993725588b3f92a55d5c9b04b7bd.jpg) + +
+text_image + +Quad Remesher +NeurCross (Ours) +
+ +Fig. 17. Comparison of quad meshes generated by Quad Remesher [Remesher 2019] and NeurCross. + +However, due to the inherent constraints ofsupervised learning, this approach shows optimal performance only on the FAUST dataset [Bogo et al. 2014], a limitation not encountered by our self-supervised method. Owing to a lack of required data, our comparison is limited to the model presented in their paper (see Fig. 14). + +Comparison with PowerFields andPolyVectors. Power Fields [Knöppel et al. 2013] eficiently constructs smooth n-direction fields on surfaces by solving a sparse eigenvalue problem, ensuring global optimality and high-quality results. PolyVectors [Diamanti et al. 2014] extends N-RoSy fields to N-PolyVector fields by relaxing orthogonality and symmetry constraints, enabling their computation via a sparse linear system without integer variables. Both methods focus on eficient computation of directional fields, with Power Fields [Knöppel et al. 2013] optimizing smoothness and PolyVectors [Diamanti et al. 2014] generalizing traditional field representations. Fig. 15 compares the quadrilateral meshes generated by our NeurCross and these methods. NeurCross not only aligns with principal curvatures but also preserves overall smoothness. + +![](images/c200ed43f6ebfd0324524a22617394ea94113b8b0a6584c9d0aa81ee90ce1d51.jpg) + +
+surface_3d + +| Method | Description | +| --- | --- | +| Input | White 3D model with a curved base structure. | +| IM | Red 3D model with a curved base structure. | +| QuadriFlow | Blue 3D model with a curved base structure. | +| QuadWild | Red 3D model with a curved base structure. | +| MIQ | Blue 3D model with a curved base structure. | +| NeurCross (Ours) | Blue 3D model with a curved base structure. | +
+ +Fig. 18. Approximation accuracy. Here we show the approximation errors between the input surface and the final quad meshes generated by diferent methods. The error is measured from each sampled point on the quad mesh to the input surface. + +Comparison with IM. IM [Jakob et al. 2015] is an efective method for generating quad meshes. To facilitate a fair comparison between IM and our approach, we use the same global seamless parameterization and extraction technique (libQEx [Ebke et al. 2013]) to extract the quad mesh. As shown in Fig. 16, our method produces fewer singularities than IM. Additionally, our method outperforms IM [Jakob et al. 2015] in terms of principal direction alignment and structural integrity, as illustrated in the close-up views. + +Comparison with Quad Remesher. Quad Remesher [Remesher 2019] excels at generating quadrilateral meshes and is available as a plugin for software like Blender. It is stable, eficient, and effective at preserving model features while maintaining topological uniformity, with our method achieving comparable results. However, its performance depends heavily on the quality of the input mesh, producing low-quality quadrilateral meshes when the input polygonal mesh is suboptimal (see Fig. 17). + +Fidelity. In practical applications, when converting a shape from a triangular mesh to a quadrilateral mesh representation, the goals extend beyond minimizing area distortion, angle distortion, and the number of singular points; maintaining fidelity to the original shape is also crucial. Recognizing that a low-resolution quad mesh may naturally lose some details, we use various methods to generate a quad mesh containing 25,000 vertices and 50,000 faces for a more detailed comparison. + +In Fig. 18, we present the approximation errors between the quad meshes generated by five methods and the input triangle mesh. The quad meshes generated by our NeurCross and MIQ [Bommes et al. 2009] faithfully represent the original input. IM [Jakob et al. 2015] and QuadriFlow [Huang et al. 2018] exhibit minor shape distortions, whereas QuadWild [Pietroni et al. 2021] produces a smoother result, leading to a loss of detail. + +![](images/9af987df6afa7a322ff8f63778cc4ce9ec84c169acfdbe45be82b0cd71ba9017.jpg) +IM + +![](images/c685e1f0176cdeaa12ec815ade19430481b8f4c34964886679303fe7a9629372.jpg) +QuadriFlow + +![](images/772533f96bbff2eb87f0f94932bfcda08985573e9999e99db04f3595e3689f47.jpg) +QuadWild + +![](images/e32263b5421af267dcd1f695c7f75720768fa2a9b9939afe44b2f47b893894b5.jpg) +MIQ + +![](images/86b4b50cbd299c636eeba84c156d0b3d31a57d3ab63fc1cba378e142be434145.jpg) +NeurCross (Ours) + +Fig. 19. The top row shows the cross field generated by our method and four other methods on a noisy input mesh. The botom row shows the resulting quad meshes produced by each approach. Note that MIQ fails to produce a valid result for this input surface with noise. +![](images/16dee25d509d1d8d63202d824b6568049f1f82a746504f2fd3fac5ff3651bf64.jpg) +Fig. 20. Quad meshes generated by all the methods on two models from ShapeNet [Chang et al. 2015] (the airplane model) and Thingi10K [Zhou and Jacobson 2016] (the grayloc model). We also show the locations of singular points, where “# of Sings” denotes the number of singular points on each quad mesh. + +Resistance to Noise. As noted in Wang et al. [2023], Wang et al. [2024], and Dong et al. [2024], the Hessian matrix possesses intrinsic smoothing properties. Benefiting from this characteristic, our method demonstrates inherent resistance to noise in cross field prediction. We used a baseline mesh with 15,000 vertices and introduced Gaussian noise (i.e., 2% relative to the normal direction of each model) to test the noise immunity of our NeurCross. For a comprehensive comparison, we evaluated the four other methods under the same noise conditions. + +In Fig. 19, we present the results of diferent methods under noisy input. Notably, our approach optimizes the SDF and the cross field simultaneously. As a result, during optimization, the underlying SDF naturally smooths out noise, leading to a more intuitive cross field. In summary, our method demonstrates stronger noise resistance compared to four other methods. + +Singular Points. It’s well acknowledged that a trade-of must be achieved between reducing singular points and aligning with principal directions. Thus, it’s preferable to position singular points in regions with high curvature variation rather than in flatter areas. As observed in Tab. 2, Tab. 3, and Fig. 20, our method produces a slightly higher number of singular points compared to MIQ [Bommes et al. 2009]. This occurrence can be attributed to MIQ’s tendency to produce distorted quadrilaterals, which consequently reduces the occurrence of singular points as well as area and angular distortions. However, MIQ’s quad mesh lacks overall consistency and tends to oversmooth areas with significant changes in the direction of the cross field. + +In Fig. 20, we visualize the locations of singular points in the quad meshes generated by all methods on two models. The placement of singular points in the quad mesh generated by our method is more reasonable, and the resulting quadrilateral mesh exhibits high overall consistency. + +Geometrically Complex Models. Various complex geometric models, such as triangular meshes with high genus, thin shells, or nonorientable surfaces, are common in many fields. In Fig. 21, we display + +![](images/dff8a0b78248ca6769c6831eae6983736f3ddc1694cf9e2a7b5de7ae4cd9893e.jpg) +IM + +![](images/f8ef2c30199fc58a342f7a58868c1c866353e25dbd178c8afbdde2e0bacd980c.jpg) +QuadriFlow + +![](images/de59dc2aca23a57eec2683f60b7f1b52cd128a449350af0692087b743987e366.jpg) +QuadWild + +![](images/e17009ff1b7da345b7a8166963a66727e4a7d1a544fa97b9096c62d02576a39a.jpg) +MIQ + +![](images/29c4f30a1150810fba89f4d08559ab15b11f482c74c84b6f6244d48b7e6d2317.jpg) +NeurCross (Ours) + +Fig. 21. Comparison of quad meshes generated by various methods for some challenging models, i.e. with high genus, thin shells, and non-orientable rings Across all tests, the quad meshes generated by NeurCross consistently exhibit higher quality compared to those produced by other methods. +![](images/82282e58612d24db85d424cbd4f9ace54d12c5adc061f798b70f69955fbbbdeb.jpg) +(a) Open boundaries (b) Feature lines (c) Free-form model +Fig. 22. Quad meshes extracted by NeurCross using diferent mesh extraction methods for various models: (a) A garment with open boundaries; (b) A CAD model with feature lines; and (c) A free-form model. The results are presented for each extraction method with or without the localized patching mechanism (LPM). + +the quad meshes generated by our method and other methods on sev eral geometrically complex models. The visualization results show that our method’s performance on the unoriented ring model is comparable to that of IM [Jakob et al. 2015] and QuadriFlow [Huang et al. 2018]. However, for the other two models, only our method consistently produces high-quality quad meshes. Specifically, on the model with a thin shell (the leaf model), only our method and MIQ [Bommes et al. 2009] managed to avoid surface damage. While MIQ produced distorted quadrilaterals at the boundary of the thin shell, our method maintained good overall consistency in the quadrilateral meshes. Fig. 26 shows more results generated by our Neur-Cros on challenging models. + +![](images/8cb9e9130675bfac20d29de5b46d07fa94de2c1b0193f562e6b31251ae567eab.jpg) +(a) w/o $\mathcal { L } _ { \mathbf { A P } }$ +(b) w/o $\mathcal { L } _ { \pmb { s } }$ +(c) w/o $\mathcal { L } _ { \mathbf { A P } }$ & $\mathcal { L } _ { \pmb { S } }$ +(d) Ours +Fig. 23. The quad meshes and cross fields generated by our NeurCross using various loss term combinations: (a) without the alignment with principa directions loss term (w/o L ); (b) without the smoothness loss term (w/o $\mathcal { L } _ { \mathbb { S } } ) ;$ (c) without both (w/o L & $\mathcal { L } _ { \mathbb { S } } ) ;$ and (d) with both (Ours). + +![](images/ab4084d217d8303fbd00db4e658d66f92537fbc607146b7a4a86caba029e47b0.jpg) + +
+natural_image + +Grid-based 3D wireframe models of human figures and objects, no text or symbols present +
+ +Fig. 24. Quad meshes generated by our NeurCross at diferent resolutions. The low-resolution models contain fewer than 1,000 vertices, while the high resolution models consist of over 5,000 vertices. + +Table 4. Ablation studies on the alignment with principal directions loss term $\mathcal { L } _ { \mathsf { A P } }$ and the smoothness loss term $\mathcal { L } _ { S }$ + +
Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
ShapeNet[Chang et al. 2015]w/o $\mathcal{L}_{\text{AP}}$ 1.5911.9689.968.050.75
w/o $\mathcal{L}_{\text{S}}$ 1.9615.12113.288.090.71
w/o $\mathcal{L}_{\text{AP}}$ & $\mathcal{L}_{\text{S}}$ 2.2520.73238.718.150.55
NeurCross (Ours)1.489.8585.328.030.78
Thingi10K[Zhou and Jacobson 2016]w/o $\mathcal{L}_{\text{AP}}$ 1.4811.8973.798.250.79
w/o $\mathcal{L}_{\text{S}}$ 1.8715.03105.378.290.73
w/o $\mathcal{L}_{\text{AP}}$ & $\mathcal{L}_{\text{S}}$ 2.2120.67225.188.310.58
NeurCross (Ours)1.339.6868.968.220.81
+ +## 5 ABLATION STUDIES + +## 5.1 Extraction Methods + +As discussed in Section 4.1, the global parameterization techniques in libigl [Jacobson et al. 2017] fail to align parameterized lines with sharp feature lines. To address this, we adopt QuadWild [Pietroni et al. 2021], leveraging the marked sharp features from Sec. 3.3 to divide the surface into patches using the localized patching mecha nism (LPM) [Pietroni et al. 2021], and using our cross field to guide the patch tessellation process. + +As illustrated in the bottom row of Fig. 22, NeurCross can successfully generate feature-aligned quadrilateral meshes, which is particularly beneficial for CAD models. For free-form models, the localized patching mechanism (LPM) [Pietroni et al. 2021] introduces singularities at the junctions of adjacent patches and even produces malformed quadrilaterals. Therefore, we generally rely on the global parameterization methods from libigl [Jacobson et al. 2017], unless the user explicitly requires the alignment of parameterized lines with sharp feature lines, in which case we employ the localized patching mechanism (LPM) [Pietroni et al. 2021]. + +## 5.2 Cross Field Loss Terms + +To further highlight the eficacy of our cross field loss terms in quad mesh generation, we conducted a comparative analysis by disabling these loss terms. We used the ShapeNet [Chang et al. 2015] and Thingi10K [Zhou and Jacobson 2016] datasets for testing and comparison, setting the weight $\lambda _ { \mathrm { A P } }$ of the alignment with principal directions loss term, the weight $\lambda _ { \mathrm { { S } } }$ of the smoothness loss term, or both, to zero, while keeping other settings unchanged. + +Fig. 23 illustrates the quadrilateral meshes and cross field generated by our method under various loss term combinations. The results show that our method produces the highest quality quadrilateral meshes. Disabling the alignment with principal directions term $\mathcal { L } _ { \mathrm { A P } }$ maintains only local correlation and lacks overall consistency. Although the mesh generated without the smoothness term $\mathcal { L } _ { S }$ shows some degree of overall consistency, it is prone to producing singular points due to the absence of constraints on the local cross field. Without constraints from neither $\mathcal { L } _ { \mathrm { A P } }$ nor $\mathcal { L } _ { \mathrm { S } } ,$ the resulting quadrilateral mesh exhibits both aforementioned defects. The quantitative results presented in Tab. 4 align with the qualitative findings in Fig. 23, further demonstrating the superiority of our method in generating quadrilateral meshes. + +## 5.3 Resolution of Quad Mesh + +In real-world applications, selecting the appropriate resolution for quad mesh extraction depends on the specific requirements of different tasks. In Fig. 24, we use the same cross field for both lowand high-resolution quad meshes, ensuring consistent placement of singular points. Interestingly, the low-resolution mesh better high lights the positioning of these singular points. Fig. 24 demonstrates that, in our approach, most singular points are strategically located in regions with high curvature rather than in flat areas. + +## 6 LIMITATION + +A significant limitation of the self-supervised optimization is its substantial time requirement. For a triangular mesh input with 50,000 faces, each iteration takes 68.34 ms, with a default setting of 10,000 iterations. However, for geometrically simple and regular shapes, NeurCross typically converges in fewer iterations to produce highquality quadrilateral meshes (see the top row of Fig. 25), whereas complex shapes may require additional iterations to achieve comparable results (see the bottom row of Fig. 25). + +![](images/6a649330551fcd77dfaed364df6f9c80b06ebe0f637b6cf540fb6808abd13a3c.jpg) + +
+natural_image + +Grid-based 3D model of a human figure with labeled iteration counts (500, 1k, 5k, 10k), no text or symbols present. +
+ +Fig. 25. Trend of convergence. Quad meshes generated by our NeurCross with diferent numbers of iterations (#iter). + +A promising future direction is to leverage this approach to gen erate ample training data for feeding generative models, such as MeshGPT [Siddiqui et al. 2024]. This would enable users to obtain high-quality quad meshing outcomes instantly. + +## 7 CONCLUSION + +In this paper, we propose a self-supervised neural representation of the cross field for quadrilateral mesh generation. To the best of our knowledge, this is the first self-supervised approach for this task. Our network, named NeurCross, consists of two modules: one to fit the SDF and another to predict the cross field. The design of our loss function addresses three key aspects: surface approximation quality, alignment with principal directions, and the spatial smooth ness of the cross field. Leveraging our network, the SDF and cross field are optimized simultaneously, achieving a desirable balance between approximation accuracy and cross field smoothness. Experimental results consistently validate improvements in singular point placement and in the approximation accuracy between the input triangular surface and the output quad mesh. + +## ACKNOWLEDGMENTS + +The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the National Key R&D Program of China (2022YFB3303200), the Na tional Natural Science Foundation of China (U23A20312, 62272277, 62102380), the Shandong Provincial Natural Science Foundation (ZR2024MF083), the Innovation and Technology Commission of the HKSAR Government under the InnoHK initiative (TransGP project) and the ITSP-Platform grant (Ref: ITS/335/23FP), and the Research Grants Council of Hong Kong (Ref: 17210222). + +## REFERENCES + +Yizhak Ben-Shabat, Chamin Hewa Koneputugodage, and Stephen Gould. 2022. DiGS: Divergence guided shape implicit neural representation for unoriented point clouds. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). + +Federica Bogo, Javier Romero, Matthew Loper, and Michael J. Black. 2014. FAUST: Dataset and Evaluation for 3D Mesh Registration. 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+natural_image + +3D wireframe models of various mythical creatures and human figures, no text or symbols present +
+ +Fig. 26. The quad meshes produced by our NeurCross method on challenging models. + +, Vol. 1, No. 1, Article . Publication date: May 2025. \ No newline at end of file diff --git a/papers/markdown/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation/hybrid_auto/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation_content_list.json b/papers/markdown/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation/hybrid_auto/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..c82075d5f97752ae81663aca873087bcb6ca67e2 --- /dev/null +++ b/papers/markdown/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation/hybrid_auto/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation_content_list.json @@ -0,0 +1,3526 @@ +[ + { + "type": "text", + "text": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation", + "text_level": 1, + "bbox": [ + 78, + 94, + 870, + 142 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "QIUJIE DONG, Shandong University, China, The University of Hong Kong, China, and TransGP, China", + "bbox": [ + 78, + 150, + 795, + 167 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "HUIBIAO WEN, Shandong University, China", + "bbox": [ + 81, + 167, + 408, + 184 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "RUI XU, The University of Hong Kong, China", + "bbox": [ + 81, + 186, + 398, + 202 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "SHUANGMIN CHEN, Qingdao University of Science and Technology, China", + "bbox": [ + 81, + 204, + 625, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "JIARAN ZHOU, Ocean University of China, China", + "bbox": [ + 81, + 220, + 441, + 237 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "SHIQING XIN∗, Shandong University, China", + "bbox": [ + 81, + 239, + 401, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "CHANGHE TU, Shandong University, China", + "bbox": [ + 81, + 256, + 403, + 272 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "TAKU KOMURA, The University of Hong Kong, China", + "bbox": [ + 81, + 273, + 470, + 290 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "WENPING WANG, Texas A&M University, United States of America", + "bbox": [ + 81, + 292, + 566, + 306 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ec5c189df3d8309359b7cb1e9ef73d98ec4ded9f2d1c1f1a4a5200bff5643d0d.jpg", + "image_caption": [ + "Fig. 1. Gallery of quad meshes generated with our NeurCros method. NeurCross excels in computing cross field for generating high-quality quad meshes. Its advantages include optimized singular point placement, insensitivity to surface noise and minor surface undulations, and faithful alignment with principa curvature directions and sharp feature curves." + ], + "image_footnote": [], + "content": "3D wireframe models of various 3D geometric structures, including human figures and torus-like forms (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 81, + 320, + 916, + 579 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Quadrilateral mesh generation plays a crucial role in numerical simulations within Computer-Aided Design and Engineering (CAD/E). Producing high quality quadrangulation typically requires satisfying four key criteria. First, the quadrilateral mesh should closely align with principal curvature direc tions. Second, singular points should be strategically placed and efectively minimized. Third, the mesh should accurately conform to sharp feature edges. Lastly, quadrangulation results should exhibit robustness against noise and minor geometric variations. Existing methods generally involve first computing a regular cross field to represent quad element orientations across the surface, followed by extracting a quadrilateral mesh aligned closely with this cross field. A primary challenge with this approach is balancing the smoothness of the cross field with its alignment to pre-computed principal curvature directions, which are sensitive to small surface perturbations and often ill-defined in spherical or planar regions.", + "bbox": [ + 78, + 632, + 482, + 720 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 511, + 632, + 916, + 719 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To tackle this challenge, we propose NeurCross, a novel framework that simultaneously optimizes a cross field and a neural signed distance function (SDF), whose zero-level set serves as a proxy of the input shape. Our joint optimization is guided by three factors: faithful approximation of the optimized SDF surface to the input surface, alignment between the cross field and the principal curvature field derived from the SDF surface, and smoothness of the cross field. Acting as an intermediary, the neural SDF contributes in two essential ways. First, it provides an alternative, optimizable base surface exhibiting more regular principal curvature directions for guiding the cross field. Second, we leverage the Hessian matrix of the neural SDF to implicitly enforce cross field alignment with principal curvature directions, thus eliminating the need for explicit curvature extraction. Extensive experiments demonstrate that NeurCross outperforms the state-of-the-art methods in terms of singular point placement, robustness against surface noise and surface undulations, and alignment with principal curvature directions and sharp feature curves.", + "bbox": [ + 511, + 720, + 916, + 872 + ], + "page_idx": 0 + }, + { + "type": "aside_text", + "text": "arXiv:2405.13745v3 [cs.CV] 9 May 2025", + "bbox": [ + 22, + 260, + 60, + 700 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "∗Corresponding author: Shiqing Xin.", + "bbox": [ + 80, + 734, + 254, + 747 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Authors’ addresses: Qiujie Dong, Shandong University, Qingdao, Shandong, China and The University of Hong Kong, Hong Kong, China and TransGP, Hong Kong, China, qiujie.jay.dong@gmail.com; Huibiao Wen, Shandong University, Qingdao, Shandong, China, ericvein@163.com; Rui Xu, The University of Hong Kong, Hong Kong, China, xrvitd@163.com; Shuangmin Chen, Qingdao University of Science and Technology, Qingdao, Shandong, China, csmqq@163.com; Jiaran Zhou, Ocean University of China, Qingdao, Shandong, China, zhoujiaran@ouc.edu.cn; Shiqing Xin, Shandong University, Qingdao, Shandong, China, xinshiqing@sdu.edu.cn; Changhe Tu, Shandong University, Qingdao, Shandong, China, chtu@sdu.edu.cn; Taku Komura, The University of Hong Kong, Hong Kong, China, taku@cs.hku.hk; Wenping Wang, Texas A&M University, Texas, United States of America, wenping@tamu.edu.", + "bbox": [ + 78, + 762, + 482, + 875 + ], + "page_idx": 0 + }, + { + "type": "footer", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 676, + 893, + 916, + 905 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 78, + 101, + 480, + 152 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "CCS Concepts: • Computing methodologies → Shape analysis; Mesh geometry models.", + "text_level": 2, + "bbox": [ + 78, + 159, + 480, + 186 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Additional Key Words and Phrases: quadrangulation, neural network, cross field, signed distance function, principal curvature", + "bbox": [ + 78, + 191, + 480, + 219 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1 INTRODUCTION", + "text_level": 2, + "bbox": [ + 80, + 234, + 228, + 248 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Quadrangulation is fundamental in both Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) [Bommes et al. 2013b; Vaxman et al. 2016], with significant applications in finite element analysis, isogeometric analysis, character animation, and physics simulations [Bommes et al. 2013a, 2009; Campen et al. 2015a; Jakob et al. 2015; Mu et al. 2023].", + "bbox": [ + 78, + 252, + 480, + 335 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing approaches typically first compute a reliable cross field to represent quad element orientations across the surface, followed by extracting quad meshes aligned closely with the computed field [Bommes et al. 2013a, 2009; Huang et al. 2018; Jakob et al. 2015; Zhang et al. 2020]. Most methods require principal curvature di rections as input. However, computing a desired cross field from principal curvature directions entails meeting four key requirements: First, the quadrilateral mesh should align closely with principal cur vature directions. Second, singular points should be strategically placed and minimized. Third, the mesh should conform accurately to sharp feature edges. Lastly, quadrangulation results should be robust against noise and minor surface variations. These challenges are particularly pronounced in geometrically or topologically complex shapes.", + "bbox": [ + 78, + 335, + 482, + 529 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fig. 2 shows quadrangulation results of some existing methods. As shown, for instance, QuadWild [Pietroni et al. 2021] fails to align properly with principal curvature directions due to an overemphasis on the smoothness of the cross field. Although principal curvature directions provide useful geometric clues, precisely controlling their influence on the inferred cross field is dificult, especially in nearly spherical or planar regions, or on a surface with small undulations, where principal curvature directions become unstable.", + "bbox": [ + 78, + 530, + 480, + 640 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We introduce an optimizable neural signed distance function (SDF) as the underlying shape representation to infer the desired cross field. The neural SDF serves as a proxy for the input shape, which often exhibits unstable principal curvature directions. Opti mizing this SDF alongside the cross field provides a smooth approximation to the input shape, generating a regular principal curvature field to guide cross field generation. More specifically, our joint optimization is guided by three factors: faithful approximation of the optimized SDF surface to the input surface, alignment between the cross field and the principal curvature field derived from the SDF surface, and smoothness of the cross field. We integrate these requirements into a unified neural optimization framework, called NeurCross, that enables simultaneous optimization of the SDF and cross field. Fig. 3 illustrates our method’s success on a dimpled el lipsoid with irregular curvature directions, compared to a naïve two-stage approach that first optimizes an SDF to properly fit the input shape and then uses the curvature field of this fixed SDF to guide the generation of the cross field. The key to the success of our method is its simultaneous optimization strategy that allows the cross field smoothness term to inform the optimal shape of the neural SDF as a proxy surface.", + "bbox": [ + 78, + 641, + 482, + 876 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 513, + 99, + 916, + 156 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Additionally, a key advantage is that the SDF-based shape operator implicitly encodes principal curvature directions, enabling enforcement of alignment between principal curvature directions and the cross field by evaluating whether the cross at each point match well with the eigenvectors of the shape operator, bypassing the need for explicit extraction of principal curvature direction, a step susciptable to unstability in nearly spherical or planar regions.", + "bbox": [ + 513, + 156, + 916, + 253 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We implement NeurCross using a SIREN-based [Sitzmann et al. 2020] module for SDF fitting and a U-Net-based [Ronneberger et al. 2015] module for cross field prediction. Over 10,000 iterations, both components are optimized simultaneously to satisfy quadrangulation criteria. Finally, we employ global-seamless parametrization from libigl [Jacobson et al. 2017] aligned with our cross field, followed by quad mesh extraction using libQEx [Ebke et al. 2013]. Fig. 4 illustrates this process. Extensive experiments validate Neur-Cross’s efectiveness, demonstrating improvements in singular point placement, robustness to noise and geometric variations, and approximation accuracy, as shown in the teaser figure.", + "bbox": [ + 513, + 253, + 916, + 405 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows:", + "bbox": [ + 529, + 406, + 808, + 417 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose NeurCross, the first self-supervised neural network for learning cross fields.", + "- We implicitly enforce cross field alignment with principal curvature directions via an SDF-based shape operator, naturally addressing potential ambiguity.", + "- We leverage an optimizable neural SDF as an underlying representation to coordinate requirements, dynamically adjusting to minor surface variations." + ], + "bbox": [ + 540, + 419, + 916, + 529 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 RELATED WORK", + "text_level": 2, + "bbox": [ + 514, + 542, + 660, + 556 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This paper focuses on developing a neural representation of the cross field for quadrilateral mesh generation. In this section, we review two main categories of related work: quad mesh generation techniques and neural SDF representations.", + "bbox": [ + 513, + 561, + 916, + 616 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1 Quad Mesh Generation", + "text_level": 2, + "bbox": [ + 514, + 622, + 712, + 636 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Quadrilateral mesh generation has attracted significant attention in recent years. While some methods, such as Dual Marching Cubes (DMC) [Nielson 2004], can directly extract quad facets without relying on direction fields, the resulting meshes often lack quality, particularly in aligning with principal directions. Most state-of-theart approaches rely on a cross field [Lai et al. 2010; Palmer et al. 2021; Ray et al. 2008] to guide the generation of high-quality quad meshes, as it ensures edge alignment and proper placement of irregular vertices. Typically, after computing a cross field, a parameterization step [Bommes et al. 2009; Chien et al. 2016; Levi and Zorin 2014; Myles et al. 2014] aligns gradients with the direction field and traces integer iso-lines across multiple charts [Ebke et al. 2013]. Although several robust quadrangulation methods [Dong et al. 2006; Gurung et al. 2011; Ling et al. 2014; Owen et al. 1999; Remacle et al. 2012; Velho and Zorin 2001; Zhang et al. 2010] operate independently of direction fields, they often fail to achieve global smoothness. Below, we review related works on direction fields.", + "bbox": [ + 511, + 640, + 916, + 875 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2", + "bbox": [ + 81, + 69, + 91, + 78 + ], + "page_idx": 1 + }, + { + "type": "header", + "text": "Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang", + "bbox": [ + 112, + 68, + 715, + 80 + ], + "page_idx": 1 + }, + { + "type": "footer", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 81, + 893, + 321, + 905 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5d8ee6e01f2c6e28b5a490858bdcb70619707e26fa8b94cabb71038b3f0d069c.jpg", + "image_caption": [ + "Fig. 2. Existing approaches typically rely on principal curvature directions as input. However, due to the inherent instability of these directions, current methods often prioritize the smoothness of the cross field at the cost of alignment with the principal curvature directions. To address this limitation, our approach avoids explicitly extracting principal curvature directions. Instead, we assess whether the cross field at each point can function as eigenvectors of the shape operator." + ], + "image_footnote": [], + "content": "", + "bbox": [ + 81, + 94, + 915, + 277 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/cdb36e7fe472f41c69f30ff6a0555ba38ab7aa8254e2b54bd9e90c9af04cad82.jpg", + "image_caption": [ + "(a) Input", + "GT surface" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 81, + 352, + 218, + 412 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/97e0129853317a23ac177a004919fd97745a6927c1b4bcc99af1367275860590.jpg", + "image_caption": [ + "GT curvature field" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 81, + 444, + 218, + 503 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ba2b9b52fbc1a845e1dd3debada5c6166729808cd3ff86628d05c3a77670a3d0.jpg", + "image_caption": [ + "(b) Two-step method" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 251, + 352, + 393, + 412 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b1ad9d112050fb0ab658a4817c97689f3676163fee1383eacd237491e3415cad.jpg", + "image_caption": [ + "(c) Our joint optimization", + "SDF shape" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 254, + 444, + 390, + 502 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/26a08368b289a1788bb03735a0dbb19ce78b304a4380a537bc2354705f053799.jpg", + "image_caption": [], + "image_footnote": [], + "content": "", + "bbox": [ + 429, + 351, + 563, + 411 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f215ec0df7daddca2a9cbcb63a92ef184379279979a0b34084925a13d085f291.jpg", + "image_caption": [ + "Fitting error" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 431, + 444, + 565, + 503 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e06b190c46ba89f80afa3b86bc90c7866478bd6defd38ff2ecf558186e498f1d.jpg", + "image_caption": [], + "image_footnote": [], + "content": "", + "bbox": [ + 570, + 343, + 607, + 402 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/70a65601f6b87a407bbc69bc05ee6bf378c6053b9a1f8a8a3af9085cba2bc355.jpg", + "image_caption": [], + "image_footnote": [], + "content": "", + "bbox": [ + 604, + 354, + 743, + 414 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e5f2577ea0ad09c7aad4dd4e85230f871971d3b796c7ac542479d950cf690ff8.jpg", + "image_caption": [ + "Cross field" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 604, + 444, + 741, + 503 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/add7ac0fb6932a9607a7892ad64969086c64df63b898c7c5eeae7584d59a08d2.jpg", + "image_caption": [], + "image_footnote": [], + "content": "", + "bbox": [ + 777, + 351, + 916, + 412 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e58c62b09e94b1ebce6a4df5d8754660e1d45e4093ae0eb1c3532ee74f8076a7.jpg", + "image_caption": [ + "Quad mesh", + "Fig. 3. (a) The input mesh and its ground-truth principal curvature directions. (b) Two-step optimization: by first precomputing an SDF that precisely fits the input shape, the subsequent optimization step still sufers from sensitivity to minor geometric variations, failing to yield the desired cross field. (c) Joint optimization: by treating the SDF as a proxy for the input shape, simultaneous optimization of the SDF and the cross field allows the SDF to approximate the input shape while remaining robust to minor geometric variations, resulting in the desired cross field. We visualize the fiting errors between the SDF surface and the original surface using a color-coded scheme" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 777, + 441, + 916, + 503 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A fundamental requirement for direction fields is to align edge directions with principal curvature directions [Bommes et al. 2013a, 2009; Fang et al. 2018; Hertzmann and Zorin 2000; Huang et al. 2018; Jakob et al. 2015; Kälberer et al. 2007; Lyon et al. 2019; Vaxman et al. 2016]. Lai et al. [2008] proposed an iterative relaxation scheme that incrementally aligns mesh edges with principal directions, though it requires additional post-processing to refine results. Jakob et al. [2015] introduced a unified local smoothing operator that optimizes both edge orientations and vertex positions in the output quad mesh. QuadriFlow [Huang et al. 2018] improved upon In stant Meshes [Jakob et al. 2015] by introducing linear and quadratic constraints, reducing singularities but struggling to preserve the original shape. Several methods [Bommes et al. 2013a; Huang et al. 2018; Jakob et al. 2015] optimize parametrization while incorporating integer constraints, a challenging mixed-integer programming (MIP) problem [Bommes et al. 2009] that is computationally inten sive. These methods typically aim to minimize distortion and reduce singularities [Bommes et al. 2013a; Levi and Zorin 2014; Myles et al.", + "bbox": [ + 78, + 607, + 483, + 857 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2014; Myles and Zorin 2013]. To address the computational complexity of IGM [Bommes et al. 2013a] on complex meshes, Ebke et al. [2016] proposed a framework using eficient decimation and coarse-to-fine mapping to improve interactive performance. Dielen et al. [2021] introduced a learning-based approach for predicting di rection fields, demonstrating its potential for quad mesh generation. However, its reliance on domain-specific networks and canonical alignment limits its generalizability and robustness to non-rigid changes.", + "bbox": [ + 511, + 607, + 916, + 732 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2 Neural SDF", + "text_level": 2, + "bbox": [ + 514, + 746, + 633, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The Signed Distance Function (SDF) is a widely used geometric representation in computer graphics, particularly for surface reconstruction. For example, radial basis functions (RBF) [Carr et al. 2001] approximate the SDF, enabling the extraction of the target surface as the zero-isosurface of the SDF.", + "bbox": [ + 513, + 763, + 916, + 833 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SDFs have also been extensively employed in deep learning-based surface reconstruction, including supervised implicit surface reconstruction methods [Erler et al. 2020; Huang et al. 2022; Park et al.", + "bbox": [ + 513, + 834, + 916, + 876 + ], + "page_idx": 2 + }, + { + "type": "header", + "text": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation", + "bbox": [ + 475, + 68, + 882, + 79 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3", + "bbox": [ + 906, + 69, + 915, + 78 + ], + "page_idx": 2 + }, + { + "type": "footer", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 676, + 893, + 915, + 904 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/989c51839f42396f1b4f800d0b8e5c888127938bec1e4096e97283a8a61ea47d.jpg", + "image_caption": [ + "(a) Triangle mesh" + ], + "image_footnote": [], + "content": "3D wireframe model of a complex, irregularly shaped mechanical structure (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 81, + 95, + 282, + 210 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cbfe4482b9c604d09b696ba6e241b1c391ca9ae535ef812e26dc8b6b3af93bfb.jpg", + "image_caption": [ + "(b) Random initialization" + ], + "image_footnote": [], + "content": "Abstract 3D sculpture of intertwined human figures in a dynamic pose (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 292, + 97, + 493, + 213 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c1adaa84e307303f5b901506152925de880749120dbe40b2415f36a68a3cd74c.jpg", + "image_caption": [ + "(c) Resultant cross field" + ], + "image_footnote": [], + "content": "3D rendered abstract mechanical structure with colorful grid pattern (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 503, + 97, + 705, + 214 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c877d31cacdb7415b6f448daea08ff7ec3c46527ddb57f1699d7a88ed5571823.jpg", + "image_caption": [ + "(d) Quad mesh", + "Fig. 4. Given the input triangular surface in (a), starting with a randomly initialized cross field in (b), our NeurCross method produces a smooth cross field in (c) that is well aligned with the principal curvature directions of the input surface. We use the global-seamless parametrization from libigl to obtain a parametrization aligned with the computed cross field, and then use libQEx to extract the final quad mesh in (d)." + ], + "image_footnote": [], + "content": "3D wireframe model of a complex geometric structure with no visible text or symbols", + "sub_type": "natural_image", + "bbox": [ + 714, + 95, + 916, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2019] and self-supervised approaches [Ma et al. 2021, 2022; Wang et al. 2021]. For instance, IGR [Gropp et al. 2020] incorporates the Eikonal term to enforce implicit geometric regularization, providing an efective mechanism for surface reconstruction. SIREN [Sitz mann et al. 2020] demonstrates that periodic activation functions are well-suited for representing complex natural signals and their derivatives using implicit neural representations. DiGS [Ben-Shabat et al. 2022] integrates Laplacian energy as a soft constraint for the SDF, proving efective for reconstructing surfaces from unoriented point clouds. Neural-Singular-Hessian [Wang et al. 2023] ensures that the Hessian of the neural implicit function has a zero determinant for points near the surface, which is particularly useful for recovering details from unoriented point clouds. Additionally, Dong et al. [2024] proposed a zero Gaussian curvature constraint for re constructing CAD-type surfaces from low-quality unoriented point clouds. All these methods leverage neural networks to approximate the SDF.", + "bbox": [ + 78, + 287, + 483, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this paper, SDFs play a central role in quad mesh generation, as the Hessian of the SDF fully encodes principal curvatures and their directions [Dong et al. 2024; Wang et al. 2023].", + "bbox": [ + 78, + 522, + 482, + 565 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3 OUR APPROACH", + "text_level": 2, + "bbox": [ + 80, + 580, + 228, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1 Overview", + "text_level": 2, + "bbox": [ + 80, + 599, + 184, + 612 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The core idea of NeurCross is to leverage the optimizable neural Signed Distance Function (SDF) as an underlying representation to coordinate various requirements. On one hand, the adjustable SDF can efectively reduce sensitivity to minor surface variations. On the other hand, the SDF-based shape operator enables us to implicitly evaluate the diference between the principal curvature directions and the cross field. NeurCross consists of two core modules: a surface fitting module and an orientation prediction module, both centered around the SDF.", + "bbox": [ + 78, + 617, + 483, + 742 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(1) Surface Fitting Module: This module aims to represent the input triangular surface using a neural SDF. Its loss incorporates the Dirichlet condition [Lipman 2021], the Eikonal condition [Gropp et al. 2020], and the singular Hessian con dition [Wang et al. 2024] to ensure high fidelity to the input surface geometry. Together, these constraints guarantee an accurate surface representation.", + "(2) Cross Field Prediction Module: This module is designed to represent the cross field while implicitly enforcing alignment" + ], + "bbox": [ + 96, + 750, + 482, + 876 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with principal curvature directions and spatial smoothness. It employs a U-Net architecture [Ronneberger et al. 2015] to predict a rotation angle for each triangular facet, yielding a geometry-aware cross field. Additionally, this module supports explicit alignment with geometric features.", + "bbox": [ + 550, + 287, + 916, + 357 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "These two modules are coordinated through a total loss function, which ensures simultaneous optimization of the SDF and the cross field during the training process. The interaction between the modules allows for dynamic updates to both the surface representation and the cross field, leading to improved accuracy and robustness. The overall network architecture is illustrated in Fig. 5.", + "bbox": [ + 513, + 359, + 916, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Total Loss. Our total loss is defined as follows.", + "bbox": [ + 529, + 446, + 808, + 460 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {L} = \\underbrace {\\lambda_ {\\mathrm{E}} \\mathcal {L} _ {\\mathrm{E}} + \\lambda_ {\\mathrm{DM}} \\mathcal {L} _ {\\mathrm{DM}} + \\lambda_ {\\mathrm{DNM}} \\mathcal {L} _ {\\mathrm{DNM}} + \\tau \\lambda_ {\\mathrm{AN}} \\mathcal {L} _ {\\mathrm{AN}}} _ {\\text {SDF}} + \\underbrace {\\lambda_ {\\mathrm{AP}} \\mathcal {L} _ {\\mathrm{AP}} + \\lambda_ {\\mathrm{S}} \\mathcal {L} _ {\\mathrm{S}}} _ {\\text {Cross Field}}, \\tag {1}\n$$", + "text_format": "latex", + "bbox": [ + 522, + 464, + 916, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where � is the annealing factor [Dong et al. 2024; Wang et al. 2024, 2023]. The individual terms, along with their corresponding weights, will be detailed in the following subsections.", + "bbox": [ + 513, + 500, + 916, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2 SDF Fiting", + "text_level": 2, + "bbox": [ + 514, + 553, + 632, + 568 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let Θ denote the parameters of a neural SDF $f ( \\boldsymbol { x } ; \\Theta ) : \\mathbb { R } ^ { 3 } \\to \\mathbb { R } ,$ where � = 0 approximates the input triangular surface. We begin by sampling the centroid of each triangle, forming a point set P, where each point is associated with a normal vector. In the following, we define a loss term to enforce alignment with the predefined surface normals, while leaving further details to Sec. 3.5.", + "bbox": [ + 513, + 570, + 916, + 654 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "SDF Based Shape Operator. The shape operator of a surface measures the rate of change of the unit normal in any direction, thereby describing how the shape changes in that direction. In diferential geometry, it is very common to assume the surface has a parametric form, such that the shape operator defines a quadratic form on the tangent space, and the eigenvectors of the shape operator correspond exactly to the principal directions. In fact, the Hessian matrix of the SDF is closely related to the shape operator. For a point � on the base surface, the Hessian matrix $H _ { P }$ of the SDF has an eigenvalue of 0, with its corresponding eigenvector being the normal vector $\\mathbf { \\Delta } _ { n _ { P } }$ [Dong et al. 2024; Wang et al. 2024, 2023]. Simultaneously, the other two eigenvectors of $H _ { p }$ correspond to the two principal curvature directions.", + "bbox": [ + 511, + 660, + 918, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Alignment with Predefined Surface Normals. Since for a point � suficiently close to the base surface, the eigenvector corresponding to the zero eigenvalue of the Hessian matrix $H _ { p }$ of the SDF aligns with the normal vector $\\scriptstyle n _ { p }$ at ${ \\pmb \\rho } .$ Given that the normal direction of $\\pmb { p } \\in \\mathcal { S }$ can be directly obtained from the input triangle mesh, we require the neural SDF to align with the predefined surface normal $\\mathbf { \\Delta } _ { n _ { P } }$ as follows:", + "bbox": [ + 514, + 847, + 916, + 876 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4", + "bbox": [ + 81, + 69, + 91, + 78 + ], + "page_idx": 3 + }, + { + "type": "header", + "text": "Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang", + "bbox": [ + 112, + 68, + 715, + 80 + ], + "page_idx": 3 + }, + { + "type": "footer", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 81, + 893, + 321, + 905 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/de77e6dbc3e8b40ddf3fe821e9c18bcdc2eb8f2daed28bf5505c5cbc863228c1.jpg", + "image_caption": [ + "Fig. 5. Our self-supervised network pipeline for representing cross fields in quad mesh generation. All layers in the network are implemented as multi-layer perceptrons (MLPs), with the SDF fiting module utilizing the SIREN [Sitzmann et al. 2020] architecture. The circled $^ { 6 } + \\prime$ symbol denotes a data-combining operation." + ], + "image_footnote": [], + "content": "```mermaid\ngraph LR\n A[\"Input Image\"] --> B[\"Image with Scatter Plot\"]\n B --> C[\"P\"]\n C --> D[\"SDF fitting module\"]\n D --> E[\"Feature Output\"]\n F[\"MLP\"] --> G[\"θ\"]\n G --> H[\"μ, ν\"]\n H --> I[\"⊕\"]\n J[\"L_SDF\"] --> K[\"min L\"]\n K --> L[\"L_CrossField\"]\n L --> M[\"Output Image\"]\n N[\"α = μcosθ + vsinθ\\nβ = vcosθ - μsinθ\"] --> I\n E --> O[\"H\"]\n O --> P[\"⊕\"]\n P --> Q[\"Output Image\"]\n```", + "sub_type": "flowchart", + "bbox": [ + 86, + 93, + 908, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "", + "bbox": [ + 78, + 372, + 482, + 444 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "$$\nH _ {p} \\cdot n _ {p} = 0. \\tag {2}\n$$", + "text_format": "latex", + "bbox": [ + 240, + 450, + 482, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall alignment with predefined surface normals can be quantified as:", + "bbox": [ + 78, + 474, + 483, + 502 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {L} _ {\\mathrm{AN}} = \\frac {1}{| \\mathcal {P} |} \\int_ {\\mathcal {P}} \\left| H _ {\\boldsymbol {p}} \\cdot \\boldsymbol {n} _ {\\boldsymbol {p}} \\right| \\mathrm{d} \\boldsymbol {p}. \\tag {3}\n$$", + "text_format": "latex", + "bbox": [ + 192, + 506, + 482, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3 Cross Field Prediction", + "text_level": 2, + "bbox": [ + 80, + 547, + 267, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Local Coordinate System. Recall that each point $\\pmb { p } \\in \\mathcal { P }$ corresponds to the centroid of a triangular face. The task of computing the cross field involves inferring a pair of orthogonal vectors, $( \\alpha _ { p } , \\beta _ { p } )$ , that align as closely as possible with the principal curvature directions. To achieve this, we assume that each triangle has a pre-defined coordinate system", + "bbox": [ + 78, + 566, + 282, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with two axes, $\\mu _ { p }$ and $\\nu _ { p } ,$ , which are mutually orthogonal unit vectors satisfying $\\mu _ { \\pmb { p } } \\times \\nu _ { \\pmb { p } } = n _ { p }$ . We introduce a rotation angle $\\theta _ { P }$ to represent $\\alpha _ { p }$ and $\\beta _ { p }$ as follows:", + "bbox": [ + 78, + 719, + 482, + 763 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "$$\n\\left\\{ \\begin{array}{l} \\boldsymbol {\\alpha} _ {p} = \\boldsymbol {\\mu} _ {p} \\cos \\theta_ {p} + \\nu_ {p} \\sin \\theta_ {p}, \\\\ \\boldsymbol {\\beta} _ {p} = \\nu_ {p} \\cos \\theta_ {p} - \\boldsymbol {\\mu} _ {p} \\sin \\theta_ {p}. \\end{array} \\right. \\tag {4}\n$$", + "text_format": "latex", + "bbox": [ + 183, + 777, + 482, + 810 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "See the inset figure for an illustration. Notably, $\\alpha _ { p }$ and $\\beta _ { p }$ are natu rally mutually orthogonal unit vectors. As a result, the optimization of the cross field reduces to computing the rotation angle $\\theta _ { P }$ for each triangle.", + "bbox": [ + 78, + 819, + 483, + 878 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implicit Alignment with Principal Directions. An explicit approach to implementing alignment with principal directions involves comparing the cross field with pre-extracted principal directions. However, most existing methods for extracting principal directions heavily rely on local shape variations, which can lead to instability, particularly when the local geometry is approximately planar or spherical. To address this limitation, we adopt an implicit alignment strategy by evaluating the compatibility between the cross field and the shape operator.", + "bbox": [ + 511, + 372, + 916, + 497 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To align the cross field with the principal directions, we encourage $\\alpha _ { p }$ and $\\beta _ { p }$ to coincide with two of the eigenvectors of $H _ { p } .$ . To enforce collinearity between $H _ { P } \\alpha _ { P }$ and $\\alpha _ { p }$ , we impose the following condition:", + "bbox": [ + 513, + 497, + 916, + 551 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "$$\nH _ {p} \\alpha_ {p} \\times \\alpha_ {p} = 0. \\tag {5}\n$$", + "text_format": "latex", + "bbox": [ + 661, + 556, + 916, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similarly, we require:", + "bbox": [ + 514, + 575, + 648, + 590 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "$$\nH _ {p} \\boldsymbol {\\beta} _ {p} \\times \\boldsymbol {\\beta} _ {p} = 0. \\tag {6}\n$$", + "text_format": "latex", + "bbox": [ + 663, + 598, + 916, + 616 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We define the loss term to measure alignment with the principal directions as follows:", + "bbox": [ + 513, + 621, + 916, + 647 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {L} _ {\\mathrm{AP}} ^ {(1)} = \\frac {1}{| \\mathcal {P} |} \\int_ {\\mathcal {P}} \\left| H _ {p} \\boldsymbol {\\alpha} _ {p} \\times \\boldsymbol {\\alpha} _ {p} \\right| + \\left| H _ {p} \\boldsymbol {\\beta} _ {p} \\times \\boldsymbol {\\beta} _ {p} \\right| \\mathrm{d} p. \\tag {7}\n$$", + "text_format": "latex", + "bbox": [ + 568, + 652, + 916, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Smoothness ofthe Cross Field. Consider two pairs of orthogonal unit vectors in a plane, denoted as $( \\pmb { \\alpha } _ { 1 } , \\pmb { \\beta } _ { 1 } )$ and $( \\alpha _ { 2 } , \\beta _ { 2 } )$ . We say that the pair $( \\alpha _ { 1 } , \\beta _ { 1 } )$ aligns with $( \\alpha _ { 2 } , \\beta _ { 2 } )$ if either $\\pmb { \\alpha } _ { 1 }$ and $\\pmb { \\alpha } _ { 2 }$ are colinear, or $\\pmb { \\alpha } _ { 1 }$ and $\\beta _ { 2 }$ are colinear.", + "bbox": [ + 513, + 686, + 916, + 743 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on the above definition, it can be proved that $( \\alpha _ { 1 } , \\beta _ { 1 } )$ aligns with $( \\alpha _ { 2 } , \\beta _ { 2 } )$ if and only if", + "bbox": [ + 513, + 743, + 915, + 771 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "$$\n\\left| \\boldsymbol {\\alpha} _ {1} \\cdot \\boldsymbol {\\alpha} _ {2} \\right| + \\left| \\boldsymbol {\\alpha} _ {1} \\cdot \\boldsymbol {\\beta} _ {2} \\right| + \\left| \\boldsymbol {\\beta} _ {1} \\cdot \\boldsymbol {\\alpha} _ {2} \\right| + \\left| \\boldsymbol {\\beta} _ {1} \\cdot \\boldsymbol {\\beta} _ {2} \\right| \\tag {8}\n$$", + "text_format": "latex", + "bbox": [ + 586, + 777, + 916, + 795 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "achieves the minimum. We explain the correctness as follows. Without loss of generality, we assume that $\\pmb { \\alpha } _ { 1 } = ( 1 , 0 )$ and $\\beta _ { 1 } = ( 0 , 1 )$ . By denoting $\\alpha _ { 2 }$ as (cos �, sin �), the above sum simplifies to", + "bbox": [ + 513, + 801, + 918, + 844 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "$$\n2 (| \\cos \\theta | + | \\sin \\theta |). \\tag {9}\n$$", + "text_format": "latex", + "bbox": [ + 653, + 849, + 916, + 866 + ], + "page_idx": 4 + }, + { + "type": "header", + "text": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation", + "bbox": [ + 475, + 68, + 882, + 80 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5", + "bbox": [ + 906, + 69, + 915, + 78 + ], + "page_idx": 4 + }, + { + "type": "footer", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 676, + 893, + 915, + 905 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e25e014b81e442d4ef1e4de0a12ae3b00366cc55c89de021c24e1ab966faba24.jpg", + "image_caption": [ + "(a) Input mesh" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 89, + 95, + 200, + 181 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/abd18d26b8968f9383ada7d35e09811fa1e6a1fce34a88de24b2504a8e51d81a.jpg", + "image_caption": [ + "(b) Cross field" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 215, + 95, + 325, + 181 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/43e9470e0ad9c0142f03591ec741c2d53247c12dbe072ad34cc88a813ba93a5a.jpg", + "image_caption": [ + "(c) Quad mesh", + "Fig. 6. The smoothness constraint of the cross field beter controls the distribution of singularity points. From left to right: (a) an input triangular mesh; (b) a cross field computed with NeurCross; (c) the quad mesh extracted from the cross field." + ], + "image_footnote": [], + "content": "", + "bbox": [ + 343, + 95, + 454, + 181 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the inset figure, we illustrate how the function value of 2(| cos �| + | sin �|) varies with �. It can be observed that the minimum is achieved at $\\begin{array} { r } { \\theta = k \\frac { \\pi } { 2 } } \\end{array}$ , while the maximum occurs at $\\begin{array} { r } { \\theta = k \\frac { \\pi } { 2 } + \\frac { \\pi } { 4 } } \\end{array}$ . Therefore, it can be concluded that", + "bbox": [ + 78, + 280, + 256, + 390 + ], + "page_idx": 5 + }, + { + "type": "chart", + "img_path": "images/19ff735f8956b3472f74ba727fe052b3bf43920b06e2e28ae05534b0b4d5d9c7.jpg", + "content": "| X | Y |\n| --- | --- |\n| 0 | 2 |\n| \\(\\pi/4\\) | \\(2\\sqrt{2}\\) |\n| \\(\\pi/2\\) | 2 |", + "chart_caption": [], + "chart_footnote": [], + "sub_type": "contour", + "bbox": [ + 259, + 267, + 464, + 388 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "only when the sum reaches the minimum value of 2, one cross aligns with another $\\begin{array} { r } { ( \\theta = k \\frac { \\pi } { 2 } ) } \\end{array}$", + "bbox": [ + 78, + 392, + 480, + 420 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We denote the three neighboring points of $\\pmb { p }$ as ${ \\pmb q } _ { 1 } , { \\pmb q } _ { 2 } , { \\pmb q } _ { 3 }$ . Since each $\\pmb { q } _ { i }$ lies on a neighboring face, a rotation around the common edge is necessary before aligning the directions between � and $\\mathbf { \\nabla } _ { q _ { i } . }$ We define $\\{ R _ { i } \\mid i = 1 , 2 , 3 \\}$ as the rotation matrices associated with dihedral angles $\\{ \\varphi _ { i } \\mid i = 1 , 2 , 3 \\}$", + "bbox": [ + 78, + 420, + 279, + 544 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/37cfd3e08b4e7dde5c6d984906df26a34bccb69c180b9a4d42ab63954739dd03.jpg", + "image_caption": [], + "image_footnote": [], + "content": "q₂\nφ₂\np\nφ₁\nφ₃\nq₃", + "sub_type": "text_image", + "bbox": [ + 282, + 421, + 444, + 530 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and shared edges, which can be precomputed. To this end, the smoothness loss can be written as", + "bbox": [ + 78, + 544, + 480, + 571 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm{S}} = \\frac {1}{3 | \\mathcal {P} |} \\int_ {\\mathcal {P}} \\sum_ {i = 1} ^ {3} \\left(\\left| \\boldsymbol {\\alpha} _ {\\boldsymbol {p}} \\cdot R _ {i} \\boldsymbol {\\alpha} _ {\\boldsymbol {q} _ {i}} \\right| + \\left| \\boldsymbol {\\alpha} _ {\\boldsymbol {p}} \\cdot R _ {i} \\boldsymbol {\\beta} _ {\\boldsymbol {q} _ {i}} \\right| \\right. \\tag {10} \\\\ \\left. + \\left| \\boldsymbol {\\beta} _ {\\boldsymbol {p}} \\cdot R _ {i} \\boldsymbol {\\alpha} _ {\\boldsymbol {q} _ {i}} \\right| + \\left| \\boldsymbol {\\beta} _ {\\boldsymbol {p}} \\cdot R _ {i} \\boldsymbol {\\beta} _ {\\boldsymbol {q} _ {i}} \\right| - 2\\right) \\mathrm{d} \\boldsymbol {p}. \\\\ \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 99, + 575, + 482, + 637 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Remark: Consider a spherical surface, as shown in Fig. 6. At each point on such a surface, the principal curvature directions are not unique. In this case, the smoothness constraint of the cross field plays a crucial role in better controlling the distribution of singular ity points. It is worth noting that our implicit principal curvature alignment is simultaneously satisfied. Moreover, Fig. 6 highlights the importance of efective cross field smoothing, which has also been addressed in prior work. Knöppel et al. [2013] and Diamanti et al. [2014] introduced convex smoothness energies to smooth N-RoSy fields. Knöppel et al. [2013]’s method achieves global optimality but requires a nonlinear transformation, which can cause extra singu larities and distortion. Jakob et al. [2015] uses an extrinsic energy to align with surface features, but its strong reliance on local information often leads to suboptimal results and unwanted singularities. In contrast, our NeurCross smooths the cross field using Equ. 10, introducing singularities only in areas with high curvature variation. A detailed comparison is provided in Section 4.2.", + "bbox": [ + 78, + 640, + 483, + 876 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cbc7bee6d39bd37e82e8ad9181a3ffcf185ff11033690bf3ce6022d134d764c5.jpg", + "image_caption": [ + "(a) w/o feature line const." + ], + "image_footnote": [], + "content": "3D wireframe model of a mechanical part with colored grid lines and highlighted regions (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 526, + 95, + 697, + 229 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5bec5fdbbdbfbb4955d8bbd9684803dea4ea2565e0e233ea4449ecb69823c87a.jpg", + "image_caption": [ + "(b) w/ feature line const.", + "Fig. 7. NeurCross supports feature line constraints. (a) The results without (w/o) the feature line constraint (const.); and (b) The result with (w/) the feature line constraint." + ], + "image_footnote": [], + "content": "3D wireframe model of a furniture or chair with colorful mesh patterns, no visible text or symbols", + "sub_type": "natural_image", + "bbox": [ + 728, + 95, + 901, + 229 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Sharp Feature Alignment. As pointed out in [Pietroni et al. 2021], in the context of quad-meshing, it is important to incorporate feature lines of the input shape, such as crease angles in CAD models, when generating quadrangulation outcomes. However, reconciling this", + "bbox": [ + 513, + 316, + 916, + 372 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "requirement with all other objectives is challenging. Generally, the influence of feature lines diminishes with increasing distance.", + "bbox": [ + 513, + 372, + 669, + 454 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As illustrated in the inset figure, let �� be the feature lines, where the cross field at each point of �� has been specified. We use $d _ { g } ( \\pmb { p } , \\pmb { F } \\pmb { L } )$ to denote the geodesic distance between a surface point � and ��. We introduce", + "bbox": [ + 514, + 455, + 669, + 579 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/417855208b3a5d7940999284be14d590e6abcf29bca0b43d7c1d240b592ec281.jpg", + "image_caption": [], + "image_footnote": [], + "content": "+FL\ndg(p,FL)\np", + "sub_type": "text_image", + "bbox": [ + 676, + 381, + 913, + 565 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "$$\nD _ {\\boldsymbol {p}} = 1 - \\exp \\left(- \\rho_ {\\text {feature}} d _ {g} (\\boldsymbol {p}, F L)\\right), \\tag {11}\n$$", + "text_format": "latex", + "bbox": [ + 607, + 585, + 916, + 602 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and redefine the principal curvature direction alignment as follows:", + "bbox": [ + 514, + 607, + 916, + 622 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {L} _ {\\mathrm{AP}} = \\frac {1}{| \\mathcal {P} |} \\int_ {\\mathcal {P}} D _ {p} \\left(\\left| H _ {p} \\boldsymbol {\\alpha} _ {p} \\times \\boldsymbol {\\alpha} _ {p} \\right| + \\left| H _ {p} \\boldsymbol {\\beta} _ {p} \\times \\boldsymbol {\\beta} _ {p} \\right|\\right) \\mathrm{d} p, \\tag {12}\n$$", + "text_format": "latex", + "bbox": [ + 540, + 626, + 916, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\rho _ { \\mathrm { f e a t u r e } }$ (10 by default) in $D _ { P }$ serves as a suficiently large constant to regulate the influence of the feature line. The color gradient in the insert figure represents the value of $D _ { P }$ , which increases with distance from the feature line, reflecting the gradual reduction in � � influence on the surface point. For ease of implementation, we approximate $d _ { g } ( \\pmb { p } , F L )$ using straight-line distances. As shown in Fig. 7, the crease line of the model is faithfully preserved in the neighborhood of $F L .$ , while its influence diminishes as the distance increases. Moreover, in regions where sharp features conflict with principal curvature directions, our NeurCross prioritizes feature alignment (see Fig. 8).", + "bbox": [ + 511, + 659, + 916, + 813 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Rotation Angle Prediction. Drawing inspiration from various object segmentation works [Hu et al. 2021; Milano et al. 2020], we employ the U-Net architecture [Ronneberger et al. 2015] to construct our rotation angle prediction network. The input to our U-Net-based network includes the point cloud P, along with the normal direction for each point, and the direction vectors � and � that represent the local coordinate system. The network outputs a scalar value $\\omega _ { p } \\in \\left[ 0 , 1 \\right]$ for each point �, allowing the rotation angle $\\theta _ { P }$ to be represented as $\\theta _ { P } = 2 \\pi \\omega _ { P }$ . For this module, we initialize the orien tation at a point � using a normal distribution with a mean of 0 and a standard deviation of 0.2.", + "bbox": [ + 511, + 820, + 916, + 876 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6", + "bbox": [ + 81, + 69, + 91, + 78 + ], + "page_idx": 5 + }, + { + "type": "header", + "text": "Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang", + "bbox": [ + 112, + 68, + 715, + 80 + ], + "page_idx": 5 + }, + { + "type": "footer", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 81, + 893, + 321, + 905 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d91125ee830bc8f885f8ace60176c3868c7c77d54794a043ade2401aab73bb22.jpg", + "image_caption": [ + "(a) Input mesh" + ], + "image_footnote": [], + "content": "3D diagram of a cube with blue curved lines on top face (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 91, + 99, + 267, + 238 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/859f91eabda563b682bdeb999b37d405ed7f8ecd026d2a5078e9a65077eee540.jpg", + "image_caption": [ + "(b) Principal curvature field" + ], + "image_footnote": [], + "content": "3D wireframe cube with colorful grid pattern, no text or symbols visible", + "sub_type": "natural_image", + "bbox": [ + 287, + 99, + 464, + 236 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/51aee388513df485afe536825e604692a93b5b7c5ac94aafd31208edc95a93ac.jpg", + "image_caption": [ + "(c) Our cross field" + ], + "image_footnote": [], + "content": "3D wireframe cube with multicolored grid pattern, no text or symbols visible", + "sub_type": "natural_image", + "bbox": [ + 89, + 273, + 269, + 412 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/73b576dd4e229a7b5bc0d1d913f80e40d1b3b29bc77c36e418c0f17cf93589d3.jpg", + "image_caption": [ + "(d) Our quad mesh", + "Fig. 8. NeurCross enforces alignment with sharp features even when they diverge from principal curvature directions. (a) An input mesh with conflict ing principal curvature directions (blue) and feature curves (red); (b) The principal curvature field of the input surface; (c) The cross field computed by NeurCross; (d) The resulting quad mesh generated using NeurCross." + ], + "image_footnote": [], + "content": "3D wireframe cube with grid pattern, no text or symbols present", + "sub_type": "natural_image", + "bbox": [ + 285, + 273, + 464, + 412 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 78, + 549, + 483, + 645 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3.4 SDF and Cross Field Joint Optimization", + "text_level": 2, + "bbox": [ + 80, + 664, + 383, + 678 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "One challenge in quad meshing is balancing the overall simplicity of the cross field with alignment to the principal directions, a dificulty that becomes more pronounced for geometrically or topologically complex shapes. In this paper, we address this challenge by using an optimizable neural SDF as a bridge to achieve this balance. Notably, the neural SDF and the cross field are optimized simultaneously.", + "bbox": [ + 78, + 681, + 482, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "An alternative approach is to first fully optimize the SDF to accu rately represent the input shape and then keep it fixed. However, in this case, the cross field may become severely constrained, as it must align with potentially irregular curvature lines of the pre-fixed SDF. As shown in Fig. 9, the fixed SDF, while providing an accurate representation, may introduce overly complex curvature lines, leading to an excessive number of singular points in the final cross field.", + "bbox": [ + 78, + 765, + 483, + 875 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/08575997b0e24ff7c2d0e51a07d30705fcf0f1763876fb57050444dad618e6c4.jpg", + "image_caption": [ + "(a) Cross field", + "(b) Quad mesh", + "(c) SDF fitting", + "(d) Fitting error", + "Fig. 9. Comparison between the two-step method (top row) and our joint optimization strategy (botom row). (a) Cross field; (b) Quad mesh; (c) The underlying SDF surface; (d) Fiting error between the SDF and the input triangular mesh. The final quad mesh is extracted based on the computed cross field and the input triangular mesh. As shown, our joint optimization strategy balances the overall smoothness of the cross field with alignment to the principal curvature directions." + ], + "image_footnote": [], + "content": "3D modeling visualization of two humanoid figures with meshed surfaces and color-coded heatmaps (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 522, + 95, + 915, + 344 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3.5 Implementation Details", + "text_level": 2, + "bbox": [ + 514, + 484, + 714, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "SDF Loss Terms. The loss terms used to regularize the SDF include the Eikonal condition [Gropp et al. 2020], the Dirichlet condition [Lipman 2021], and the alignment condition [Wang et al. 2024, 2023]. For further details on these loss terms, we refer readers to the existing literature [Dong et al. 2024; Wang et al. 2024, 2023].", + "bbox": [ + 513, + 503, + 916, + 573 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Sampling Strategy. A neural SDF is employed to approximate the base surface, with regularization at sample points, as detailed in previous works [Ben-Shabat et al. 2022; Boulch and Marlet 2022; Dong et al. 2024; Gropp et al. 2020; Hou et al. 2022; Huang et al. 2022; Kazhdan and Hoppe 2013; Ma et al. 2021; Sitzmann et al. 2020; Wang et al. 2024, 2023; Xu et al. 2022]. We extract centroids from all triangles in the mesh to define the sample set P, chosen for their representative nature of the surface. For each point $\\pmb { \\mathscr { p } } \\in \\mathscr { P }$ the normal vector $\\scriptstyle n _ { p }$ is derived from the corresponding triangular face’s normal.", + "bbox": [ + 511, + 585, + 916, + 720 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Given that each triangular face has three neighboring faces, neighboring relationships between points in $\\mathcal { P }$ can be thus established. The SDF is assumed diferentiable within a narrow, thin-shell space Ω, which closely encloses the base surface. Following previous studies [Dong et al. 2024; Gropp et al. 2020; Ma et al. 2021; Wang et al. 2024, 2023], Ω is sampled using random displacements around each point $\\pmb { \\mathscr { p } } \\in \\mathscr { P }$ . A Gaussian distribution centered at each �, with a standard deviation based on the distance to its �-th nearest neighbor (typically $k = 5 0 )$ , is used for this purpose. A one-point sampling technique is then applied to generate the sample set Ω, which is the same size as $\\mathcal { P }$", + "bbox": [ + 511, + 723, + 918, + 875 + ], + "page_idx": 6 + }, + { + "type": "header", + "text": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation", + "bbox": [ + 477, + 68, + 882, + 79 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7", + "bbox": [ + 906, + 69, + 915, + 78 + ], + "page_idx": 6 + }, + { + "type": "footer", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 676, + 893, + 915, + 905 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/180acd3c13b491fd98c00e77c891d82db3583462811d747d1ca344de205641c3.jpg", + "image_caption": [ + "Fig. 10. An overview of our U-Net-based module designed for predicting the rotation angle �. The network architecture incorporates the ResNet struc ture, with all layers being Multi-Layer Perceptrons (MLPs). The “ResNets” represents a combination of multiple ResNet blocks, the “FC” denotes the Fully Connected Layer, and the circled $^ { * } C ^ { * }$ symbol indicates the concatena tion operation." + ], + "image_footnote": [], + "content": "This diagram illustrates a neural network architecture for ResNet activation, showing the flow of data through FC (Functional Component) and Concatenation layers to generate output.", + "sub_type": "flowchart", + "bbox": [ + 84, + 93, + 475, + 280 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To prevent outlier zero iso-surfaces far from ${ \\mathcal { P } } ,$ we uniformly sample the bounding box (assuming input points are normalized within $[ - 0 . 5 , 0 . 5 ] ^ { 3 } )$ , generating a sample set Q.", + "bbox": [ + 78, + 382, + 482, + 425 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Eikonal Condition. The Eikonal condition is crucial for ensuring that the SDF $f ( \\boldsymbol { x } ; \\Theta )$ maintains a unit gradient at every point, i.e., $\\| \\nabla f \\| = 1$ , particularly in the vicinity of the surface. The corresponding loss term is defined as:", + "bbox": [ + 78, + 431, + 483, + 486 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {L} _ {E} = \\frac {1}{| \\mathcal {P} | + | \\Omega |} \\int_ {\\mathcal {P} \\cup \\Omega} \\left| 1 - \\| \\nabla f (\\boldsymbol {x}; \\Theta) \\| \\right| \\mathrm{d} \\boldsymbol {x}, \\tag {13}\n$$", + "text_format": "latex", + "bbox": [ + 148, + 489, + 480, + 520 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $\\mathcal { P }$ represents the sample points $( \\mathrm { e . g . }$ , centroids of mesh triangles), and Ω encodes a narrow band around the surface where the SDF is diferentiable. Notably, the point set $\\scriptstyle Q ,$ which represents regions far from the base surface, is excluded from this loss term and serves to prevent outlier zero isosurfaces in distant regions.", + "bbox": [ + 78, + 522, + 483, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Dirichlet Condition. For every point $\\pmb { p } \\in \\mathcal { P }$ , it is essential that they lie as close as possible to the underlying surface, ideally satisfying $f ( \\pmb { \\mathscr { p } } ; \\Theta ) = 0 .$ . Conversely, for points $q \\in { \\cal Q }$ , which lie away from the underlying surface, we aim to partition Q into interior and exterior regions, preventing � from degenerating. These conditions are formalized as the following loss terms:", + "bbox": [ + 78, + 598, + 483, + 681 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {L} _ {\\mathrm{DM}} = \\frac {1}{| \\mathcal {P} |} \\int_ {\\mathcal {P}} \\left| f (\\boldsymbol {p}; \\Theta) \\right| \\mathrm{d} \\boldsymbol {p}, \\tag {14}\n$$", + "text_format": "latex", + "bbox": [ + 192, + 685, + 480, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and", + "bbox": [ + 80, + 718, + 107, + 729 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {L} _ {\\mathrm{DNM}} = \\frac {1}{| Q |} \\int_ {Q} \\exp \\left(- \\rho_ {\\mathrm{DNM}} \\big | f (\\boldsymbol {q}; \\Theta) \\big |\\right) \\mathrm{d} \\boldsymbol {q}, \\tag {15}\n$$", + "text_format": "latex", + "bbox": [ + 148, + 728, + 480, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $\\rho _ { \\mathrm { D N M } }$ (defaulting to 100) is the exponential weight controlling the penalty for deviations from the surface.", + "bbox": [ + 78, + 758, + 482, + 786 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "SIREN-based Module. Similar to various implicit surface reconstruction methods [Ben-Shabat et al. 2022; Lipman 2021; Wang et al. 2024, 2022b, 2023], our NeurCross employs the SIREN [Sitzmann et al. 2020] network architecture, which consists of four hidden layers with 256 units each. The SIREN architecture is based on multi-layer perceptrons (MLPs), where inputs are first normalized to the range $[ - 1 , 1 ] ^ { 3 }$ before being processed by the network. The activation function used in this architecture is the sine periodic function, which operates on the input point cloud $\\mathcal { P }$ to produce the SDF field required for computing the Hessian matrix. For initializing this SIREN-based module, we follow SIREN’s initialization strategy [Sitzmann et al. 2020], which ensures that the distribution of activations remains consistent across all layers of the network.", + "bbox": [ + 78, + 792, + 483, + 876 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/828d3c466afe86167a698f661eb1d9ac58df2b72238a6a62f0c45d42bfc5a6f8.jpg", + "table_caption": [ + "Table 1. The sizes of the building blocks within our U-Net-based module. �b l k denotes the number of botleneck layers within each ResNet block. From the 1st to the 7th block, the values of �b l k are set to 3, 4, 6, 3, 3, 4, and 6, respectively." + ], + "table_footnote": [], + "table_body": "
Layer NameLayer ArchitectureOutput Size
$1 \\times 1, input\\_size=12$ 256
ResNets #1, #2, #3 $\\begin{bmatrix} 1 \\times 1, 256 \\\\ 1 \\times 1, 64 \\\\ 1 \\times 1, 64 \\end{bmatrix} \\times n_{bottleneck}$ 256
ResNets #4, #5, #6, #7 $\\begin{bmatrix} 1 \\times 1, 512 \\\\ 1 \\times 1, 128 \\\\ 1 \\times 1, 128 \\end{bmatrix} \\times n_{bottleneck}$ 512
$1 \\times 1, 512$ 32
$1 \\times 1, 32$ 1
", + "bbox": [ + 539, + 164, + 897, + 308 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 513, + 335, + 916, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "U-Net-based Module. We adopt a U-Net architecture [Ronneberger et al. 2015] as the backbone for predicting rotation angles. To address the vanishing gradient issue in deep networks, we incorporate ResNet blocks [He et al. 2016] as the core components of the U-Net. As shown in Fig. 10, our network consists of ResNet blocks (ResNets) and fully connected layers (FC), with all layers implemented using MLPs. A detailed configuration of each ResNet block is provided in Tab. 1.", + "bbox": [ + 513, + 441, + 916, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Parameter Setting. In this paper, we set the weights as follows based on our tailored configurations: $\\lambda _ { \\mathrm { E } } = 5 0 , \\lambda _ { \\mathrm { D M } } = 7 0 0 0 , \\lambda _ { \\mathrm { D N M } } =$ 600, $\\lambda _ { \\mathrm { A N } } = 3 , \\lambda _ { \\mathrm { A P } } = 1 0 .$ , and $\\lambda _ { S } = 3 0$ . The annealing factor � remains 1 during the initial 20% of iterations, then linearly decreases to $3 \\times 1 0 ^ { - 4 }$ from 20% to 40% of the iteration span, and finally drops to 0 towards the end. Throughout the training phase, we apply the Adam optimizer [Kingma and Ba 2014] with a default learning rate of $5 \\times 1 0 ^ { - 5 }$ and complete 10,000 iterations.", + "bbox": [ + 513, + 560, + 916, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Quad Mesh Extraction. The extraction of the quad mesh from our cross field follows a two-step scheme, as detailed in references Bommes et al. [2009], Ebke et al. [2013], and Dielen et al. [2021], to achieve a high-quality outcome. This process begins with a step of parametrization based on our cross field. In implementation, we utilize the global-seamless parametrization technique from libigl [Jacobson et al. 2017] to align the parametrization with our cross field. Subsequently, we employ libQEx [Ebke et al. 2013] to extract the quad mesh from this parameterization.", + "bbox": [ + 511, + 679, + 918, + 804 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4 EXPERIMENTS", + "text_level": 2, + "bbox": [ + 514, + 816, + 648, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Evaluation Metrics and Platform. To evaluate the accuracy of the quad mesh, we utilize four primary metrics [Huang et al. 2018; Wang et al. 2023]: area distortion (Area), angle distortion (Angle), the number of singularities (# of Sings), chamfer distance (CD), and Jacobian Ratio (JR). The area distortion metric, scaled by 10,000, represents the standard deviation of the areas of the quadrilateral faces within a mesh. The angle distortion is quantified using the formula $\\begin{array} { r } { \\sqrt { \\frac { 1 } { N } \\sum _ { i } ( \\phi _ { i } - \\frac { \\pi } { 2 } ) ^ { 2 } } } \\end{array}$ , where the summation extends over all angles $\\phi$ in the quad mesh, and � denotes their count. Chamfer distance, scaled by 10,000 and calculated using the �1-norm, quantifies the similarity between two surfaces. The Jacobian Ratio quantifies the uniformity of local deformation in quadrilateral elements. It is defined as the ratio of the smallest to the largest determinant of the Jacobian matrices at element corners, providing a dimensionless measure from 0 (degenerate element) to 1 (perfect parallelogram). The experiments detailed in this paper were executed on an NVIDIA GeForce RTX 3090 graphics card equipped with 24GB of video mem ory and powered by an AMD EPYC 7642 processor.", + "bbox": [ + 513, + 834, + 918, + 876 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8", + "bbox": [ + 81, + 69, + 91, + 78 + ], + "page_idx": 7 + }, + { + "type": "header", + "text": "Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang", + "bbox": [ + 112, + 68, + 715, + 80 + ], + "page_idx": 7 + }, + { + "type": "footer", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 81, + 893, + 321, + 905 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d3234236f683909e2ffd9df3f83a583e3333e2acd52920c683db8773aa05bf28.jpg", + "image_caption": [ + "Fig. 11. Quad meshes generated by NeurCross and four other methods on the table model in the ShapeNet dataset [Chang et al. 2015]." + ], + "image_footnote": [], + "content": "", + "bbox": [ + 81, + 89, + 918, + 229 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "", + "bbox": [ + 78, + 258, + 483, + 474 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Datasets. We carry out quad mesh generation experiments on two popular datasets: ShapeNet [Chang et al. 2015] and Thingi10K [Zhou and Jacobson 2016]. To maintain uniformity in evaluation, all input meshes are scaled to fit within the range of $[ - 0 . 5 , 0 . 5 ] ^ { 3 }$ ensuring a consistent and fair basis for comparison across all datasets.", + "bbox": [ + 78, + 479, + 480, + 549 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.1 Comparison on Open Datasets", + "text_level": 2, + "bbox": [ + 78, + 560, + 326, + 574 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We assess the eficacy of our proposed method, NeurCross, by con ducting evaluations on two distinct datasets and comparing its performance against four contemporary state-of-the-art quadrilateral mesh generation methods. For the three methods, namely Instant Meshes (IM) [Jakob et al. 2015], QuadriFlow [Huang et al. 2018], and QuadWild [Pietroni et al. 2021], we employed the open-source imple mentations that are readily available. It is worth noting that Quad Wild [Pietroni et al. 2021] is primarily a quadrangulation method rather than a cross field generation approach. The Mixed-Integer Quadrangulation (MIQ) method [Bommes et al. 2009] does not re lease its source code; therefore, we use the implementation provided by libigl [Jacobson et al. 2017]. However, the available implementation does not support the feature alignment constraint. For a fair comparison with MIQ, we employ the same parameterization and extraction techniques, namely global-seamless parameterization and libQEx [Ebke et al. 2013].", + "bbox": [ + 78, + 577, + 482, + 800 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "ShapeNet Dataset. The ShapeNet dataset [Chang et al. 2015] con sists of a diverse range of human-made models. As the global seamless parametrization from libigl [Jacobson et al. 2017] cannot handle non-manifold meshes, we use manifold ShapeNet meshes repaired with DualOctreeGNN [Wang et al. 2022a]. We apply our", + "bbox": [ + 78, + 806, + 483, + 876 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/24c7c2967125183d50cc64176184088cf2ff50f3419dd3e40231b5b82b8bffb8.jpg", + "table_caption": [ + "Table 2. Quantitative comparison on the ShapeNet dataset [Chang et al. 2015]. Within each column, the best scores are emphasized with bold and underlining (best), whereas the second-best scores are highlighted in bold (second best). The quad mesh generated by all the methods comprises an average of 6,000 vertices and 12,000 faces." + ], + "table_footnote": [], + "table_body": "
Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
IM [Jakob et al. 2015]1.5711.78200.528.970.70
QuadriFlow [Huang et al. 2018]2.2813.2491.5850.180.65
QuadWild [Pietroni et al. 2021]1.5211.0593.0410.340.73
MIQ [Bommes et al. 2009]5.2312.89 $\\underline{82.12}$ 8.250.58
NeurCross (Ours) $\\underline{1.48}$ $\\underline{9.85}$ 85.32 $\\underline{8.03}$ $\\underline{0.78}$
", + "bbox": [ + 521, + 338, + 908, + 426 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/c3f24835c59260fc54b3ad7d9e67f6ebb1a18570efa296567af9d56d199da364.jpg", + "table_caption": [ + "Table 3. Quantitative comparison on the Thingi10K dataset [Zhou and Jacobson 2016]. The quad mesh generated by all methods comprises an average of 10,000 vertices and 20,000 faces. Within each column, the best scores are emphasized with bold and underlining (best), whereas the secondbest scores are simply highlighted in bold (second best)." + ], + "table_footnote": [], + "table_body": "
Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
IM [Jakob et al. 2015]1.4510.57397.189.830.75
QuadriFlow [Huang et al. 2018]1.5812.3978.3226.890.72
QuadWild [Pietroni et al. 2021]1.4010.1685.1128.120.77
MIQ [Bommes et al. 2009]1.389.8566.548.570.67
NeurCross (Ours)1.339.6868.968.220.81
", + "bbox": [ + 521, + 516, + 908, + 604 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "NeurCross to three randomly selected categories—airplane, bench, and cabinet—which together contain 7433 models. For a fair comparison, all generated quad meshes are standardized to contain an average of 6,000 vertices and 12,000 faces.", + "bbox": [ + 511, + 618, + 916, + 672 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In Fig. 11, we display the quad meshes generated by our Neur-Cross alongside four other methods. For this example, although IM [Jakob et al. 2015] produces a regular quadrilateral mesh, the outcome includes some triangular elements. More comparisons between IM and our method will be provided in Sec. 4.2. Quadri-Flow [Huang et al. 2018], MIQ [Bommes et al. 2009], and Quad-Wild [Pietroni et al. 2021] generate some misaligned quadrilateral elements, as seen in the highlighted windows. In contrast, our method yields a better quadrilateral mesh. Tab. 2 shows the quantitative comparison of our method against the four approaches.", + "bbox": [ + 511, + 674, + 916, + 813 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Thingi10K Dataset. The Thingi10K dataset [Zhou and Jacobson 2016] features a variety of shapes with intricate geometric details. For our analysis based on Thingi10K, we tested 1,000 randomly selected triangle meshes from the dataset, which were also used as inputs for all comparative methods. The quad meshes generated by all methods contain, on average, 10,000 vertices and 20,000 faces to maintain fidelity to the original models.", + "bbox": [ + 513, + 819, + 916, + 876 + ], + "page_idx": 8 + }, + { + "type": "header", + "text": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation", + "bbox": [ + 475, + 68, + 882, + 79 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "9", + "bbox": [ + 903, + 69, + 915, + 78 + ], + "page_idx": 8 + }, + { + "type": "footer", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 676, + 893, + 915, + 904 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/4bd962ed3e1ea479a69cd57aaa89aea978fc3daa34396d7fca61a84b739dc821.jpg", + "image_caption": [ + "Fig. 12. Quad meshes generated by NeurCross and four other methods on a cup model in the Thingi10K dataset [Zhou and Jacobson 2016]." + ], + "image_footnote": [], + "content": "", + "bbox": [ + 83, + 97, + 915, + 239 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/b6825fb9918d39e8f312f63ebde7015297c773d90604b0c047d02e8edfaa2917.jpg", + "image_caption": [ + "IGM" + ], + "image_footnote": [], + "content": "Three 3D wireframe models of a vase-like object with mesh surfaces and bounding boxes, no text or symbols present.", + "sub_type": "natural_image", + "bbox": [ + 104, + 272, + 455, + 402 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/cbbcd70cf0c8a4de657d5efa22dead0fda074d25d931b0c002ea85bc1e994a9f.jpg", + "image_caption": [ + "IM" + ], + "image_footnote": [], + "content": "3D wireframe model of a vase-like object with geometric cutouts, no visible text or symbols", + "sub_type": "natural_image", + "bbox": [ + 218, + 273, + 336, + 402 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/baf456f6bdcd214dad0d890be2800e3964714f633be8628e3770db97cb1055e1.jpg", + "image_caption": [ + "QuadriFlow" + ], + "image_footnote": [], + "content": "3D wireframe model of a jug with mesh structure and inset showing cross-section (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 333, + 273, + 455, + 402 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/28db9c04fb0fcf8702bba759d2eb75cdcf657149cc0078f6ce4d7a8f2e881c33.jpg", + "image_caption": [ + "QuadWild" + ], + "image_footnote": [], + "content": "3D wireframe model of a vase with a square inset showing internal mesh structure (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 102, + 431, + 222, + 561 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/420ade657de8989f3176bc463fc7bd07e12456c84a98fe49420edf0c949fd573.jpg", + "image_caption": [ + "MIQ" + ], + "image_footnote": [], + "content": "3D wireframe model of a knitted object with mesh grid and inset showing circular pattern (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 218, + 431, + 336, + 561 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/a49940b47cae5d6b5f8214fcb31435795d190291761b2e30327d7f4e52b661b8.jpg", + "image_caption": [ + "NeurCross (Ours)", + "Fig. 13. Comparison with five state-of-the-art methods using data provided in IGM [Bommes et al. 2013a]." + ], + "image_footnote": [], + "content": "3D wireframe model of a jug with mesh structure and inset showing mesh grid (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 334, + 431, + 455, + 561 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "", + "bbox": [ + 78, + 667, + 482, + 709 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Quantitative comparison statistics are presented in Tab. 3. Our method consistently outperforms others on average across this dataset. Interestingly, MIQ [Bommes et al. 2009] shows commend able performance on this dataset. However, it is important to note that despite this improvement, the issue of producing distorted quadrilaterals in the resulting quad mesh remains (see Fig. 12 and the JR metric in Tab. 3). Quadwild [Pietroni et al. 2021] requires smoothing of the generated quad mesh, which compromises geo metric details and increases the Chamfer Distance (CD). In contrast, our method produces a more intuitive cross field without needing to introduce excessive singular points (see zoom-in windows in Fig. 12).", + "bbox": [ + 78, + 710, + 482, + 876 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/47770f35d9ed1106c7301a54173f218e014bca3011454c5bc1bee39658e9a82d.jpg", + "image_caption": [ + "Fig. 14. Comparison with five methods on Human Body data. Dielen et al. [2021] proposed a supervised learning-based approach designed to generate quad meshes on human body data from the FAUST dataset [Bogo et al. 2014]. Due to the absence of available open-source data, the comparison result in the upper left is taken from Dielen et al. [2021]’s paper." + ], + "image_footnote": [], + "content": "", + "bbox": [ + 526, + 270, + 901, + 559 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "4.2 Further Comparison", + "text_level": 2, + "bbox": [ + 514, + 643, + 691, + 657 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Comparison with IGM. IGM [Bommes et al. 2013a] is characterized as a global approach, primarily focused on the joint optimization of parametrization with integer constraints. Like our method, it also utilizes libQEx [Ebke et al. 2013] for extracting quad meshes from the parametrization. Although IGM provides full control over edge alignment and singularity placement, yielding high-quality quad meshes, its lack of scalability can lead to severely distorted quadrilaterals (see Fig. 13).", + "bbox": [ + 511, + 660, + 916, + 772 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Comparison with Learning Methods. Dielen et al. [2021] represents a pioneering efort in quad mesh generation through deep learning methodologies. Their method uses a supervised network architecture to predict the frame field, comprising both a global network and a local network for field prediction. Subsequently, the parametrization-based quadrangulation method proposed in Campen et al. [2015b] is employed to generate the quad meshes.", + "bbox": [ + 511, + 777, + 918, + 876 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10", + "bbox": [ + 81, + 69, + 94, + 78 + ], + "page_idx": 9 + }, + { + "type": "header", + "text": "• Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang", + "bbox": [ + 104, + 68, + 720, + 80 + ], + "page_idx": 9 + }, + { + "type": "footer", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 81, + 893, + 321, + 905 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/9a2a08412c7f36afe57072ddff0fe3f9e94217d7e42405da1bd0a41660d5d2e9.jpg", + "image_caption": [ + "Fig. 15. Comparison of quad meshes generated by Power Fields [Knöppel et al. 2013], PolyVectors [Diamanti et al. 2014], and NeurCross." + ], + "image_footnote": [], + "content": "Power Fields\nPolyVectors\nNeurCross (Ours)", + "sub_type": "text_image", + "bbox": [ + 91, + 95, + 472, + 229 + ], + "page_idx": 10 + }, + { + "type": "image", + "img_path": "images/d50c48406bee2d709601f7f465d5f6fa5f4213fde40647fff6c37e264cb82ed2.jpg", + "image_caption": [], + "image_footnote": [], + "content": "3D wireframe models of mechanical components with grid patterns, comparing IM and NeurCross (Ours) methods (no text or symbols on models)", + "sub_type": "natural_image", + "bbox": [ + 89, + 263, + 472, + 441 + ], + "page_idx": 10 + }, + { + "type": "image", + "img_path": "images/126bc8f58e5f3485846f850a50b2649ddfb2993725588b3f92a55d5c9b04b7bd.jpg", + "image_caption": [ + "Fig. 16. Comparison with IM. Here, the same approach—applying globa seamless parameterization [Jacobson et al. 2017] and libQEx [Ebke et al. 2013]— is used to extract quadrilateral meshes from the respective cross fields of IM and our NeurCross.", + "Fig. 17. Comparison of quad meshes generated by Quad Remesher [Remesher 2019] and NeurCross." + ], + "image_footnote": [], + "content": "Quad Remesher\nNeurCross (Ours)", + "sub_type": "text_image", + "bbox": [ + 89, + 498, + 468, + 670 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "However, due to the inherent constraints ofsupervised learning, this approach shows optimal performance only on the FAUST dataset [Bogo et al. 2014], a limitation not encountered by our self-supervised method. Owing to a lack of required data, our comparison is limited to the model presented in their paper (see Fig. 14).", + "bbox": [ + 78, + 715, + 483, + 786 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Comparison with PowerFields andPolyVectors. Power Fields [Knöppel et al. 2013] eficiently constructs smooth n-direction fields on surfaces by solving a sparse eigenvalue problem, ensuring global optimality and high-quality results. PolyVectors [Diamanti et al. 2014] extends N-RoSy fields to N-PolyVector fields by relaxing orthogonality and symmetry constraints, enabling their computation via a sparse linear system without integer variables. Both methods focus on eficient computation of directional fields, with Power Fields [Knöppel et al. 2013] optimizing smoothness and PolyVectors [Diamanti et al. 2014] generalizing traditional field representations. Fig. 15 compares the quadrilateral meshes generated by our NeurCross and these methods. NeurCross not only aligns with principal curvatures but also preserves overall smoothness.", + "bbox": [ + 78, + 792, + 483, + 876 + ], + "page_idx": 10 + }, + { + "type": "chart", + "img_path": "images/c200ed43f6ebfd0324524a22617394ea94113b8b0a6584c9d0aa81ee90ce1d51.jpg", + "content": "| Method | Description |\n| --- | --- |\n| Input | White 3D model with a curved base structure. |\n| IM | Red 3D model with a curved base structure. |\n| QuadriFlow | Blue 3D model with a curved base structure. |\n| QuadWild | Red 3D model with a curved base structure. |\n| MIQ | Blue 3D model with a curved base structure. |\n| NeurCross (Ours) | Blue 3D model with a curved base structure. |", + "chart_caption": [ + "Fig. 18. Approximation accuracy. Here we show the approximation errors between the input surface and the final quad meshes generated by diferent methods. The error is measured from each sampled point on the quad mesh to the input surface." + ], + "chart_footnote": [], + "sub_type": "surface_3d", + "bbox": [ + 537, + 94, + 906, + 334 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "", + "bbox": [ + 513, + 398, + 916, + 494 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Comparison with IM. IM [Jakob et al. 2015] is an efective method for generating quad meshes. To facilitate a fair comparison between IM and our approach, we use the same global seamless parameterization and extraction technique (libQEx [Ebke et al. 2013]) to extract the quad mesh. As shown in Fig. 16, our method produces fewer singularities than IM. Additionally, our method outperforms IM [Jakob et al. 2015] in terms of principal direction alignment and structural integrity, as illustrated in the close-up views.", + "bbox": [ + 513, + 501, + 916, + 613 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Comparison with Quad Remesher. Quad Remesher [Remesher 2019] excels at generating quadrilateral meshes and is available as a plugin for software like Blender. It is stable, eficient, and effective at preserving model features while maintaining topological uniformity, with our method achieving comparable results. However, its performance depends heavily on the quality of the input mesh, producing low-quality quadrilateral meshes when the input polygonal mesh is suboptimal (see Fig. 17).", + "bbox": [ + 513, + 619, + 916, + 731 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Fidelity. In practical applications, when converting a shape from a triangular mesh to a quadrilateral mesh representation, the goals extend beyond minimizing area distortion, angle distortion, and the number of singular points; maintaining fidelity to the original shape is also crucial. Recognizing that a low-resolution quad mesh may naturally lose some details, we use various methods to generate a quad mesh containing 25,000 vertices and 50,000 faces for a more detailed comparison.", + "bbox": [ + 513, + 737, + 916, + 847 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "In Fig. 18, we present the approximation errors between the quad meshes generated by five methods and the input triangle mesh. The quad meshes generated by our NeurCross and MIQ [Bommes et al. 2009] faithfully represent the original input. IM [Jakob et al. 2015] and QuadriFlow [Huang et al. 2018] exhibit minor shape distortions, whereas QuadWild [Pietroni et al. 2021] produces a smoother result, leading to a loss of detail.", + "bbox": [ + 514, + 848, + 916, + 876 + ], + "page_idx": 10 + }, + { + "type": "header", + "text": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation", + "bbox": [ + 470, + 68, + 879, + 79 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "• 11", + "bbox": [ + 885, + 69, + 915, + 78 + ], + "page_idx": 10 + }, + { + "type": "footer", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 676, + 893, + 915, + 904 + ], + "page_idx": 10 + }, + { + "type": "image", + "img_path": "images/9af987df6afa7a322ff8f63778cc4ce9ec84c169acfdbe45be82b0cd71ba9017.jpg", + "image_caption": [ + "IM" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 101, + 97, + 272, + 242 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/c685e1f0176cdeaa12ec815ade19430481b8f4c34964886679303fe7a9629372.jpg", + "image_caption": [ + "QuadriFlow" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 279, + 97, + 446, + 242 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/772533f96bbff2eb87f0f94932bfcda08985573e9999e99db04f3595e3689f47.jpg", + "image_caption": [ + "QuadWild" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 454, + 97, + 625, + 239 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/e32263b5421af267dcd1f695c7f75720768fa2a9b9939afe44b2f47b893894b5.jpg", + "image_caption": [ + "MIQ" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 629, + 98, + 715, + 239 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/86b4b50cbd299c636eeba84c156d0b3d31a57d3ab63fc1cba378e142be434145.jpg", + "image_caption": [ + "NeurCross (Ours)" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 722, + 98, + 890, + 239 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/16dee25d509d1d8d63202d824b6568049f1f82a746504f2fd3fac5ff3651bf64.jpg", + "image_caption": [ + "Fig. 19. The top row shows the cross field generated by our method and four other methods on a noisy input mesh. The botom row shows the resulting quad meshes produced by each approach. Note that MIQ fails to produce a valid result for this input surface with noise.", + "Fig. 20. Quad meshes generated by all the methods on two models from ShapeNet [Chang et al. 2015] (the airplane model) and Thingi10K [Zhou and Jacobson 2016] (the grayloc model). We also show the locations of singular points, where “# of Sings” denotes the number of singular points on each quad mesh." + ], + "image_footnote": [], + "content": "", + "bbox": [ + 84, + 301, + 908, + 523 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "", + "bbox": [ + 78, + 574, + 483, + 643 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Resistance to Noise. As noted in Wang et al. [2023], Wang et al. [2024], and Dong et al. [2024], the Hessian matrix possesses intrinsic smoothing properties. Benefiting from this characteristic, our method demonstrates inherent resistance to noise in cross field prediction. We used a baseline mesh with 15,000 vertices and introduced Gaussian noise (i.e., 2% relative to the normal direction of each model) to test the noise immunity of our NeurCross. For a comprehensive comparison, we evaluated the four other methods under the same noise conditions.", + "bbox": [ + 78, + 667, + 483, + 791 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "In Fig. 19, we present the results of diferent methods under noisy input. Notably, our approach optimizes the SDF and the cross field simultaneously. As a result, during optimization, the underlying SDF naturally smooths out noise, leading to a more intuitive cross field. In summary, our method demonstrates stronger noise resistance compared to four other methods.", + "bbox": [ + 78, + 792, + 483, + 875 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Singular Points. It’s well acknowledged that a trade-of must be achieved between reducing singular points and aligning with principal directions. Thus, it’s preferable to position singular points in regions with high curvature variation rather than in flatter areas. As observed in Tab. 2, Tab. 3, and Fig. 20, our method produces a slightly higher number of singular points compared to MIQ [Bommes et al. 2009]. This occurrence can be attributed to MIQ’s tendency to produce distorted quadrilaterals, which consequently reduces the occurrence of singular points as well as area and angular distortions. However, MIQ’s quad mesh lacks overall consistency and tends to oversmooth areas with significant changes in the direction of the cross field.", + "bbox": [ + 511, + 575, + 916, + 739 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "In Fig. 20, we visualize the locations of singular points in the quad meshes generated by all methods on two models. The placement of singular points in the quad mesh generated by our method is more reasonable, and the resulting quadrilateral mesh exhibits high overall consistency.", + "bbox": [ + 513, + 741, + 916, + 810 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Geometrically Complex Models. Various complex geometric models, such as triangular meshes with high genus, thin shells, or nonorientable surfaces, are common in many fields. In Fig. 21, we display", + "bbox": [ + 513, + 834, + 918, + 876 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "12", + "bbox": [ + 81, + 69, + 94, + 78 + ], + "page_idx": 11 + }, + { + "type": "header", + "text": "• Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang", + "bbox": [ + 104, + 68, + 720, + 80 + ], + "page_idx": 11 + }, + { + "type": "footer", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 81, + 893, + 320, + 905 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/dff8a0b78248ca6769c6831eae6983736f3ddc1694cf9e2a7b5de7ae4cd9893e.jpg", + "image_caption": [ + "IM" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 86, + 92, + 243, + 348 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/f8ef2c30199fc58a342f7a58868c1c866353e25dbd178c8afbdde2e0bacd980c.jpg", + "image_caption": [ + "QuadriFlow" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 253, + 92, + 410, + 347 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/de59dc2aca23a57eec2683f60b7f1b52cd128a449350af0692087b743987e366.jpg", + "image_caption": [ + "QuadWild" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 419, + 92, + 573, + 347 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/e17009ff1b7da345b7a8166963a66727e4a7d1a544fa97b9096c62d02576a39a.jpg", + "image_caption": [ + "MIQ" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 584, + 92, + 741, + 347 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/29c4f30a1150810fba89f4d08559ab15b11f482c74c84b6f6244d48b7e6d2317.jpg", + "image_caption": [ + "NeurCross (Ours)" + ], + "image_footnote": [], + "content": "", + "bbox": [ + 750, + 92, + 906, + 347 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/82282e58612d24db85d424cbd4f9ace54d12c5adc061f798b70f69955fbbbdeb.jpg", + "image_caption": [ + "Fig. 21. Comparison of quad meshes generated by various methods for some challenging models, i.e. with high genus, thin shells, and non-orientable rings Across all tests, the quad meshes generated by NeurCross consistently exhibit higher quality compared to those produced by other methods.", + "(a) Open boundaries (b) Feature lines (c) Free-form model", + "Fig. 22. Quad meshes extracted by NeurCross using diferent mesh extraction methods for various models: (a) A garment with open boundaries; (b) A CAD model with feature lines; and (c) A free-form model. The results are presented for each extraction method with or without the localized patching mechanism (LPM)." + ], + "image_footnote": [], + "content": "", + "bbox": [ + 81, + 411, + 472, + 728 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "the quad meshes generated by our method and other methods on sev eral geometrically complex models. The visualization results show that our method’s performance on the unoriented ring model is comparable to that of IM [Jakob et al. 2015] and QuadriFlow [Huang et al. 2018]. However, for the other two models, only our method consistently produces high-quality quad meshes. Specifically, on the model with a thin shell (the leaf model), only our method and MIQ [Bommes et al. 2009] managed to avoid surface damage. While MIQ produced distorted quadrilaterals at the boundary of the thin shell, our method maintained good overall consistency in the quadrilateral meshes. Fig. 26 shows more results generated by our Neur-Cros on challenging models.", + "bbox": [ + 78, + 834, + 483, + 876 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/8cb9e9130675bfac20d29de5b46d07fa94de2c1b0193f562e6b31251ae567eab.jpg", + "image_caption": [ + "(a) w/o $\\mathcal { L } _ { \\mathbf { A P } }$", + "(b) w/o $\\mathcal { L } _ { \\pmb { s } }$", + "(c) w/o $\\mathcal { L } _ { \\mathbf { A P } }$ & $\\mathcal { L } _ { \\pmb { S } }$", + "(d) Ours", + "Fig. 23. The quad meshes and cross fields generated by our NeurCross using various loss term combinations: (a) without the alignment with principa directions loss term (w/o L ); (b) without the smoothness loss term (w/o $\\mathcal { L } _ { \\mathbb { S } } ) ;$ (c) without both (w/o L & $\\mathcal { L } _ { \\mathbb { S } } ) ;$ and (d) with both (Ours)." + ], + "image_footnote": [], + "content": "", + "bbox": [ + 522, + 411, + 906, + 635 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "", + "bbox": [ + 513, + 750, + 916, + 876 + ], + "page_idx": 12 + }, + { + "type": "header", + "text": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation", + "bbox": [ + 470, + 68, + 879, + 80 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "• 13", + "bbox": [ + 885, + 69, + 915, + 78 + ], + "page_idx": 12 + }, + { + "type": "footer", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 676, + 893, + 915, + 905 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/ab4084d217d8303fbd00db4e658d66f92537fbc607146b7a4a86caba029e47b0.jpg", + "image_caption": [ + "Fig. 24. Quad meshes generated by our NeurCross at diferent resolutions. The low-resolution models contain fewer than 1,000 vertices, while the high resolution models consist of over 5,000 vertices." + ], + "image_footnote": [], + "content": "Grid-based 3D wireframe models of human figures and objects, no text or symbols present", + "sub_type": "natural_image", + "bbox": [ + 111, + 95, + 880, + 305 + ], + "page_idx": 13 + }, + { + "type": "table", + "img_path": "images/75062270809ee0a2c949ba87ccf162c377c8f4a2dd17d1c8e5c034ad7f75c253.jpg", + "table_caption": [ + "Table 4. Ablation studies on the alignment with principal directions loss term $\\mathcal { L } _ { \\mathsf { A P } }$ and the smoothness loss term $\\mathcal { L } _ { S }$" + ], + "table_footnote": [], + "table_body": "
Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
ShapeNet[Chang et al. 2015]w/o $\\mathcal{L}_{\\text{AP}}$ 1.5911.9689.968.050.75
w/o $\\mathcal{L}_{\\text{S}}$ 1.9615.12113.288.090.71
w/o $\\mathcal{L}_{\\text{AP}}$ & $\\mathcal{L}_{\\text{S}}$ 2.2520.73238.718.150.55
NeurCross (Ours)1.489.8585.328.030.78
Thingi10K[Zhou and Jacobson 2016]w/o $\\mathcal{L}_{\\text{AP}}$ 1.4811.8973.798.250.79
w/o $\\mathcal{L}_{\\text{S}}$ 1.8715.03105.378.290.73
w/o $\\mathcal{L}_{\\text{AP}}$ & $\\mathcal{L}_{\\text{S}}$ 2.2120.67225.188.310.58
NeurCross (Ours)1.339.6868.968.220.81
", + "bbox": [ + 86, + 407, + 475, + 512 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "5 ABLATION STUDIES", + "text_level": 2, + "bbox": [ + 78, + 532, + 250, + 546 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "5.1 Extraction Methods", + "text_level": 2, + "bbox": [ + 78, + 551, + 253, + 564 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "As discussed in Section 4.1, the global parameterization techniques in libigl [Jacobson et al. 2017] fail to align parameterized lines with sharp feature lines. To address this, we adopt QuadWild [Pietroni et al. 2021], leveraging the marked sharp features from Sec. 3.3 to divide the surface into patches using the localized patching mecha nism (LPM) [Pietroni et al. 2021], and using our cross field to guide the patch tessellation process.", + "bbox": [ + 78, + 569, + 482, + 666 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "As illustrated in the bottom row of Fig. 22, NeurCross can successfully generate feature-aligned quadrilateral meshes, which is particularly beneficial for CAD models. For free-form models, the localized patching mechanism (LPM) [Pietroni et al. 2021] introduces singularities at the junctions of adjacent patches and even produces malformed quadrilaterals. Therefore, we generally rely on the global parameterization methods from libigl [Jacobson et al. 2017], unless the user explicitly requires the alignment of parameterized lines with sharp feature lines, in which case we employ the localized patching mechanism (LPM) [Pietroni et al. 2021].", + "bbox": [ + 78, + 666, + 482, + 805 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "5.2 Cross Field Loss Terms", + "text_level": 2, + "bbox": [ + 78, + 816, + 272, + 830 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "To further highlight the eficacy of our cross field loss terms in quad mesh generation, we conducted a comparative analysis by disabling these loss terms. We used the ShapeNet [Chang et al. 2015] and Thingi10K [Zhou and Jacobson 2016] datasets for testing and comparison, setting the weight $\\lambda _ { \\mathrm { A P } }$ of the alignment with principal directions loss term, the weight $\\lambda _ { \\mathrm { { S } } }$ of the smoothness loss term, or both, to zero, while keeping other settings unchanged.", + "bbox": [ + 78, + 834, + 480, + 876 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "", + "bbox": [ + 511, + 367, + 916, + 422 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Fig. 23 illustrates the quadrilateral meshes and cross field generated by our method under various loss term combinations. The results show that our method produces the highest quality quadrilateral meshes. Disabling the alignment with principal directions term $\\mathcal { L } _ { \\mathrm { A P } }$ maintains only local correlation and lacks overall consistency. Although the mesh generated without the smoothness term $\\mathcal { L } _ { S }$ shows some degree of overall consistency, it is prone to producing singular points due to the absence of constraints on the local cross field. Without constraints from neither $\\mathcal { L } _ { \\mathrm { A P } }$ nor $\\mathcal { L } _ { \\mathrm { S } } ,$ the resulting quadrilateral mesh exhibits both aforementioned defects. The quantitative results presented in Tab. 4 align with the qualitative findings in Fig. 23, further demonstrating the superiority of our method in generating quadrilateral meshes.", + "bbox": [ + 511, + 422, + 918, + 603 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "5.3 Resolution of Quad Mesh", + "text_level": 2, + "bbox": [ + 514, + 625, + 725, + 638 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "In real-world applications, selecting the appropriate resolution for quad mesh extraction depends on the specific requirements of different tasks. In Fig. 24, we use the same cross field for both lowand high-resolution quad meshes, ensuring consistent placement of singular points. Interestingly, the low-resolution mesh better high lights the positioning of these singular points. Fig. 24 demonstrates that, in our approach, most singular points are strategically located in regions with high curvature rather than in flat areas.", + "bbox": [ + 511, + 641, + 916, + 753 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "6 LIMITATION", + "text_level": 2, + "bbox": [ + 514, + 773, + 632, + 787 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "A significant limitation of the self-supervised optimization is its substantial time requirement. For a triangular mesh input with 50,000 faces, each iteration takes 68.34 ms, with a default setting of 10,000 iterations. However, for geometrically simple and regular shapes, NeurCross typically converges in fewer iterations to produce highquality quadrilateral meshes (see the top row of Fig. 25), whereas complex shapes may require additional iterations to achieve comparable results (see the bottom row of Fig. 25).", + "bbox": [ + 511, + 792, + 916, + 876 + ], + "page_idx": 13 + }, + { + "type": "page_number", + "text": "14", + "bbox": [ + 81, + 69, + 94, + 78 + ], + "page_idx": 13 + }, + { + "type": "header", + "text": "• Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang", + "bbox": [ + 104, + 68, + 720, + 80 + ], + "page_idx": 13 + }, + { + "type": "page_footnote", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 81, + 893, + 321, + 905 + ], + "page_idx": 13 + }, + { + "type": "image", + "img_path": "images/6a649330551fcd77dfaed364df6f9c80b06ebe0f637b6cf540fb6808abd13a3c.jpg", + "image_caption": [ + "Fig. 25. Trend of convergence. Quad meshes generated by our NeurCross with diferent numbers of iterations (#iter)." + ], + "image_footnote": [], + "content": "Grid-based 3D model of a human figure with labeled iteration counts (500, 1k, 5k, 10k), no text or symbols present.", + "sub_type": "natural_image", + "bbox": [ + 81, + 97, + 480, + 286 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "", + "bbox": [ + 78, + 353, + 482, + 380 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "A promising future direction is to leverage this approach to gen erate ample training data for feeding generative models, such as MeshGPT [Siddiqui et al. 2024]. This would enable users to obtain high-quality quad meshing outcomes instantly.", + "bbox": [ + 78, + 380, + 483, + 436 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "7 CONCLUSION", + "text_level": 2, + "bbox": [ + 80, + 450, + 210, + 462 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "In this paper, we propose a self-supervised neural representation of the cross field for quadrilateral mesh generation. To the best of our knowledge, this is the first self-supervised approach for this task. Our network, named NeurCross, consists of two modules: one to fit the SDF and another to predict the cross field. The design of our loss function addresses three key aspects: surface approximation quality, alignment with principal directions, and the spatial smooth ness of the cross field. Leveraging our network, the SDF and cross field are optimized simultaneously, achieving a desirable balance between approximation accuracy and cross field smoothness. Experimental results consistently validate improvements in singular point placement and in the approximation accuracy between the input triangular surface and the output quad mesh.", + "bbox": [ + 78, + 467, + 483, + 648 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "ACKNOWLEDGMENTS", + "text_level": 2, + "bbox": [ + 80, + 661, + 248, + 674 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the National Key R&D Program of China (2022YFB3303200), the Na tional Natural Science Foundation of China (U23A20312, 62272277, 62102380), the Shandong Provincial Natural Science Foundation (ZR2024MF083), the Innovation and Technology Commission of the HKSAR Government under the InnoHK initiative (TransGP project) and the ITSP-Platform grant (Ref: ITS/335/23FP), and the Research Grants Council of Hong Kong (Ref: 17210222).", + "bbox": [ + 78, + 679, + 483, + 804 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "REFERENCES", + "text_level": 2, + "bbox": [ + 81, + 816, + 179, + 829 + ], + "page_idx": 14 + }, + { + "type": "ref_text", + "text": "Yizhak Ben-Shabat, Chamin Hewa Koneputugodage, and Stephen Gould. 2022. DiGS: Divergence guided shape implicit neural representation for unoriented point clouds. 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Publication date: May 2025.", + "bbox": [ + 678, + 893, + 915, + 904 + ], + "page_idx": 14 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [], + "bbox": [ + 81, + 103, + 480, + 869 + ], + "page_idx": 15 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [], + "bbox": [ + 516, + 103, + 916, + 345 + ], + "page_idx": 15 + }, + { + "type": "page_number", + "text": "16", + "bbox": [ + 81, + 69, + 94, + 78 + ], + "page_idx": 15 + }, + { + "type": "header", + "text": "• Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang", + "bbox": [ + 104, + 68, + 720, + 80 + ], + "page_idx": 15 + }, + { + "type": "footer", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 81, + 893, + 320, + 905 + ], + "page_idx": 15 + }, + { + "type": "image", + "img_path": "images/7acc75b5cb48c073b2e919b23387ee66af718025ecf10719fdec7b8dd2b08ad6.jpg", + "image_caption": [ + "Fig. 26. The quad meshes produced by our NeurCross method on challenging models." + ], + "image_footnote": [], + "content": "3D wireframe models of various mythical creatures and human figures, no text or symbols present", + "sub_type": "natural_image", + "bbox": [ + 130, + 97, + 870, + 864 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "bbox": [ + 676, + 893, + 915, + 905 + ], + "page_idx": 16 + }, + { + "type": "header", + "text": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation", + "bbox": [ + 472, + 68, + 879, + 79 + ], + "page_idx": 16 + }, + { + "type": "page_number", + "text": "• 17", + "bbox": [ + 885, + 69, + 915, + 78 + ], + "page_idx": 16 + } +] \ No newline at end of file diff --git a/papers/markdown/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation/hybrid_auto/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation_content_list_v2.json b/papers/markdown/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation/hybrid_auto/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation_content_list_v2.json new file mode 100644 index 0000000000000000000000000000000000000000..9d77ebbd95d57a2f0ad3c8ddd146a549bce4e8fa --- /dev/null +++ b/papers/markdown/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation/hybrid_auto/2405.13745_NeurCross_A_Neural_Approach_to_Computing_Cross_Fields_for_Quad_Mesh_Generation_content_list_v2.json @@ -0,0 +1,6492 @@ +[ + [ + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation" + } + ], + "level": 1 + }, + "bbox": [ + 78, + 94, + 870, + 142 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "QIUJIE DONG, Shandong University, China, The University of Hong Kong, China, and TransGP, China" + } + ] + }, + "bbox": [ + 78, + 150, + 795, + 167 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "HUIBIAO WEN, Shandong University, China" + } + ] + }, + "bbox": [ + 81, + 167, + 408, + 184 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "RUI XU, The University of Hong Kong, China" + } + ] + }, + "bbox": [ + 81, + 186, + 398, + 202 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "SHUANGMIN CHEN, Qingdao University of Science and Technology, China" + } + ] + }, + "bbox": [ + 81, + 204, + 625, + 220 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "JIARAN ZHOU, Ocean University of China, China" + } + ] + }, + "bbox": [ + 81, + 220, + 441, + 237 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "SHIQING XIN∗, Shandong University, China" + } + ] + }, + "bbox": [ + 81, + 239, + 401, + 255 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "CHANGHE TU, Shandong University, China" + } + ] + }, + "bbox": [ + 81, + 256, + 403, + 272 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "TAKU KOMURA, The University of Hong Kong, China" + } + ] + }, + "bbox": [ + 81, + 273, + 470, + 290 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "WENPING WANG, Texas A&M University, United States of America" + } + ] + }, + "bbox": [ + 81, + 292, + 566, + 306 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/ec5c189df3d8309359b7cb1e9ef73d98ec4ded9f2d1c1f1a4a5200bff5643d0d.jpg" + }, + "content": "3D wireframe models of various 3D geometric structures, including human figures and torus-like forms (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "Fig. 1. Gallery of quad meshes generated with our NeurCros method. NeurCross excels in computing cross field for generating high-quality quad meshes. Its advantages include optimized singular point placement, insensitivity to surface noise and minor surface undulations, and faithful alignment with principa curvature directions and sharp feature curves." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 81, + 320, + 916, + 579 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Quadrilateral mesh generation plays a crucial role in numerical simulations within Computer-Aided Design and Engineering (CAD/E). Producing high quality quadrangulation typically requires satisfying four key criteria. First, the quadrilateral mesh should closely align with principal curvature direc tions. Second, singular points should be strategically placed and efectively minimized. Third, the mesh should accurately conform to sharp feature edges. Lastly, quadrangulation results should exhibit robustness against noise and minor geometric variations. Existing methods generally involve first computing a regular cross field to represent quad element orientations across the surface, followed by extracting a quadrilateral mesh aligned closely with this cross field. A primary challenge with this approach is balancing the smoothness of the cross field with its alignment to pre-computed principal curvature directions, which are sensitive to small surface perturbations and often ill-defined in spherical or planar regions." + } + ] + }, + "bbox": [ + 78, + 632, + 482, + 720 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 511, + 632, + 916, + 719 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "To tackle this challenge, we propose NeurCross, a novel framework that simultaneously optimizes a cross field and a neural signed distance function (SDF), whose zero-level set serves as a proxy of the input shape. Our joint optimization is guided by three factors: faithful approximation of the optimized SDF surface to the input surface, alignment between the cross field and the principal curvature field derived from the SDF surface, and smoothness of the cross field. Acting as an intermediary, the neural SDF contributes in two essential ways. First, it provides an alternative, optimizable base surface exhibiting more regular principal curvature directions for guiding the cross field. Second, we leverage the Hessian matrix of the neural SDF to implicitly enforce cross field alignment with principal curvature directions, thus eliminating the need for explicit curvature extraction. Extensive experiments demonstrate that NeurCross outperforms the state-of-the-art methods in terms of singular point placement, robustness against surface noise and surface undulations, and alignment with principal curvature directions and sharp feature curves." + } + ] + }, + "bbox": [ + 511, + 720, + 916, + 872 + ] + }, + { + "type": "page_aside_text", + "content": { + "page_aside_text_content": [ + { + "type": "text", + "content": "arXiv:2405.13745v3 [cs.CV] 9 May 2025" + } + ] + }, + "bbox": [ + 22, + 260, + 60, + 700 + ] + }, + { + "type": "page_footnote", + "content": { + "page_footnote_content": [ + { + "type": "text", + "content": "∗Corresponding author: Shiqing Xin." + } + ] + }, + "bbox": [ + 80, + 734, + 254, + 747 + ] + }, + { + "type": "page_footnote", + "content": { + "page_footnote_content": [ + { + "type": "text", + "content": "Authors’ addresses: Qiujie Dong, Shandong University, Qingdao, Shandong, China and The University of Hong Kong, Hong Kong, China and TransGP, Hong Kong, China, qiujie.jay.dong@gmail.com; Huibiao Wen, Shandong University, Qingdao, Shandong, China, ericvein@163.com; Rui Xu, The University of Hong Kong, Hong Kong, China, xrvitd@163.com; Shuangmin Chen, Qingdao University of Science and Technology, Qingdao, Shandong, China, csmqq@163.com; Jiaran Zhou, Ocean University of China, Qingdao, Shandong, China, zhoujiaran@ouc.edu.cn; Shiqing Xin, Shandong University, Qingdao, Shandong, China, xinshiqing@sdu.edu.cn; Changhe Tu, Shandong University, Qingdao, Shandong, China, chtu@sdu.edu.cn; Taku Komura, The University of Hong Kong, Hong Kong, China, taku@cs.hku.hk; Wenping Wang, Texas A&M University, Texas, United States of America, wenping@tamu.edu." + } + ] + }, + "bbox": [ + 78, + 762, + 482, + 875 + ] + }, + { + "type": "page_footer", + "content": { + "page_footer_content": [ + { + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025." + } + ] + }, + "bbox": [ + 676, + 893, + 916, + 905 + ] + } + ], + [ + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 78, + 101, + 480, + 152 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "CCS Concepts: • Computing methodologies → Shape analysis; Mesh geometry models." + } + ], + "level": 2 + }, + "bbox": [ + 78, + 159, + 480, + 186 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Additional Key Words and Phrases: quadrangulation, neural network, cross field, signed distance function, principal curvature" + } + ] + }, + "bbox": [ + 78, + 191, + 480, + 219 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "1 INTRODUCTION" + } + ], + "level": 2 + }, + "bbox": [ + 80, + 234, + 228, + 248 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Quadrangulation is fundamental in both Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) [Bommes et al. 2013b; Vaxman et al. 2016], with significant applications in finite element analysis, isogeometric analysis, character animation, and physics simulations [Bommes et al. 2013a, 2009; Campen et al. 2015a; Jakob et al. 2015; Mu et al. 2023]." + } + ] + }, + "bbox": [ + 78, + 252, + 480, + 335 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Existing approaches typically first compute a reliable cross field to represent quad element orientations across the surface, followed by extracting quad meshes aligned closely with the computed field [Bommes et al. 2013a, 2009; Huang et al. 2018; Jakob et al. 2015; Zhang et al. 2020]. Most methods require principal curvature di rections as input. However, computing a desired cross field from principal curvature directions entails meeting four key requirements: First, the quadrilateral mesh should align closely with principal cur vature directions. Second, singular points should be strategically placed and minimized. Third, the mesh should conform accurately to sharp feature edges. Lastly, quadrangulation results should be robust against noise and minor surface variations. These challenges are particularly pronounced in geometrically or topologically complex shapes." + } + ] + }, + "bbox": [ + 78, + 335, + 482, + 529 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Fig. 2 shows quadrangulation results of some existing methods. As shown, for instance, QuadWild [Pietroni et al. 2021] fails to align properly with principal curvature directions due to an overemphasis on the smoothness of the cross field. Although principal curvature directions provide useful geometric clues, precisely controlling their influence on the inferred cross field is dificult, especially in nearly spherical or planar regions, or on a surface with small undulations, where principal curvature directions become unstable." + } + ] + }, + "bbox": [ + 78, + 530, + 480, + 640 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We introduce an optimizable neural signed distance function (SDF) as the underlying shape representation to infer the desired cross field. The neural SDF serves as a proxy for the input shape, which often exhibits unstable principal curvature directions. Opti mizing this SDF alongside the cross field provides a smooth approximation to the input shape, generating a regular principal curvature field to guide cross field generation. More specifically, our joint optimization is guided by three factors: faithful approximation of the optimized SDF surface to the input surface, alignment between the cross field and the principal curvature field derived from the SDF surface, and smoothness of the cross field. We integrate these requirements into a unified neural optimization framework, called NeurCross, that enables simultaneous optimization of the SDF and cross field. Fig. 3 illustrates our method’s success on a dimpled el lipsoid with irregular curvature directions, compared to a naïve two-stage approach that first optimizes an SDF to properly fit the input shape and then uses the curvature field of this fixed SDF to guide the generation of the cross field. The key to the success of our method is its simultaneous optimization strategy that allows the cross field smoothness term to inform the optimal shape of the neural SDF as a proxy surface." + } + ] + }, + "bbox": [ + 78, + 641, + 482, + 876 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 513, + 99, + 916, + 156 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Additionally, a key advantage is that the SDF-based shape operator implicitly encodes principal curvature directions, enabling enforcement of alignment between principal curvature directions and the cross field by evaluating whether the cross at each point match well with the eigenvectors of the shape operator, bypassing the need for explicit extraction of principal curvature direction, a step susciptable to unstability in nearly spherical or planar regions." + } + ] + }, + "bbox": [ + 513, + 156, + 916, + 253 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We implement NeurCross using a SIREN-based [Sitzmann et al. 2020] module for SDF fitting and a U-Net-based [Ronneberger et al. 2015] module for cross field prediction. Over 10,000 iterations, both components are optimized simultaneously to satisfy quadrangulation criteria. Finally, we employ global-seamless parametrization from libigl [Jacobson et al. 2017] aligned with our cross field, followed by quad mesh extraction using libQEx [Ebke et al. 2013]. Fig. 4 illustrates this process. Extensive experiments validate Neur-Cross’s efectiveness, demonstrating improvements in singular point placement, robustness to noise and geometric variations, and approximation accuracy, as shown in the teaser figure." + } + ] + }, + "bbox": [ + 513, + 253, + 916, + 405 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Our contributions are summarized as follows:" + } + ] + }, + "bbox": [ + 529, + 406, + 808, + 417 + ] + }, + { + "type": "list", + "content": { + "list_type": "text_list", + "list_items": [ + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "- We propose NeurCross, the first self-supervised neural network for learning cross fields." + } + ] + }, + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "- We implicitly enforce cross field alignment with principal curvature directions via an SDF-based shape operator, naturally addressing potential ambiguity." + } + ] + }, + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "- We leverage an optimizable neural SDF as an underlying representation to coordinate requirements, dynamically adjusting to minor surface variations." + } + ] + } + ] + }, + "bbox": [ + 540, + 419, + 916, + 529 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "2 RELATED WORK" + } + ], + "level": 2 + }, + "bbox": [ + 514, + 542, + 660, + 556 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "This paper focuses on developing a neural representation of the cross field for quadrilateral mesh generation. In this section, we review two main categories of related work: quad mesh generation techniques and neural SDF representations." + } + ] + }, + "bbox": [ + 513, + 561, + 916, + 616 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "2.1 Quad Mesh Generation" + } + ], + "level": 2 + }, + "bbox": [ + 514, + 622, + 712, + 636 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Quadrilateral mesh generation has attracted significant attention in recent years. While some methods, such as Dual Marching Cubes (DMC) [Nielson 2004], can directly extract quad facets without relying on direction fields, the resulting meshes often lack quality, particularly in aligning with principal directions. Most state-of-theart approaches rely on a cross field [Lai et al. 2010; Palmer et al. 2021; Ray et al. 2008] to guide the generation of high-quality quad meshes, as it ensures edge alignment and proper placement of irregular vertices. Typically, after computing a cross field, a parameterization step [Bommes et al. 2009; Chien et al. 2016; Levi and Zorin 2014; Myles et al. 2014] aligns gradients with the direction field and traces integer iso-lines across multiple charts [Ebke et al. 2013]. Although several robust quadrangulation methods [Dong et al. 2006; Gurung et al. 2011; Ling et al. 2014; Owen et al. 1999; Remacle et al. 2012; Velho and Zorin 2001; Zhang et al. 2010] operate independently of direction fields, they often fail to achieve global smoothness. Below, we review related works on direction fields." + } + ] + }, + "bbox": [ + 511, + 640, + 916, + 875 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "2" + } + ] + }, + "bbox": [ + 81, + 69, + 91, + 78 + ] + }, + { + "type": "page_header", + "content": { + "page_header_content": [ + { + "type": "text", + "content": "Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang" + } + ] + }, + "bbox": [ + 112, + 68, + 715, + 80 + ] + }, + { + "type": "page_footer", + "content": { + "page_footer_content": [ + { + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025." + } + ] + }, + "bbox": [ + 81, + 893, + 321, + 905 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/5d8ee6e01f2c6e28b5a490858bdcb70619707e26fa8b94cabb71038b3f0d069c.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "Fig. 2. Existing approaches typically rely on principal curvature directions as input. However, due to the inherent instability of these directions, current methods often prioritize the smoothness of the cross field at the cost of alignment with the principal curvature directions. To address this limitation, our approach avoids explicitly extracting principal curvature directions. Instead, we assess whether the cross field at each point can function as eigenvectors of the shape operator." + } + ], + "image_footnote": [] + }, + "bbox": [ + 81, + 94, + 915, + 277 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/cdb36e7fe472f41c69f30ff6a0555ba38ab7aa8254e2b54bd9e90c9af04cad82.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "(a) Input" + }, + { + "type": "text", + "content": "GT surface" + } + ], + "image_footnote": [] + }, + "bbox": [ + 81, + 352, + 218, + 412 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/97e0129853317a23ac177a004919fd97745a6927c1b4bcc99af1367275860590.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "GT curvature field" + } + ], + "image_footnote": [] + }, + "bbox": [ + 81, + 444, + 218, + 503 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/ba2b9b52fbc1a845e1dd3debada5c6166729808cd3ff86628d05c3a77670a3d0.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "(b) Two-step method" + } + ], + "image_footnote": [] + }, + "bbox": [ + 251, + 352, + 393, + 412 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/b1ad9d112050fb0ab658a4817c97689f3676163fee1383eacd237491e3415cad.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "(c) Our joint optimization" + }, + { + "type": "text", + "content": "SDF shape" + } + ], + "image_footnote": [] + }, + "bbox": [ + 254, + 444, + 390, + 502 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/26a08368b289a1788bb03735a0dbb19ce78b304a4380a537bc2354705f053799.jpg" + }, + "content": "", + "image_caption": [], + "image_footnote": [] + }, + "bbox": [ + 429, + 351, + 563, + 411 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/f215ec0df7daddca2a9cbcb63a92ef184379279979a0b34084925a13d085f291.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "Fitting error" + } + ], + "image_footnote": [] + }, + "bbox": [ + 431, + 444, + 565, + 503 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/e06b190c46ba89f80afa3b86bc90c7866478bd6defd38ff2ecf558186e498f1d.jpg" + }, + "content": "", + "image_caption": [], + "image_footnote": [] + }, + "bbox": [ + 570, + 343, + 607, + 402 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/70a65601f6b87a407bbc69bc05ee6bf378c6053b9a1f8a8a3af9085cba2bc355.jpg" + }, + "content": "", + "image_caption": [], + "image_footnote": [] + }, + "bbox": [ + 604, + 354, + 743, + 414 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/e5f2577ea0ad09c7aad4dd4e85230f871971d3b796c7ac542479d950cf690ff8.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "Cross field" + } + ], + "image_footnote": [] + }, + "bbox": [ + 604, + 444, + 741, + 503 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/add7ac0fb6932a9607a7892ad64969086c64df63b898c7c5eeae7584d59a08d2.jpg" + }, + "content": "", + "image_caption": [], + "image_footnote": [] + }, + "bbox": [ + 777, + 351, + 916, + 412 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/e58c62b09e94b1ebce6a4df5d8754660e1d45e4093ae0eb1c3532ee74f8076a7.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "Quad mesh" + }, + { + "type": "text", + "content": "Fig. 3. (a) The input mesh and its ground-truth principal curvature directions. (b) Two-step optimization: by first precomputing an SDF that precisely fits the input shape, the subsequent optimization step still sufers from sensitivity to minor geometric variations, failing to yield the desired cross field. (c) Joint optimization: by treating the SDF as a proxy for the input shape, simultaneous optimization of the SDF and the cross field allows the SDF to approximate the input shape while remaining robust to minor geometric variations, resulting in the desired cross field. We visualize the fiting errors between the SDF surface and the original surface using a color-coded scheme" + } + ], + "image_footnote": [] + }, + "bbox": [ + 777, + 441, + 916, + 503 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "A fundamental requirement for direction fields is to align edge directions with principal curvature directions [Bommes et al. 2013a, 2009; Fang et al. 2018; Hertzmann and Zorin 2000; Huang et al. 2018; Jakob et al. 2015; Kälberer et al. 2007; Lyon et al. 2019; Vaxman et al. 2016]. Lai et al. [2008] proposed an iterative relaxation scheme that incrementally aligns mesh edges with principal directions, though it requires additional post-processing to refine results. Jakob et al. [2015] introduced a unified local smoothing operator that optimizes both edge orientations and vertex positions in the output quad mesh. QuadriFlow [Huang et al. 2018] improved upon In stant Meshes [Jakob et al. 2015] by introducing linear and quadratic constraints, reducing singularities but struggling to preserve the original shape. Several methods [Bommes et al. 2013a; Huang et al. 2018; Jakob et al. 2015] optimize parametrization while incorporating integer constraints, a challenging mixed-integer programming (MIP) problem [Bommes et al. 2009] that is computationally inten sive. These methods typically aim to minimize distortion and reduce singularities [Bommes et al. 2013a; Levi and Zorin 2014; Myles et al." + } + ] + }, + "bbox": [ + 78, + 607, + 483, + 857 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "2014; Myles and Zorin 2013]. To address the computational complexity of IGM [Bommes et al. 2013a] on complex meshes, Ebke et al. [2016] proposed a framework using eficient decimation and coarse-to-fine mapping to improve interactive performance. Dielen et al. [2021] introduced a learning-based approach for predicting di rection fields, demonstrating its potential for quad mesh generation. However, its reliance on domain-specific networks and canonical alignment limits its generalizability and robustness to non-rigid changes." + } + ] + }, + "bbox": [ + 511, + 607, + 916, + 732 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "2.2 Neural SDF" + } + ], + "level": 2 + }, + "bbox": [ + 514, + 746, + 633, + 758 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The Signed Distance Function (SDF) is a widely used geometric representation in computer graphics, particularly for surface reconstruction. For example, radial basis functions (RBF) [Carr et al. 2001] approximate the SDF, enabling the extraction of the target surface as the zero-isosurface of the SDF." + } + ] + }, + "bbox": [ + 513, + 763, + 916, + 833 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "SDFs have also been extensively employed in deep learning-based surface reconstruction, including supervised implicit surface reconstruction methods [Erler et al. 2020; Huang et al. 2022; Park et al." + } + ] + }, + "bbox": [ + 513, + 834, + 916, + 876 + ] + }, + { + "type": "page_header", + "content": { + "page_header_content": [ + { + "type": "text", + "content": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation" + } + ] + }, + "bbox": [ + 475, + 68, + 882, + 79 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "3" + } + ] + }, + "bbox": [ + 906, + 69, + 915, + 78 + ] + }, + { + "type": "page_footer", + "content": { + "page_footer_content": [ + { + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025." + } + ] + }, + "bbox": [ + 676, + 893, + 915, + 904 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/989c51839f42396f1b4f800d0b8e5c888127938bec1e4096e97283a8a61ea47d.jpg" + }, + "content": "3D wireframe model of a complex, irregularly shaped mechanical structure (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "(a) Triangle mesh" + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 81, + 95, + 282, + 210 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/cbfe4482b9c604d09b696ba6e241b1c391ca9ae535ef812e26dc8b6b3af93bfb.jpg" + }, + "content": "Abstract 3D sculpture of intertwined human figures in a dynamic pose (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "(b) Random initialization" + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 292, + 97, + 493, + 213 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/c1adaa84e307303f5b901506152925de880749120dbe40b2415f36a68a3cd74c.jpg" + }, + "content": "3D rendered abstract mechanical structure with colorful grid pattern (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "(c) Resultant cross field" + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 503, + 97, + 705, + 214 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/c877d31cacdb7415b6f448daea08ff7ec3c46527ddb57f1699d7a88ed5571823.jpg" + }, + "content": "3D wireframe model of a complex geometric structure with no visible text or symbols", + "image_caption": [ + { + "type": "text", + "content": "(d) Quad mesh" + }, + { + "type": "text", + "content": "Fig. 4. Given the input triangular surface in (a), starting with a randomly initialized cross field in (b), our NeurCross method produces a smooth cross field in (c) that is well aligned with the principal curvature directions of the input surface. We use the global-seamless parametrization from libigl to obtain a parametrization aligned with the computed cross field, and then use libQEx to extract the final quad mesh in (d)." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 714, + 95, + 916, + 212 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "2019] and self-supervised approaches [Ma et al. 2021, 2022; Wang et al. 2021]. For instance, IGR [Gropp et al. 2020] incorporates the Eikonal term to enforce implicit geometric regularization, providing an efective mechanism for surface reconstruction. SIREN [Sitz mann et al. 2020] demonstrates that periodic activation functions are well-suited for representing complex natural signals and their derivatives using implicit neural representations. DiGS [Ben-Shabat et al. 2022] integrates Laplacian energy as a soft constraint for the SDF, proving efective for reconstructing surfaces from unoriented point clouds. Neural-Singular-Hessian [Wang et al. 2023] ensures that the Hessian of the neural implicit function has a zero determinant for points near the surface, which is particularly useful for recovering details from unoriented point clouds. Additionally, Dong et al. [2024] proposed a zero Gaussian curvature constraint for re constructing CAD-type surfaces from low-quality unoriented point clouds. All these methods leverage neural networks to approximate the SDF." + } + ] + }, + "bbox": [ + 78, + 287, + 483, + 521 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In this paper, SDFs play a central role in quad mesh generation, as the Hessian of the SDF fully encodes principal curvatures and their directions [Dong et al. 2024; Wang et al. 2023]." + } + ] + }, + "bbox": [ + 78, + 522, + 482, + 565 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "3 OUR APPROACH" + } + ], + "level": 2 + }, + "bbox": [ + 80, + 580, + 228, + 594 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "3.1 Overview" + } + ], + "level": 2 + }, + "bbox": [ + 80, + 599, + 184, + 612 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The core idea of NeurCross is to leverage the optimizable neural Signed Distance Function (SDF) as an underlying representation to coordinate various requirements. On one hand, the adjustable SDF can efectively reduce sensitivity to minor surface variations. On the other hand, the SDF-based shape operator enables us to implicitly evaluate the diference between the principal curvature directions and the cross field. NeurCross consists of two core modules: a surface fitting module and an orientation prediction module, both centered around the SDF." + } + ] + }, + "bbox": [ + 78, + 617, + 483, + 742 + ] + }, + { + "type": "list", + "content": { + "list_type": "text_list", + "list_items": [ + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "(1) Surface Fitting Module: This module aims to represent the input triangular surface using a neural SDF. Its loss incorporates the Dirichlet condition [Lipman 2021], the Eikonal condition [Gropp et al. 2020], and the singular Hessian con dition [Wang et al. 2024] to ensure high fidelity to the input surface geometry. Together, these constraints guarantee an accurate surface representation." + } + ] + }, + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "(2) Cross Field Prediction Module: This module is designed to represent the cross field while implicitly enforcing alignment" + } + ] + } + ] + }, + "bbox": [ + 96, + 750, + 482, + 876 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "with principal curvature directions and spatial smoothness. It employs a U-Net architecture [Ronneberger et al. 2015] to predict a rotation angle for each triangular facet, yielding a geometry-aware cross field. Additionally, this module supports explicit alignment with geometric features." + } + ] + }, + "bbox": [ + 550, + 287, + 916, + 357 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "These two modules are coordinated through a total loss function, which ensures simultaneous optimization of the SDF and the cross field during the training process. The interaction between the modules allows for dynamic updates to both the surface representation and the cross field, leading to improved accuracy and robustness. The overall network architecture is illustrated in Fig. 5." + } + ] + }, + "bbox": [ + 513, + 359, + 916, + 441 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Total Loss. Our total loss is defined as follows." + } + ] + }, + "bbox": [ + 529, + 446, + 808, + 460 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {L} = \\underbrace {\\lambda_ {\\mathrm{E}} \\mathcal {L} _ {\\mathrm{E}} + \\lambda_ {\\mathrm{DM}} \\mathcal {L} _ {\\mathrm{DM}} + \\lambda_ {\\mathrm{DNM}} \\mathcal {L} _ {\\mathrm{DNM}} + \\tau \\lambda_ {\\mathrm{AN}} \\mathcal {L} _ {\\mathrm{AN}}} _ {\\text {SDF}} + \\underbrace {\\lambda_ {\\mathrm{AP}} \\mathcal {L} _ {\\mathrm{AP}} + \\lambda_ {\\mathrm{S}} \\mathcal {L} _ {\\mathrm{S}}} _ {\\text {Cross Field}}, \\tag {1}", + "math_type": "latex", + "image_source": { + "path": "images/64892da0464725ca27ca5170b8f751aa5c9f644ab19c54b942bed765b639297e.jpg" + } + }, + "bbox": [ + 522, + 464, + 916, + 498 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "where � is the annealing factor [Dong et al. 2024; Wang et al. 2024, 2023]. The individual terms, along with their corresponding weights, will be detailed in the following subsections." + } + ] + }, + "bbox": [ + 513, + 500, + 916, + 542 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "3.2 SDF Fiting" + } + ], + "level": 2 + }, + "bbox": [ + 514, + 553, + 632, + 568 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Let Θ denote the parameters of a neural SDF " + }, + { + "type": "equation_inline", + "content": "f ( \\boldsymbol { x } ; \\Theta ) : \\mathbb { R } ^ { 3 } \\to \\mathbb { R } ," + }, + { + "type": "text", + "content": "where � = 0 approximates the input triangular surface. We begin by sampling the centroid of each triangle, forming a point set P, where each point is associated with a normal vector. In the following, we define a loss term to enforce alignment with the predefined surface normals, while leaving further details to Sec. 3.5." + } + ] + }, + "bbox": [ + 513, + 570, + 916, + 654 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "SDF Based Shape Operator. The shape operator of a surface measures the rate of change of the unit normal in any direction, thereby describing how the shape changes in that direction. In diferential geometry, it is very common to assume the surface has a parametric form, such that the shape operator defines a quadratic form on the tangent space, and the eigenvectors of the shape operator correspond exactly to the principal directions. In fact, the Hessian matrix of the SDF is closely related to the shape operator. For a point � on the base surface, the Hessian matrix " + }, + { + "type": "equation_inline", + "content": "H _ { P }" + }, + { + "type": "text", + "content": "of the SDF has an eigenvalue of 0, with its corresponding eigenvector being the normal vector " + }, + { + "type": "equation_inline", + "content": "\\mathbf { \\Delta } _ { n _ { P } }" + }, + { + "type": "text", + "content": "[Dong et al. 2024; Wang et al. 2024, 2023]. Simultaneously, the other two eigenvectors of " + }, + { + "type": "equation_inline", + "content": "H _ { p }" + }, + { + "type": "text", + "content": "correspond to the two principal curvature directions." + } + ] + }, + "bbox": [ + 511, + 660, + 918, + 840 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Alignment with Predefined Surface Normals. Since for a point � suficiently close to the base surface, the eigenvector corresponding to the zero eigenvalue of the Hessian matrix " + }, + { + "type": "equation_inline", + "content": "H _ { p }" + }, + { + "type": "text", + "content": "of the SDF aligns with the normal vector " + }, + { + "type": "equation_inline", + "content": "\\scriptstyle n _ { p }" + }, + { + "type": "text", + "content": "at " + }, + { + "type": "equation_inline", + "content": "{ \\pmb \\rho } ." + }, + { + "type": "text", + "content": "Given that the normal direction of " + }, + { + "type": "equation_inline", + "content": "\\pmb { p } \\in \\mathcal { S }" + }, + { + "type": "text", + "content": "can be directly obtained from the input triangle mesh, we require the neural SDF to align with the predefined surface normal " + }, + { + "type": "equation_inline", + "content": "\\mathbf { \\Delta } _ { n _ { P } }" + }, + { + "type": "text", + "content": "as follows:" + } + ] + }, + "bbox": [ + 514, + 847, + 916, + 876 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "4" + } + ] + }, + "bbox": [ + 81, + 69, + 91, + 78 + ] + }, + { + "type": "page_header", + "content": { + "page_header_content": [ + { + "type": "text", + "content": "Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang" + } + ] + }, + "bbox": [ + 112, + 68, + 715, + 80 + ] + }, + { + "type": "page_footer", + "content": { + "page_footer_content": [ + { + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025." + } + ] + }, + "bbox": [ + 81, + 893, + 321, + 905 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/de77e6dbc3e8b40ddf3fe821e9c18bcdc2eb8f2daed28bf5505c5cbc863228c1.jpg" + }, + "content": "```mermaid\ngraph LR\n A[\"Input Image\"] --> B[\"Image with Scatter Plot\"]\n B --> C[\"P\"]\n C --> D[\"SDF fitting module\"]\n D --> E[\"Feature Output\"]\n F[\"MLP\"] --> G[\"θ\"]\n G --> H[\"μ, ν\"]\n H --> I[\"⊕\"]\n J[\"L_SDF\"] --> K[\"min L\"]\n K --> L[\"L_CrossField\"]\n L --> M[\"Output Image\"]\n N[\"α = μcosθ + vsinθ\\nβ = vcosθ - μsinθ\"] --> I\n E --> O[\"H\"]\n O --> P[\"⊕\"]\n P --> Q[\"Output Image\"]\n```", + "image_caption": [ + { + "type": "text", + "content": "Fig. 5. Our self-supervised network pipeline for representing cross fields in quad mesh generation. All layers in the network are implemented as multi-layer perceptrons (MLPs), with the SDF fiting module utilizing the SIREN [Sitzmann et al. 2020] architecture. The circled " + }, + { + "type": "equation_inline", + "content": "^ { 6 } + \\prime" + }, + { + "type": "text", + "content": "symbol denotes a data-combining operation." + } + ], + "image_footnote": [] + }, + "sub_type": "flowchart", + "bbox": [ + 86, + 93, + 908, + 306 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 78, + 372, + 482, + 444 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "H _ {p} \\cdot n _ {p} = 0. \\tag {2}", + "math_type": "latex", + "image_source": { + "path": "images/1f752ff95ef86055b54cee891bd0db5d6f17ccf9d1cffa97fcdd85379c89aadd.jpg" + } + }, + "bbox": [ + 240, + 450, + 482, + 465 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The overall alignment with predefined surface normals can be quantified as:" + } + ] + }, + "bbox": [ + 78, + 474, + 483, + 502 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {L} _ {\\mathrm{AN}} = \\frac {1}{| \\mathcal {P} |} \\int_ {\\mathcal {P}} \\left| H _ {\\boldsymbol {p}} \\cdot \\boldsymbol {n} _ {\\boldsymbol {p}} \\right| \\mathrm{d} \\boldsymbol {p}. \\tag {3}", + "math_type": "latex", + "image_source": { + "path": "images/b2e7b8b162da66c4314c04c7a7fe8c7288f21d2a176b6139b1a3984453319dd8.jpg" + } + }, + "bbox": [ + 192, + 506, + 482, + 536 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "3.3 Cross Field Prediction" + } + ], + "level": 2 + }, + "bbox": [ + 80, + 547, + 267, + 561 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Local Coordinate System. Recall that each point " + }, + { + "type": "equation_inline", + "content": "\\pmb { p } \\in \\mathcal { P }" + }, + { + "type": "text", + "content": "corresponds to the centroid of a triangular face. The task of computing the cross field involves inferring a pair of orthogonal vectors, " + }, + { + "type": "equation_inline", + "content": "( \\alpha _ { p } , \\beta _ { p } )" + }, + { + "type": "text", + "content": ", that align as closely as possible with the principal curvature directions. To achieve this, we assume that each triangle has a pre-defined coordinate system" + } + ] + }, + "bbox": [ + 78, + 566, + 282, + 718 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "with two axes, " + }, + { + "type": "equation_inline", + "content": "\\mu _ { p }" + }, + { + "type": "text", + "content": "and " + }, + { + "type": "equation_inline", + "content": "\\nu _ { p } ," + }, + { + "type": "text", + "content": ", which are mutually orthogonal unit vectors satisfying " + }, + { + "type": "equation_inline", + "content": "\\mu _ { \\pmb { p } } \\times \\nu _ { \\pmb { p } } = n _ { p }" + }, + { + "type": "text", + "content": ". We introduce a rotation angle " + }, + { + "type": "equation_inline", + "content": "\\theta _ { P }" + }, + { + "type": "text", + "content": "to represent " + }, + { + "type": "equation_inline", + "content": "\\alpha _ { p }" + }, + { + "type": "text", + "content": "and " + }, + { + "type": "equation_inline", + "content": "\\beta _ { p }" + }, + { + "type": "text", + "content": "as follows:" + } + ] + }, + "bbox": [ + 78, + 719, + 482, + 763 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\left\\{ \\begin{array}{l} \\boldsymbol {\\alpha} _ {p} = \\boldsymbol {\\mu} _ {p} \\cos \\theta_ {p} + \\nu_ {p} \\sin \\theta_ {p}, \\\\ \\boldsymbol {\\beta} _ {p} = \\nu_ {p} \\cos \\theta_ {p} - \\boldsymbol {\\mu} _ {p} \\sin \\theta_ {p}. \\end{array} \\right. \\tag {4}", + "math_type": "latex", + "image_source": { + "path": "images/d720af463f495cdd34ead4e0581a6b5454b6b687c16a8fddd02a60e8ed3f6e7d.jpg" + } + }, + "bbox": [ + 183, + 777, + 482, + 810 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "See the inset figure for an illustration. Notably, " + }, + { + "type": "equation_inline", + "content": "\\alpha _ { p }" + }, + { + "type": "text", + "content": "and " + }, + { + "type": "equation_inline", + "content": "\\beta _ { p }" + }, + { + "type": "text", + "content": "are natu rally mutually orthogonal unit vectors. As a result, the optimization of the cross field reduces to computing the rotation angle " + }, + { + "type": "equation_inline", + "content": "\\theta _ { P }" + }, + { + "type": "text", + "content": "for each triangle." + } + ] + }, + "bbox": [ + 78, + 819, + 483, + 878 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Implicit Alignment with Principal Directions. An explicit approach to implementing alignment with principal directions involves comparing the cross field with pre-extracted principal directions. However, most existing methods for extracting principal directions heavily rely on local shape variations, which can lead to instability, particularly when the local geometry is approximately planar or spherical. To address this limitation, we adopt an implicit alignment strategy by evaluating the compatibility between the cross field and the shape operator." + } + ] + }, + "bbox": [ + 511, + 372, + 916, + 497 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "To align the cross field with the principal directions, we encourage " + }, + { + "type": "equation_inline", + "content": "\\alpha _ { p }" + }, + { + "type": "text", + "content": "and " + }, + { + "type": "equation_inline", + "content": "\\beta _ { p }" + }, + { + "type": "text", + "content": "to coincide with two of the eigenvectors of " + }, + { + "type": "equation_inline", + "content": "H _ { p } ." + }, + { + "type": "text", + "content": ". To enforce collinearity between " + }, + { + "type": "equation_inline", + "content": "H _ { P } \\alpha _ { P }" + }, + { + "type": "text", + "content": "and " + }, + { + "type": "equation_inline", + "content": "\\alpha _ { p }" + }, + { + "type": "text", + "content": ", we impose the following condition:" + } + ] + }, + "bbox": [ + 513, + 497, + 916, + 551 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "H _ {p} \\alpha_ {p} \\times \\alpha_ {p} = 0. \\tag {5}", + "math_type": "latex", + "image_source": { + "path": "images/ba223402a3f0f5675424b75d93b1d18b33179e644082143138ea3174fcee21cb.jpg" + } + }, + "bbox": [ + 661, + 556, + 916, + 571 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Similarly, we require:" + } + ] + }, + "bbox": [ + 514, + 575, + 648, + 590 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "H _ {p} \\boldsymbol {\\beta} _ {p} \\times \\boldsymbol {\\beta} _ {p} = 0. \\tag {6}", + "math_type": "latex", + "image_source": { + "path": "images/d2f2996bd0e982450b135a0a04c0b28e5bf469fed517ae49ea407c1673c8b758.jpg" + } + }, + "bbox": [ + 663, + 598, + 916, + 616 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We define the loss term to measure alignment with the principal directions as follows:" + } + ] + }, + "bbox": [ + 513, + 621, + 916, + 647 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {L} _ {\\mathrm{AP}} ^ {(1)} = \\frac {1}{| \\mathcal {P} |} \\int_ {\\mathcal {P}} \\left| H _ {p} \\boldsymbol {\\alpha} _ {p} \\times \\boldsymbol {\\alpha} _ {p} \\right| + \\left| H _ {p} \\boldsymbol {\\beta} _ {p} \\times \\boldsymbol {\\beta} _ {p} \\right| \\mathrm{d} p. \\tag {7}", + "math_type": "latex", + "image_source": { + "path": "images/466e06c66c3646a5156b3c2252276d8c6e594d88dd0560bdd2250ef0a3b704dd.jpg" + } + }, + "bbox": [ + 568, + 652, + 916, + 681 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Smoothness ofthe Cross Field. Consider two pairs of orthogonal unit vectors in a plane, denoted as " + }, + { + "type": "equation_inline", + "content": "( \\pmb { \\alpha } _ { 1 } , \\pmb { \\beta } _ { 1 } )" + }, + { + "type": "text", + "content": "and " + }, + { + "type": "equation_inline", + "content": "( \\alpha _ { 2 } , \\beta _ { 2 } )" + }, + { + "type": "text", + "content": ". We say that the pair " + }, + { + "type": "equation_inline", + "content": "( \\alpha _ { 1 } , \\beta _ { 1 } )" + }, + { + "type": "text", + "content": "aligns with " + }, + { + "type": "equation_inline", + "content": "( \\alpha _ { 2 } , \\beta _ { 2 } )" + }, + { + "type": "text", + "content": "if either " + }, + { + "type": "equation_inline", + "content": "\\pmb { \\alpha } _ { 1 }" + }, + { + "type": "text", + "content": "and " + }, + { + "type": "equation_inline", + "content": "\\pmb { \\alpha } _ { 2 }" + }, + { + "type": "text", + "content": "are colinear, or " + }, + { + "type": "equation_inline", + "content": "\\pmb { \\alpha } _ { 1 }" + }, + { + "type": "text", + "content": "and " + }, + { + "type": "equation_inline", + "content": "\\beta _ { 2 }" + }, + { + "type": "text", + "content": "are colinear." + } + ] + }, + "bbox": [ + 513, + 686, + 916, + 743 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Based on the above definition, it can be proved that " + }, + { + "type": "equation_inline", + "content": "( \\alpha _ { 1 } , \\beta _ { 1 } )" + }, + { + "type": "text", + "content": "aligns with " + }, + { + "type": "equation_inline", + "content": "( \\alpha _ { 2 } , \\beta _ { 2 } )" + }, + { + "type": "text", + "content": "if and only if" + } + ] + }, + "bbox": [ + 513, + 743, + 915, + 771 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\left| \\boldsymbol {\\alpha} _ {1} \\cdot \\boldsymbol {\\alpha} _ {2} \\right| + \\left| \\boldsymbol {\\alpha} _ {1} \\cdot \\boldsymbol {\\beta} _ {2} \\right| + \\left| \\boldsymbol {\\beta} _ {1} \\cdot \\boldsymbol {\\alpha} _ {2} \\right| + \\left| \\boldsymbol {\\beta} _ {1} \\cdot \\boldsymbol {\\beta} _ {2} \\right| \\tag {8}", + "math_type": "latex", + "image_source": { + "path": "images/f01737464d818fdeb13928a3cd61be66ab023b2108355b601995436cee35d53d.jpg" + } + }, + "bbox": [ + 586, + 777, + 916, + 795 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "achieves the minimum. We explain the correctness as follows. Without loss of generality, we assume that " + }, + { + "type": "equation_inline", + "content": "\\pmb { \\alpha } _ { 1 } = ( 1 , 0 )" + }, + { + "type": "text", + "content": "and " + }, + { + "type": "equation_inline", + "content": "\\beta _ { 1 } = ( 0 , 1 )" + }, + { + "type": "text", + "content": ". By denoting " + }, + { + "type": "equation_inline", + "content": "\\alpha _ { 2 }" + }, + { + "type": "text", + "content": "as (cos �, sin �), the above sum simplifies to" + } + ] + }, + "bbox": [ + 513, + 801, + 918, + 844 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "2 (| \\cos \\theta | + | \\sin \\theta |). \\tag {9}", + "math_type": "latex", + "image_source": { + "path": "images/0f8780af8a8d312f9ed5760bf3b5bccc8611c984dba8c2a44dcd8fa4e70d286c.jpg" + } + }, + "bbox": [ + 653, + 849, + 916, + 866 + ] + }, + { + "type": "page_header", + "content": { + "page_header_content": [ + { + "type": "text", + "content": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation" + } + ] + }, + "bbox": [ + 475, + 68, + 882, + 80 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "5" + } + ] + }, + "bbox": [ + 906, + 69, + 915, + 78 + ] + }, + { + "type": "page_footer", + "content": { + "page_footer_content": [ + { + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025." + } + ] + }, + "bbox": [ + 676, + 893, + 915, + 905 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/e25e014b81e442d4ef1e4de0a12ae3b00366cc55c89de021c24e1ab966faba24.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "(a) Input mesh" + } + ], + "image_footnote": [] + }, + "bbox": [ + 89, + 95, + 200, + 181 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/abd18d26b8968f9383ada7d35e09811fa1e6a1fce34a88de24b2504a8e51d81a.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "(b) Cross field" + } + ], + "image_footnote": [] + }, + "bbox": [ + 215, + 95, + 325, + 181 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/43e9470e0ad9c0142f03591ec741c2d53247c12dbe072ad34cc88a813ba93a5a.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "(c) Quad mesh" + }, + { + "type": "text", + "content": "Fig. 6. The smoothness constraint of the cross field beter controls the distribution of singularity points. From left to right: (a) an input triangular mesh; (b) a cross field computed with NeurCross; (c) the quad mesh extracted from the cross field." + } + ], + "image_footnote": [] + }, + "bbox": [ + 343, + 95, + 454, + 181 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In the inset figure, we illustrate how the function value of 2(| cos �| + | sin �|) varies with �. It can be observed that the minimum is achieved at " + }, + { + "type": "equation_inline", + "content": "\\begin{array} { r } { \\theta = k \\frac { \\pi } { 2 } } \\end{array}" + }, + { + "type": "text", + "content": ", while the maximum occurs at " + }, + { + "type": "equation_inline", + "content": "\\begin{array} { r } { \\theta = k \\frac { \\pi } { 2 } + \\frac { \\pi } { 4 } } \\end{array}" + }, + { + "type": "text", + "content": ". Therefore, it can be concluded that" + } + ] + }, + "bbox": [ + 78, + 280, + 256, + 390 + ] + }, + { + "type": "chart", + "content": { + "image_source": { + "path": "images/19ff735f8956b3472f74ba727fe052b3bf43920b06e2e28ae05534b0b4d5d9c7.jpg" + }, + "content": "| X | Y |\n| --- | --- |\n| 0 | 2 |\n| \\(\\pi/4\\) | \\(2\\sqrt{2}\\) |\n| \\(\\pi/2\\) | 2 |", + "chart_caption": [], + "chart_footnote": [] + }, + "sub_type": "contour", + "bbox": [ + 259, + 267, + 464, + 388 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "only when the sum reaches the minimum value of 2, one cross aligns with another " + }, + { + "type": "equation_inline", + "content": "\\begin{array} { r } { ( \\theta = k \\frac { \\pi } { 2 } ) } \\end{array}" + } + ] + }, + "bbox": [ + 78, + 392, + 480, + 420 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We denote the three neighboring points of " + }, + { + "type": "equation_inline", + "content": "\\pmb { p }" + }, + { + "type": "text", + "content": "as " + }, + { + "type": "equation_inline", + "content": "{ \\pmb q } _ { 1 } , { \\pmb q } _ { 2 } , { \\pmb q } _ { 3 }" + }, + { + "type": "text", + "content": ". Since each " + }, + { + "type": "equation_inline", + "content": "\\pmb { q } _ { i }" + }, + { + "type": "text", + "content": "lies on a neighboring face, a rotation around the common edge is necessary before aligning the directions between � and " + }, + { + "type": "equation_inline", + "content": "\\mathbf { \\nabla } _ { q _ { i } . }" + }, + { + "type": "text", + "content": "We define " + }, + { + "type": "equation_inline", + "content": "\\{ R _ { i } \\mid i = 1 , 2 , 3 \\}" + }, + { + "type": "text", + "content": "as the rotation matrices associated with dihedral angles " + }, + { + "type": "equation_inline", + "content": "\\{ \\varphi _ { i } \\mid i = 1 , 2 , 3 \\}" + } + ] + }, + "bbox": [ + 78, + 420, + 279, + 544 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/37cfd3e08b4e7dde5c6d984906df26a34bccb69c180b9a4d42ab63954739dd03.jpg" + }, + "content": "q₂\nφ₂\np\nφ₁\nφ₃\nq₃", + "image_caption": [], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 282, + 421, + 444, + 530 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "and shared edges, which can be precomputed. To this end, the smoothness loss can be written as" + } + ] + }, + "bbox": [ + 78, + 544, + 480, + 571 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm{S}} = \\frac {1}{3 | \\mathcal {P} |} \\int_ {\\mathcal {P}} \\sum_ {i = 1} ^ {3} \\left(\\left| \\boldsymbol {\\alpha} _ {\\boldsymbol {p}} \\cdot R _ {i} \\boldsymbol {\\alpha} _ {\\boldsymbol {q} _ {i}} \\right| + \\left| \\boldsymbol {\\alpha} _ {\\boldsymbol {p}} \\cdot R _ {i} \\boldsymbol {\\beta} _ {\\boldsymbol {q} _ {i}} \\right| \\right. \\tag {10} \\\\ \\left. + \\left| \\boldsymbol {\\beta} _ {\\boldsymbol {p}} \\cdot R _ {i} \\boldsymbol {\\alpha} _ {\\boldsymbol {q} _ {i}} \\right| + \\left| \\boldsymbol {\\beta} _ {\\boldsymbol {p}} \\cdot R _ {i} \\boldsymbol {\\beta} _ {\\boldsymbol {q} _ {i}} \\right| - 2\\right) \\mathrm{d} \\boldsymbol {p}. \\\\ \\end{array}", + "math_type": "latex", + "image_source": { + "path": "images/0b12161ebfd5b2b473d7a57b236705a92341f7aace13706712236169962e8c70.jpg" + } + }, + "bbox": [ + 99, + 575, + 482, + 637 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Remark: Consider a spherical surface, as shown in Fig. 6. At each point on such a surface, the principal curvature directions are not unique. In this case, the smoothness constraint of the cross field plays a crucial role in better controlling the distribution of singular ity points. It is worth noting that our implicit principal curvature alignment is simultaneously satisfied. Moreover, Fig. 6 highlights the importance of efective cross field smoothing, which has also been addressed in prior work. Knöppel et al. [2013] and Diamanti et al. [2014] introduced convex smoothness energies to smooth N-RoSy fields. Knöppel et al. [2013]’s method achieves global optimality but requires a nonlinear transformation, which can cause extra singu larities and distortion. Jakob et al. [2015] uses an extrinsic energy to align with surface features, but its strong reliance on local information often leads to suboptimal results and unwanted singularities. In contrast, our NeurCross smooths the cross field using Equ. 10, introducing singularities only in areas with high curvature variation. A detailed comparison is provided in Section 4.2." + } + ] + }, + "bbox": [ + 78, + 640, + 483, + 876 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/cbc7bee6d39bd37e82e8ad9181a3ffcf185ff11033690bf3ce6022d134d764c5.jpg" + }, + "content": "3D wireframe model of a mechanical part with colored grid lines and highlighted regions (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "(a) w/o feature line const." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 526, + 95, + 697, + 229 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/5bec5fdbbdbfbb4955d8bbd9684803dea4ea2565e0e233ea4449ecb69823c87a.jpg" + }, + "content": "3D wireframe model of a furniture or chair with colorful mesh patterns, no visible text or symbols", + "image_caption": [ + { + "type": "text", + "content": "(b) w/ feature line const." + }, + { + "type": "text", + "content": "Fig. 7. NeurCross supports feature line constraints. (a) The results without (w/o) the feature line constraint (const.); and (b) The result with (w/) the feature line constraint." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 728, + 95, + 901, + 229 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Sharp Feature Alignment. As pointed out in [Pietroni et al. 2021], in the context of quad-meshing, it is important to incorporate feature lines of the input shape, such as crease angles in CAD models, when generating quadrangulation outcomes. However, reconciling this" + } + ] + }, + "bbox": [ + 513, + 316, + 916, + 372 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "requirement with all other objectives is challenging. Generally, the influence of feature lines diminishes with increasing distance." + } + ] + }, + "bbox": [ + 513, + 372, + 669, + 454 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "As illustrated in the inset figure, let �� be the feature lines, where the cross field at each point of �� has been specified. We use " + }, + { + "type": "equation_inline", + "content": "d _ { g } ( \\pmb { p } , \\pmb { F } \\pmb { L } )" + }, + { + "type": "text", + "content": "to denote the geodesic distance between a surface point � and ��. We introduce" + } + ] + }, + "bbox": [ + 514, + 455, + 669, + 579 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/417855208b3a5d7940999284be14d590e6abcf29bca0b43d7c1d240b592ec281.jpg" + }, + "content": "+FL\ndg(p,FL)\np", + "image_caption": [], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 676, + 381, + 913, + 565 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "D _ {\\boldsymbol {p}} = 1 - \\exp \\left(- \\rho_ {\\text {feature}} d _ {g} (\\boldsymbol {p}, F L)\\right), \\tag {11}", + "math_type": "latex", + "image_source": { + "path": "images/6e67cc0c70572aec2b0382ff463481c9df3e7a26b9dbd29dcaa11890fe951f2e.jpg" + } + }, + "bbox": [ + 607, + 585, + 916, + 602 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "and redefine the principal curvature direction alignment as follows:" + } + ] + }, + "bbox": [ + 514, + 607, + 916, + 622 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {L} _ {\\mathrm{AP}} = \\frac {1}{| \\mathcal {P} |} \\int_ {\\mathcal {P}} D _ {p} \\left(\\left| H _ {p} \\boldsymbol {\\alpha} _ {p} \\times \\boldsymbol {\\alpha} _ {p} \\right| + \\left| H _ {p} \\boldsymbol {\\beta} _ {p} \\times \\boldsymbol {\\beta} _ {p} \\right|\\right) \\mathrm{d} p, \\tag {12}", + "math_type": "latex", + "image_source": { + "path": "images/8af96d66082a3970cc94140db16442e8891c26fc0ad312c189a437fbe6b9de56.jpg" + } + }, + "bbox": [ + 540, + 626, + 916, + 655 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "where " + }, + { + "type": "equation_inline", + "content": "\\rho _ { \\mathrm { f e a t u r e } }" + }, + { + "type": "text", + "content": "(10 by default) in " + }, + { + "type": "equation_inline", + "content": "D _ { P }" + }, + { + "type": "text", + "content": "serves as a suficiently large constant to regulate the influence of the feature line. The color gradient in the insert figure represents the value of " + }, + { + "type": "equation_inline", + "content": "D _ { P }" + }, + { + "type": "text", + "content": ", which increases with distance from the feature line, reflecting the gradual reduction in � � influence on the surface point. For ease of implementation, we approximate " + }, + { + "type": "equation_inline", + "content": "d _ { g } ( \\pmb { p } , F L )" + }, + { + "type": "text", + "content": "using straight-line distances. As shown in Fig. 7, the crease line of the model is faithfully preserved in the neighborhood of " + }, + { + "type": "equation_inline", + "content": "F L ." + }, + { + "type": "text", + "content": ", while its influence diminishes as the distance increases. Moreover, in regions where sharp features conflict with principal curvature directions, our NeurCross prioritizes feature alignment (see Fig. 8)." + } + ] + }, + "bbox": [ + 511, + 659, + 916, + 813 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Rotation Angle Prediction. Drawing inspiration from various object segmentation works [Hu et al. 2021; Milano et al. 2020], we employ the U-Net architecture [Ronneberger et al. 2015] to construct our rotation angle prediction network. The input to our U-Net-based network includes the point cloud P, along with the normal direction for each point, and the direction vectors � and � that represent the local coordinate system. The network outputs a scalar value " + }, + { + "type": "equation_inline", + "content": "\\omega _ { p } \\in \\left[ 0 , 1 \\right]" + }, + { + "type": "text", + "content": "for each point �, allowing the rotation angle " + }, + { + "type": "equation_inline", + "content": "\\theta _ { P }" + }, + { + "type": "text", + "content": "to be represented as " + }, + { + "type": "equation_inline", + "content": "\\theta _ { P } = 2 \\pi \\omega _ { P }" + }, + { + "type": "text", + "content": ". For this module, we initialize the orien tation at a point � using a normal distribution with a mean of 0 and a standard deviation of 0.2." + } + ] + }, + "bbox": [ + 511, + 820, + 916, + 876 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "6" + } + ] + }, + "bbox": [ + 81, + 69, + 91, + 78 + ] + }, + { + "type": "page_header", + "content": { + "page_header_content": [ + { + "type": "text", + "content": "Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang" + } + ] + }, + "bbox": [ + 112, + 68, + 715, + 80 + ] + }, + { + "type": "page_footer", + "content": { + "page_footer_content": [ + { + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025." + } + ] + }, + "bbox": [ + 81, + 893, + 321, + 905 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/d91125ee830bc8f885f8ace60176c3868c7c77d54794a043ade2401aab73bb22.jpg" + }, + "content": "3D diagram of a cube with blue curved lines on top face (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "(a) Input mesh" + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 91, + 99, + 267, + 238 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/859f91eabda563b682bdeb999b37d405ed7f8ecd026d2a5078e9a65077eee540.jpg" + }, + "content": "3D wireframe cube with colorful grid pattern, no text or symbols visible", + "image_caption": [ + { + "type": "text", + "content": "(b) Principal curvature field" + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 287, + 99, + 464, + 236 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/51aee388513df485afe536825e604692a93b5b7c5ac94aafd31208edc95a93ac.jpg" + }, + "content": "3D wireframe cube with multicolored grid pattern, no text or symbols visible", + "image_caption": [ + { + "type": "text", + "content": "(c) Our cross field" + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 89, + 273, + 269, + 412 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/73b576dd4e229a7b5bc0d1d913f80e40d1b3b29bc77c36e418c0f17cf93589d3.jpg" + }, + "content": "3D wireframe cube with grid pattern, no text or symbols present", + "image_caption": [ + { + "type": "text", + "content": "(d) Our quad mesh" + }, + { + "type": "text", + "content": "Fig. 8. NeurCross enforces alignment with sharp features even when they diverge from principal curvature directions. (a) An input mesh with conflict ing principal curvature directions (blue) and feature curves (red); (b) The principal curvature field of the input surface; (c) The cross field computed by NeurCross; (d) The resulting quad mesh generated using NeurCross." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 285, + 273, + 464, + 412 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 78, + 549, + 483, + 645 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "3.4 SDF and Cross Field Joint Optimization" + } + ], + "level": 2 + }, + "bbox": [ + 80, + 664, + 383, + 678 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "One challenge in quad meshing is balancing the overall simplicity of the cross field with alignment to the principal directions, a dificulty that becomes more pronounced for geometrically or topologically complex shapes. In this paper, we address this challenge by using an optimizable neural SDF as a bridge to achieve this balance. Notably, the neural SDF and the cross field are optimized simultaneously." + } + ] + }, + "bbox": [ + 78, + 681, + 482, + 763 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "An alternative approach is to first fully optimize the SDF to accu rately represent the input shape and then keep it fixed. However, in this case, the cross field may become severely constrained, as it must align with potentially irregular curvature lines of the pre-fixed SDF. As shown in Fig. 9, the fixed SDF, while providing an accurate representation, may introduce overly complex curvature lines, leading to an excessive number of singular points in the final cross field." + } + ] + }, + "bbox": [ + 78, + 765, + 483, + 875 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/08575997b0e24ff7c2d0e51a07d30705fcf0f1763876fb57050444dad618e6c4.jpg" + }, + "content": "3D modeling visualization of two humanoid figures with meshed surfaces and color-coded heatmaps (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "(a) Cross field" + }, + { + "type": "text", + "content": "(b) Quad mesh" + }, + { + "type": "text", + "content": "(c) SDF fitting" + }, + { + "type": "text", + "content": "(d) Fitting error" + }, + { + "type": "text", + "content": "Fig. 9. Comparison between the two-step method (top row) and our joint optimization strategy (botom row). (a) Cross field; (b) Quad mesh; (c) The underlying SDF surface; (d) Fiting error between the SDF and the input triangular mesh. The final quad mesh is extracted based on the computed cross field and the input triangular mesh. As shown, our joint optimization strategy balances the overall smoothness of the cross field with alignment to the principal curvature directions." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 522, + 95, + 915, + 344 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "3.5 Implementation Details" + } + ], + "level": 2 + }, + "bbox": [ + 514, + 484, + 714, + 500 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "SDF Loss Terms. The loss terms used to regularize the SDF include the Eikonal condition [Gropp et al. 2020], the Dirichlet condition [Lipman 2021], and the alignment condition [Wang et al. 2024, 2023]. For further details on these loss terms, we refer readers to the existing literature [Dong et al. 2024; Wang et al. 2024, 2023]." + } + ] + }, + "bbox": [ + 513, + 503, + 916, + 573 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Sampling Strategy. A neural SDF is employed to approximate the base surface, with regularization at sample points, as detailed in previous works [Ben-Shabat et al. 2022; Boulch and Marlet 2022; Dong et al. 2024; Gropp et al. 2020; Hou et al. 2022; Huang et al. 2022; Kazhdan and Hoppe 2013; Ma et al. 2021; Sitzmann et al. 2020; Wang et al. 2024, 2023; Xu et al. 2022]. We extract centroids from all triangles in the mesh to define the sample set P, chosen for their representative nature of the surface. For each point " + }, + { + "type": "equation_inline", + "content": "\\pmb { \\mathscr { p } } \\in \\mathscr { P }" + }, + { + "type": "text", + "content": "the normal vector " + }, + { + "type": "equation_inline", + "content": "\\scriptstyle n _ { p }" + }, + { + "type": "text", + "content": "is derived from the corresponding triangular face’s normal." + } + ] + }, + "bbox": [ + 511, + 585, + 916, + 720 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Given that each triangular face has three neighboring faces, neighboring relationships between points in " + }, + { + "type": "equation_inline", + "content": "\\mathcal { P }" + }, + { + "type": "text", + "content": "can be thus established. The SDF is assumed diferentiable within a narrow, thin-shell space Ω, which closely encloses the base surface. Following previous studies [Dong et al. 2024; Gropp et al. 2020; Ma et al. 2021; Wang et al. 2024, 2023], Ω is sampled using random displacements around each point " + }, + { + "type": "equation_inline", + "content": "\\pmb { \\mathscr { p } } \\in \\mathscr { P }" + }, + { + "type": "text", + "content": ". A Gaussian distribution centered at each �, with a standard deviation based on the distance to its �-th nearest neighbor (typically " + }, + { + "type": "equation_inline", + "content": "k = 5 0 )" + }, + { + "type": "text", + "content": ", is used for this purpose. A one-point sampling technique is then applied to generate the sample set Ω, which is the same size as " + }, + { + "type": "equation_inline", + "content": "\\mathcal { P }" + } + ] + }, + "bbox": [ + 511, + 723, + 918, + 875 + ] + }, + { + "type": "page_header", + "content": { + "page_header_content": [ + { + "type": "text", + "content": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation" + } + ] + }, + "bbox": [ + 477, + 68, + 882, + 79 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "7" + } + ] + }, + "bbox": [ + 906, + 69, + 915, + 78 + ] + }, + { + "type": "page_footer", + "content": { + "page_footer_content": [ + { + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025." + } + ] + }, + "bbox": [ + 676, + 893, + 915, + 905 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/180acd3c13b491fd98c00e77c891d82db3583462811d747d1ca344de205641c3.jpg" + }, + "content": "This diagram illustrates a neural network architecture for ResNet activation, showing the flow of data through FC (Functional Component) and Concatenation layers to generate output.", + "image_caption": [ + { + "type": "text", + "content": "Fig. 10. An overview of our U-Net-based module designed for predicting the rotation angle �. The network architecture incorporates the ResNet struc ture, with all layers being Multi-Layer Perceptrons (MLPs). The “ResNets” represents a combination of multiple ResNet blocks, the “FC” denotes the Fully Connected Layer, and the circled " + }, + { + "type": "equation_inline", + "content": "^ { * } C ^ { * }" + }, + { + "type": "text", + "content": "symbol indicates the concatena tion operation." + } + ], + "image_footnote": [] + }, + "sub_type": "flowchart", + "bbox": [ + 84, + 93, + 475, + 280 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "To prevent outlier zero iso-surfaces far from " + }, + { + "type": "equation_inline", + "content": "{ \\mathcal { P } } ," + }, + { + "type": "text", + "content": "we uniformly sample the bounding box (assuming input points are normalized within " + }, + { + "type": "equation_inline", + "content": "[ - 0 . 5 , 0 . 5 ] ^ { 3 } )" + }, + { + "type": "text", + "content": ", generating a sample set Q." + } + ] + }, + "bbox": [ + 78, + 382, + 482, + 425 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Eikonal Condition. The Eikonal condition is crucial for ensuring that the SDF " + }, + { + "type": "equation_inline", + "content": "f ( \\boldsymbol { x } ; \\Theta )" + }, + { + "type": "text", + "content": "maintains a unit gradient at every point, i.e., " + }, + { + "type": "equation_inline", + "content": "\\| \\nabla f \\| = 1" + }, + { + "type": "text", + "content": ", particularly in the vicinity of the surface. The corresponding loss term is defined as:" + } + ] + }, + "bbox": [ + 78, + 431, + 483, + 486 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {L} _ {E} = \\frac {1}{| \\mathcal {P} | + | \\Omega |} \\int_ {\\mathcal {P} \\cup \\Omega} \\left| 1 - \\| \\nabla f (\\boldsymbol {x}; \\Theta) \\| \\right| \\mathrm{d} \\boldsymbol {x}, \\tag {13}", + "math_type": "latex", + "image_source": { + "path": "images/58be8eb4f97a57321f8b95cb53d08cabb402bfb8c712ef3de982541e8e672268.jpg" + } + }, + "bbox": [ + 148, + 489, + 480, + 520 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "where " + }, + { + "type": "equation_inline", + "content": "\\mathcal { P }" + }, + { + "type": "text", + "content": "represents the sample points " + }, + { + "type": "equation_inline", + "content": "( \\mathrm { e . g . }" + }, + { + "type": "text", + "content": ", centroids of mesh triangles), and Ω encodes a narrow band around the surface where the SDF is diferentiable. Notably, the point set " + }, + { + "type": "equation_inline", + "content": "\\scriptstyle Q ," + }, + { + "type": "text", + "content": "which represents regions far from the base surface, is excluded from this loss term and serves to prevent outlier zero isosurfaces in distant regions." + } + ] + }, + "bbox": [ + 78, + 522, + 483, + 592 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Dirichlet Condition. For every point " + }, + { + "type": "equation_inline", + "content": "\\pmb { p } \\in \\mathcal { P }" + }, + { + "type": "text", + "content": ", it is essential that they lie as close as possible to the underlying surface, ideally satisfying " + }, + { + "type": "equation_inline", + "content": "f ( \\pmb { \\mathscr { p } } ; \\Theta ) = 0 ." + }, + { + "type": "text", + "content": ". Conversely, for points " + }, + { + "type": "equation_inline", + "content": "q \\in { \\cal Q }" + }, + { + "type": "text", + "content": ", which lie away from the underlying surface, we aim to partition Q into interior and exterior regions, preventing � from degenerating. These conditions are formalized as the following loss terms:" + } + ] + }, + "bbox": [ + 78, + 598, + 483, + 681 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {L} _ {\\mathrm{DM}} = \\frac {1}{| \\mathcal {P} |} \\int_ {\\mathcal {P}} \\left| f (\\boldsymbol {p}; \\Theta) \\right| \\mathrm{d} \\boldsymbol {p}, \\tag {14}", + "math_type": "latex", + "image_source": { + "path": "images/dd0d89d3f770fbf530659640b5b859b63a34d6e2934090cde7494f72232b2e7e.jpg" + } + }, + "bbox": [ + 192, + 685, + 480, + 715 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "and" + } + ] + }, + "bbox": [ + 80, + 718, + 107, + 729 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {L} _ {\\mathrm{DNM}} = \\frac {1}{| Q |} \\int_ {Q} \\exp \\left(- \\rho_ {\\mathrm{DNM}} \\big | f (\\boldsymbol {q}; \\Theta) \\big |\\right) \\mathrm{d} \\boldsymbol {q}, \\tag {15}", + "math_type": "latex", + "image_source": { + "path": "images/3b811dc559d9720424806a775d5ae8b9af9d6b64d41d511d05d851f90c2c86b8.jpg" + } + }, + "bbox": [ + 148, + 728, + 480, + 757 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "where " + }, + { + "type": "equation_inline", + "content": "\\rho _ { \\mathrm { D N M } }" + }, + { + "type": "text", + "content": "(defaulting to 100) is the exponential weight controlling the penalty for deviations from the surface." + } + ] + }, + "bbox": [ + 78, + 758, + 482, + 786 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "SIREN-based Module. Similar to various implicit surface reconstruction methods [Ben-Shabat et al. 2022; Lipman 2021; Wang et al. 2024, 2022b, 2023], our NeurCross employs the SIREN [Sitzmann et al. 2020] network architecture, which consists of four hidden layers with 256 units each. The SIREN architecture is based on multi-layer perceptrons (MLPs), where inputs are first normalized to the range " + }, + { + "type": "equation_inline", + "content": "[ - 1 , 1 ] ^ { 3 }" + }, + { + "type": "text", + "content": "before being processed by the network. The activation function used in this architecture is the sine periodic function, which operates on the input point cloud " + }, + { + "type": "equation_inline", + "content": "\\mathcal { P }" + }, + { + "type": "text", + "content": "to produce the SDF field required for computing the Hessian matrix. For initializing this SIREN-based module, we follow SIREN’s initialization strategy [Sitzmann et al. 2020], which ensures that the distribution of activations remains consistent across all layers of the network." + } + ] + }, + "bbox": [ + 78, + 792, + 483, + 876 + ] + }, + { + "type": "table", + "content": { + "image_source": { + "path": "images/828d3c466afe86167a698f661eb1d9ac58df2b72238a6a62f0c45d42bfc5a6f8.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 1. The sizes of the building blocks within our U-Net-based module. �b l k denotes the number of botleneck layers within each ResNet block. From the 1st to the 7th block, the values of �b l k are set to 3, 4, 6, 3, 3, 4, and 6, respectively." + } + ], + "table_footnote": [], + "html": "
Layer NameLayer ArchitectureOutput Size
$1 \\times 1, input\\_size=12$ 256
ResNets #1, #2, #3 $\\begin{bmatrix} 1 \\times 1, 256 \\\\ 1 \\times 1, 64 \\\\ 1 \\times 1, 64 \\end{bmatrix} \\times n_{bottleneck}$ 256
ResNets #4, #5, #6, #7 $\\begin{bmatrix} 1 \\times 1, 512 \\\\ 1 \\times 1, 128 \\\\ 1 \\times 1, 128 \\end{bmatrix} \\times n_{bottleneck}$ 512
$1 \\times 1, 512$ 32
$1 \\times 1, 32$ 1
", + "table_type": "simple_table", + "table_nest_level": 1 + }, + "bbox": [ + 539, + 164, + 897, + 308 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 513, + 335, + 916, + 434 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "U-Net-based Module. We adopt a U-Net architecture [Ronneberger et al. 2015] as the backbone for predicting rotation angles. To address the vanishing gradient issue in deep networks, we incorporate ResNet blocks [He et al. 2016] as the core components of the U-Net. As shown in Fig. 10, our network consists of ResNet blocks (ResNets) and fully connected layers (FC), with all layers implemented using MLPs. A detailed configuration of each ResNet block is provided in Tab. 1." + } + ] + }, + "bbox": [ + 513, + 441, + 916, + 551 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Parameter Setting. In this paper, we set the weights as follows based on our tailored configurations: " + }, + { + "type": "equation_inline", + "content": "\\lambda _ { \\mathrm { E } } = 5 0 , \\lambda _ { \\mathrm { D M } } = 7 0 0 0 , \\lambda _ { \\mathrm { D N M } } =" + }, + { + "type": "text", + "content": "600, " + }, + { + "type": "equation_inline", + "content": "\\lambda _ { \\mathrm { A N } } = 3 , \\lambda _ { \\mathrm { A P } } = 1 0 ." + }, + { + "type": "text", + "content": ", and " + }, + { + "type": "equation_inline", + "content": "\\lambda _ { S } = 3 0" + }, + { + "type": "text", + "content": ". The annealing factor � remains 1 during the initial 20% of iterations, then linearly decreases to " + }, + { + "type": "equation_inline", + "content": "3 \\times 1 0 ^ { - 4 }" + }, + { + "type": "text", + "content": "from 20% to 40% of the iteration span, and finally drops to 0 towards the end. Throughout the training phase, we apply the Adam optimizer [Kingma and Ba 2014] with a default learning rate of " + }, + { + "type": "equation_inline", + "content": "5 \\times 1 0 ^ { - 5 }" + }, + { + "type": "text", + "content": "and complete 10,000 iterations." + } + ] + }, + "bbox": [ + 513, + 560, + 916, + 672 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Quad Mesh Extraction. The extraction of the quad mesh from our cross field follows a two-step scheme, as detailed in references Bommes et al. [2009], Ebke et al. [2013], and Dielen et al. [2021], to achieve a high-quality outcome. This process begins with a step of parametrization based on our cross field. In implementation, we utilize the global-seamless parametrization technique from libigl [Jacobson et al. 2017] to align the parametrization with our cross field. Subsequently, we employ libQEx [Ebke et al. 2013] to extract the quad mesh from this parameterization." + } + ] + }, + "bbox": [ + 511, + 679, + 918, + 804 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "4 EXPERIMENTS" + } + ], + "level": 2 + }, + "bbox": [ + 514, + 816, + 648, + 829 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Evaluation Metrics and Platform. To evaluate the accuracy of the quad mesh, we utilize four primary metrics [Huang et al. 2018; Wang et al. 2023]: area distortion (Area), angle distortion (Angle), the number of singularities (# of Sings), chamfer distance (CD), and Jacobian Ratio (JR). The area distortion metric, scaled by 10,000, represents the standard deviation of the areas of the quadrilateral faces within a mesh. The angle distortion is quantified using the formula " + }, + { + "type": "equation_inline", + "content": "\\begin{array} { r } { \\sqrt { \\frac { 1 } { N } \\sum _ { i } ( \\phi _ { i } - \\frac { \\pi } { 2 } ) ^ { 2 } } } \\end{array}" + }, + { + "type": "text", + "content": ", where the summation extends over all angles " + }, + { + "type": "equation_inline", + "content": "\\phi" + }, + { + "type": "text", + "content": "in the quad mesh, and � denotes their count. Chamfer distance, scaled by 10,000 and calculated using the �1-norm, quantifies the similarity between two surfaces. The Jacobian Ratio quantifies the uniformity of local deformation in quadrilateral elements. It is defined as the ratio of the smallest to the largest determinant of the Jacobian matrices at element corners, providing a dimensionless measure from 0 (degenerate element) to 1 (perfect parallelogram). The experiments detailed in this paper were executed on an NVIDIA GeForce RTX 3090 graphics card equipped with 24GB of video mem ory and powered by an AMD EPYC 7642 processor." + } + ] + }, + "bbox": [ + 513, + 834, + 918, + 876 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "8" + } + ] + }, + "bbox": [ + 81, + 69, + 91, + 78 + ] + }, + { + "type": "page_header", + "content": { + "page_header_content": [ + { + "type": "text", + "content": "Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang" + } + ] + }, + "bbox": [ + 112, + 68, + 715, + 80 + ] + }, + { + "type": "page_footer", + "content": { + "page_footer_content": [ + { + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025." + } + ] + }, + "bbox": [ + 81, + 893, + 321, + 905 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/d3234236f683909e2ffd9df3f83a583e3333e2acd52920c683db8773aa05bf28.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "Fig. 11. Quad meshes generated by NeurCross and four other methods on the table model in the ShapeNet dataset [Chang et al. 2015]." + } + ], + "image_footnote": [] + }, + "bbox": [ + 81, + 89, + 918, + 229 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 78, + 258, + 483, + 474 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Datasets. We carry out quad mesh generation experiments on two popular datasets: ShapeNet [Chang et al. 2015] and Thingi10K [Zhou and Jacobson 2016]. To maintain uniformity in evaluation, all input meshes are scaled to fit within the range of " + }, + { + "type": "equation_inline", + "content": "[ - 0 . 5 , 0 . 5 ] ^ { 3 }" + }, + { + "type": "text", + "content": "ensuring a consistent and fair basis for comparison across all datasets." + } + ] + }, + "bbox": [ + 78, + 479, + 480, + 549 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "4.1 Comparison on Open Datasets" + } + ], + "level": 2 + }, + "bbox": [ + 78, + 560, + 326, + 574 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We assess the eficacy of our proposed method, NeurCross, by con ducting evaluations on two distinct datasets and comparing its performance against four contemporary state-of-the-art quadrilateral mesh generation methods. For the three methods, namely Instant Meshes (IM) [Jakob et al. 2015], QuadriFlow [Huang et al. 2018], and QuadWild [Pietroni et al. 2021], we employed the open-source imple mentations that are readily available. It is worth noting that Quad Wild [Pietroni et al. 2021] is primarily a quadrangulation method rather than a cross field generation approach. The Mixed-Integer Quadrangulation (MIQ) method [Bommes et al. 2009] does not re lease its source code; therefore, we use the implementation provided by libigl [Jacobson et al. 2017]. However, the available implementation does not support the feature alignment constraint. For a fair comparison with MIQ, we employ the same parameterization and extraction techniques, namely global-seamless parameterization and libQEx [Ebke et al. 2013]." + } + ] + }, + "bbox": [ + 78, + 577, + 482, + 800 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "ShapeNet Dataset. The ShapeNet dataset [Chang et al. 2015] con sists of a diverse range of human-made models. As the global seamless parametrization from libigl [Jacobson et al. 2017] cannot handle non-manifold meshes, we use manifold ShapeNet meshes repaired with DualOctreeGNN [Wang et al. 2022a]. We apply our" + } + ] + }, + "bbox": [ + 78, + 806, + 483, + 876 + ] + }, + { + "type": "table", + "content": { + "image_source": { + "path": "images/24c7c2967125183d50cc64176184088cf2ff50f3419dd3e40231b5b82b8bffb8.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 2. Quantitative comparison on the ShapeNet dataset [Chang et al. 2015]. Within each column, the best scores are emphasized with bold and underlining (best), whereas the second-best scores are highlighted in bold (second best). The quad mesh generated by all the methods comprises an average of 6,000 vertices and 12,000 faces." + } + ], + "table_footnote": [], + "html": "
Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
IM [Jakob et al. 2015]1.5711.78200.528.970.70
QuadriFlow [Huang et al. 2018]2.2813.2491.5850.180.65
QuadWild [Pietroni et al. 2021]1.5211.0593.0410.340.73
MIQ [Bommes et al. 2009]5.2312.89 $\\underline{82.12}$ 8.250.58
NeurCross (Ours) $\\underline{1.48}$ $\\underline{9.85}$ 85.32 $\\underline{8.03}$ $\\underline{0.78}$
", + "table_type": "simple_table", + "table_nest_level": 1 + }, + "bbox": [ + 521, + 338, + 908, + 426 + ] + }, + { + "type": "table", + "content": { + "image_source": { + "path": "images/c3f24835c59260fc54b3ad7d9e67f6ebb1a18570efa296567af9d56d199da364.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 3. Quantitative comparison on the Thingi10K dataset [Zhou and Jacobson 2016]. The quad mesh generated by all methods comprises an average of 10,000 vertices and 20,000 faces. Within each column, the best scores are emphasized with bold and underlining (best), whereas the secondbest scores are simply highlighted in bold (second best)." + } + ], + "table_footnote": [], + "html": "
Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
IM [Jakob et al. 2015]1.4510.57397.189.830.75
QuadriFlow [Huang et al. 2018]1.5812.3978.3226.890.72
QuadWild [Pietroni et al. 2021]1.4010.1685.1128.120.77
MIQ [Bommes et al. 2009]1.389.8566.548.570.67
NeurCross (Ours)1.339.6868.968.220.81
", + "table_type": "simple_table", + "table_nest_level": 1 + }, + "bbox": [ + 521, + 516, + 908, + 604 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "NeurCross to three randomly selected categories—airplane, bench, and cabinet—which together contain 7433 models. For a fair comparison, all generated quad meshes are standardized to contain an average of 6,000 vertices and 12,000 faces." + } + ] + }, + "bbox": [ + 511, + 618, + 916, + 672 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In Fig. 11, we display the quad meshes generated by our Neur-Cross alongside four other methods. For this example, although IM [Jakob et al. 2015] produces a regular quadrilateral mesh, the outcome includes some triangular elements. More comparisons between IM and our method will be provided in Sec. 4.2. Quadri-Flow [Huang et al. 2018], MIQ [Bommes et al. 2009], and Quad-Wild [Pietroni et al. 2021] generate some misaligned quadrilateral elements, as seen in the highlighted windows. In contrast, our method yields a better quadrilateral mesh. Tab. 2 shows the quantitative comparison of our method against the four approaches." + } + ] + }, + "bbox": [ + 511, + 674, + 916, + 813 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Thingi10K Dataset. The Thingi10K dataset [Zhou and Jacobson 2016] features a variety of shapes with intricate geometric details. For our analysis based on Thingi10K, we tested 1,000 randomly selected triangle meshes from the dataset, which were also used as inputs for all comparative methods. The quad meshes generated by all methods contain, on average, 10,000 vertices and 20,000 faces to maintain fidelity to the original models." + } + ] + }, + "bbox": [ + 513, + 819, + 916, + 876 + ] + }, + { + "type": "page_header", + "content": { + "page_header_content": [ + { + "type": "text", + "content": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation" + } + ] + }, + "bbox": [ + 475, + 68, + 882, + 79 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "9" + } + ] + }, + "bbox": [ + 903, + 69, + 915, + 78 + ] + }, + { + "type": "page_footer", + "content": { + "page_footer_content": [ + { + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025." + } + ] + }, + "bbox": [ + 676, + 893, + 915, + 904 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/4bd962ed3e1ea479a69cd57aaa89aea978fc3daa34396d7fca61a84b739dc821.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "Fig. 12. Quad meshes generated by NeurCross and four other methods on a cup model in the Thingi10K dataset [Zhou and Jacobson 2016]." + } + ], + "image_footnote": [] + }, + "bbox": [ + 83, + 97, + 915, + 239 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/b6825fb9918d39e8f312f63ebde7015297c773d90604b0c047d02e8edfaa2917.jpg" + }, + "content": "Three 3D wireframe models of a vase-like object with mesh surfaces and bounding boxes, no text or symbols present.", + "image_caption": [ + { + "type": "text", + "content": "IGM" + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 104, + 272, + 455, + 402 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/cbbcd70cf0c8a4de657d5efa22dead0fda074d25d931b0c002ea85bc1e994a9f.jpg" + }, + "content": "3D wireframe model of a vase-like object with geometric cutouts, no visible text or symbols", + "image_caption": [ + { + "type": "text", + "content": "IM" + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 218, + 273, + 336, + 402 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/baf456f6bdcd214dad0d890be2800e3964714f633be8628e3770db97cb1055e1.jpg" + }, + "content": "3D wireframe model of a jug with mesh structure and inset showing cross-section (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "QuadriFlow" + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 333, + 273, + 455, + 402 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/28db9c04fb0fcf8702bba759d2eb75cdcf657149cc0078f6ce4d7a8f2e881c33.jpg" + }, + "content": "3D wireframe model of a vase with a square inset showing internal mesh structure (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "QuadWild" + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 102, + 431, + 222, + 561 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/420ade657de8989f3176bc463fc7bd07e12456c84a98fe49420edf0c949fd573.jpg" + }, + "content": "3D wireframe model of a knitted object with mesh grid and inset showing circular pattern (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "MIQ" + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 218, + 431, + 336, + 561 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/a49940b47cae5d6b5f8214fcb31435795d190291761b2e30327d7f4e52b661b8.jpg" + }, + "content": "3D wireframe model of a jug with mesh structure and inset showing mesh grid (no text or symbols)", + "image_caption": [ + { + "type": "text", + "content": "NeurCross (Ours)" + }, + { + "type": "text", + "content": "Fig. 13. Comparison with five state-of-the-art methods using data provided in IGM [Bommes et al. 2013a]." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 334, + 431, + 455, + 561 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 78, + 667, + 482, + 709 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Quantitative comparison statistics are presented in Tab. 3. Our method consistently outperforms others on average across this dataset. Interestingly, MIQ [Bommes et al. 2009] shows commend able performance on this dataset. However, it is important to note that despite this improvement, the issue of producing distorted quadrilaterals in the resulting quad mesh remains (see Fig. 12 and the JR metric in Tab. 3). Quadwild [Pietroni et al. 2021] requires smoothing of the generated quad mesh, which compromises geo metric details and increases the Chamfer Distance (CD). In contrast, our method produces a more intuitive cross field without needing to introduce excessive singular points (see zoom-in windows in Fig. 12)." + } + ] + }, + "bbox": [ + 78, + 710, + 482, + 876 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/47770f35d9ed1106c7301a54173f218e014bca3011454c5bc1bee39658e9a82d.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "Fig. 14. Comparison with five methods on Human Body data. Dielen et al. [2021] proposed a supervised learning-based approach designed to generate quad meshes on human body data from the FAUST dataset [Bogo et al. 2014]. Due to the absence of available open-source data, the comparison result in the upper left is taken from Dielen et al. [2021]’s paper." + } + ], + "image_footnote": [] + }, + "bbox": [ + 526, + 270, + 901, + 559 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "4.2 Further Comparison" + } + ], + "level": 2 + }, + "bbox": [ + 514, + 643, + 691, + 657 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Comparison with IGM. IGM [Bommes et al. 2013a] is characterized as a global approach, primarily focused on the joint optimization of parametrization with integer constraints. Like our method, it also utilizes libQEx [Ebke et al. 2013] for extracting quad meshes from the parametrization. Although IGM provides full control over edge alignment and singularity placement, yielding high-quality quad meshes, its lack of scalability can lead to severely distorted quadrilaterals (see Fig. 13)." + } + ] + }, + "bbox": [ + 511, + 660, + 916, + 772 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Comparison with Learning Methods. Dielen et al. [2021] represents a pioneering efort in quad mesh generation through deep learning methodologies. Their method uses a supervised network architecture to predict the frame field, comprising both a global network and a local network for field prediction. Subsequently, the parametrization-based quadrangulation method proposed in Campen et al. [2015b] is employed to generate the quad meshes." + } + ] + }, + "bbox": [ + 511, + 777, + 918, + 876 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "10" + } + ] + }, + "bbox": [ + 81, + 69, + 94, + 78 + ] + }, + { + "type": "page_header", + "content": { + "page_header_content": [ + { + "type": "text", + "content": "• Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang" + } + ] + }, + "bbox": [ + 104, + 68, + 720, + 80 + ] + }, + { + "type": "page_footer", + "content": { + "page_footer_content": [ + { + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025." + } + ] + }, + "bbox": [ + 81, + 893, + 321, + 905 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/9a2a08412c7f36afe57072ddff0fe3f9e94217d7e42405da1bd0a41660d5d2e9.jpg" + }, + "content": "Power Fields\nPolyVectors\nNeurCross (Ours)", + "image_caption": [ + { + "type": "text", + "content": "Fig. 15. Comparison of quad meshes generated by Power Fields [Knöppel et al. 2013], PolyVectors [Diamanti et al. 2014], and NeurCross." + } + ], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 91, + 95, + 472, + 229 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/d50c48406bee2d709601f7f465d5f6fa5f4213fde40647fff6c37e264cb82ed2.jpg" + }, + "content": "3D wireframe models of mechanical components with grid patterns, comparing IM and NeurCross (Ours) methods (no text or symbols on models)", + "image_caption": [], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 89, + 263, + 472, + 441 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/126bc8f58e5f3485846f850a50b2649ddfb2993725588b3f92a55d5c9b04b7bd.jpg" + }, + "content": "Quad Remesher\nNeurCross (Ours)", + "image_caption": [ + { + "type": "text", + "content": "Fig. 16. Comparison with IM. Here, the same approach—applying globa seamless parameterization [Jacobson et al. 2017] and libQEx [Ebke et al. 2013]— is used to extract quadrilateral meshes from the respective cross fields of IM and our NeurCross." + }, + { + "type": "text", + "content": "Fig. 17. Comparison of quad meshes generated by Quad Remesher [Remesher 2019] and NeurCross." + } + ], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 89, + 498, + 468, + 670 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "However, due to the inherent constraints ofsupervised learning, this approach shows optimal performance only on the FAUST dataset [Bogo et al. 2014], a limitation not encountered by our self-supervised method. Owing to a lack of required data, our comparison is limited to the model presented in their paper (see Fig. 14)." + } + ] + }, + "bbox": [ + 78, + 715, + 483, + 786 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Comparison with PowerFields andPolyVectors. Power Fields [Knöppel et al. 2013] eficiently constructs smooth n-direction fields on surfaces by solving a sparse eigenvalue problem, ensuring global optimality and high-quality results. PolyVectors [Diamanti et al. 2014] extends N-RoSy fields to N-PolyVector fields by relaxing orthogonality and symmetry constraints, enabling their computation via a sparse linear system without integer variables. Both methods focus on eficient computation of directional fields, with Power Fields [Knöppel et al. 2013] optimizing smoothness and PolyVectors [Diamanti et al. 2014] generalizing traditional field representations. Fig. 15 compares the quadrilateral meshes generated by our NeurCross and these methods. NeurCross not only aligns with principal curvatures but also preserves overall smoothness." + } + ] + }, + "bbox": [ + 78, + 792, + 483, + 876 + ] + }, + { + "type": "chart", + "content": { + "image_source": { + "path": "images/c200ed43f6ebfd0324524a22617394ea94113b8b0a6584c9d0aa81ee90ce1d51.jpg" + }, + "content": "| Method | Description |\n| --- | --- |\n| Input | White 3D model with a curved base structure. |\n| IM | Red 3D model with a curved base structure. |\n| QuadriFlow | Blue 3D model with a curved base structure. |\n| QuadWild | Red 3D model with a curved base structure. |\n| MIQ | Blue 3D model with a curved base structure. |\n| NeurCross (Ours) | Blue 3D model with a curved base structure. |", + "chart_caption": [ + { + "type": "text", + "content": "Fig. 18. Approximation accuracy. Here we show the approximation errors between the input surface and the final quad meshes generated by diferent methods. The error is measured from each sampled point on the quad mesh to the input surface." + } + ], + "chart_footnote": [] + }, + "sub_type": "surface_3d", + "bbox": [ + 537, + 94, + 906, + 334 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 513, + 398, + 916, + 494 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Comparison with IM. IM [Jakob et al. 2015] is an efective method for generating quad meshes. To facilitate a fair comparison between IM and our approach, we use the same global seamless parameterization and extraction technique (libQEx [Ebke et al. 2013]) to extract the quad mesh. As shown in Fig. 16, our method produces fewer singularities than IM. Additionally, our method outperforms IM [Jakob et al. 2015] in terms of principal direction alignment and structural integrity, as illustrated in the close-up views." + } + ] + }, + "bbox": [ + 513, + 501, + 916, + 613 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Comparison with Quad Remesher. Quad Remesher [Remesher 2019] excels at generating quadrilateral meshes and is available as a plugin for software like Blender. It is stable, eficient, and effective at preserving model features while maintaining topological uniformity, with our method achieving comparable results. However, its performance depends heavily on the quality of the input mesh, producing low-quality quadrilateral meshes when the input polygonal mesh is suboptimal (see Fig. 17)." + } + ] + }, + "bbox": [ + 513, + 619, + 916, + 731 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Fidelity. In practical applications, when converting a shape from a triangular mesh to a quadrilateral mesh representation, the goals extend beyond minimizing area distortion, angle distortion, and the number of singular points; maintaining fidelity to the original shape is also crucial. Recognizing that a low-resolution quad mesh may naturally lose some details, we use various methods to generate a quad mesh containing 25,000 vertices and 50,000 faces for a more detailed comparison." + } + ] + }, + "bbox": [ + 513, + 737, + 916, + 847 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In Fig. 18, we present the approximation errors between the quad meshes generated by five methods and the input triangle mesh. The quad meshes generated by our NeurCross and MIQ [Bommes et al. 2009] faithfully represent the original input. IM [Jakob et al. 2015] and QuadriFlow [Huang et al. 2018] exhibit minor shape distortions, whereas QuadWild [Pietroni et al. 2021] produces a smoother result, leading to a loss of detail." + } + ] + }, + "bbox": [ + 514, + 848, + 916, + 876 + ] + }, + { + "type": "page_header", + "content": { + "page_header_content": [ + { + "type": "text", + "content": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation" + } + ] + }, + "bbox": [ + 470, + 68, + 879, + 79 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "• 11" + } + ] + }, + "bbox": [ + 885, + 69, + 915, + 78 + ] + }, + { + "type": "page_footer", + "content": { + "page_footer_content": [ + { + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025." + } + ] + }, + "bbox": [ + 676, + 893, + 915, + 904 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/9af987df6afa7a322ff8f63778cc4ce9ec84c169acfdbe45be82b0cd71ba9017.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "IM" + } + ], + "image_footnote": [] + }, + "bbox": [ + 101, + 97, + 272, + 242 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/c685e1f0176cdeaa12ec815ade19430481b8f4c34964886679303fe7a9629372.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "QuadriFlow" + } + ], + "image_footnote": [] + }, + "bbox": [ + 279, + 97, + 446, + 242 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/772533f96bbff2eb87f0f94932bfcda08985573e9999e99db04f3595e3689f47.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "QuadWild" + } + ], + "image_footnote": [] + }, + "bbox": [ + 454, + 97, + 625, + 239 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/e32263b5421af267dcd1f695c7f75720768fa2a9b9939afe44b2f47b893894b5.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "MIQ" + } + ], + "image_footnote": [] + }, + "bbox": [ + 629, + 98, + 715, + 239 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/86b4b50cbd299c636eeba84c156d0b3d31a57d3ab63fc1cba378e142be434145.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "NeurCross (Ours)" + } + ], + "image_footnote": [] + }, + "bbox": [ + 722, + 98, + 890, + 239 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/16dee25d509d1d8d63202d824b6568049f1f82a746504f2fd3fac5ff3651bf64.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "Fig. 19. The top row shows the cross field generated by our method and four other methods on a noisy input mesh. The botom row shows the resulting quad meshes produced by each approach. Note that MIQ fails to produce a valid result for this input surface with noise." + }, + { + "type": "text", + "content": "Fig. 20. Quad meshes generated by all the methods on two models from ShapeNet [Chang et al. 2015] (the airplane model) and Thingi10K [Zhou and Jacobson 2016] (the grayloc model). We also show the locations of singular points, where “# of Sings” denotes the number of singular points on each quad mesh." + } + ], + "image_footnote": [] + }, + "bbox": [ + 84, + 301, + 908, + 523 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 78, + 574, + 483, + 643 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Resistance to Noise. As noted in Wang et al. [2023], Wang et al. [2024], and Dong et al. [2024], the Hessian matrix possesses intrinsic smoothing properties. Benefiting from this characteristic, our method demonstrates inherent resistance to noise in cross field prediction. We used a baseline mesh with 15,000 vertices and introduced Gaussian noise (i.e., 2% relative to the normal direction of each model) to test the noise immunity of our NeurCross. For a comprehensive comparison, we evaluated the four other methods under the same noise conditions." + } + ] + }, + "bbox": [ + 78, + 667, + 483, + 791 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In Fig. 19, we present the results of diferent methods under noisy input. Notably, our approach optimizes the SDF and the cross field simultaneously. As a result, during optimization, the underlying SDF naturally smooths out noise, leading to a more intuitive cross field. In summary, our method demonstrates stronger noise resistance compared to four other methods." + } + ] + }, + "bbox": [ + 78, + 792, + 483, + 875 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Singular Points. It’s well acknowledged that a trade-of must be achieved between reducing singular points and aligning with principal directions. Thus, it’s preferable to position singular points in regions with high curvature variation rather than in flatter areas. As observed in Tab. 2, Tab. 3, and Fig. 20, our method produces a slightly higher number of singular points compared to MIQ [Bommes et al. 2009]. This occurrence can be attributed to MIQ’s tendency to produce distorted quadrilaterals, which consequently reduces the occurrence of singular points as well as area and angular distortions. However, MIQ’s quad mesh lacks overall consistency and tends to oversmooth areas with significant changes in the direction of the cross field." + } + ] + }, + "bbox": [ + 511, + 575, + 916, + 739 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In Fig. 20, we visualize the locations of singular points in the quad meshes generated by all methods on two models. The placement of singular points in the quad mesh generated by our method is more reasonable, and the resulting quadrilateral mesh exhibits high overall consistency." + } + ] + }, + "bbox": [ + 513, + 741, + 916, + 810 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Geometrically Complex Models. Various complex geometric models, such as triangular meshes with high genus, thin shells, or nonorientable surfaces, are common in many fields. In Fig. 21, we display" + } + ] + }, + "bbox": [ + 513, + 834, + 918, + 876 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "12" + } + ] + }, + "bbox": [ + 81, + 69, + 94, + 78 + ] + }, + { + "type": "page_header", + "content": { + "page_header_content": [ + { + "type": "text", + "content": "• Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang" + } + ] + }, + "bbox": [ + 104, + 68, + 720, + 80 + ] + }, + { + "type": "page_footer", + "content": { + "page_footer_content": [ + { + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025." + } + ] + }, + "bbox": [ + 81, + 893, + 320, + 905 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/dff8a0b78248ca6769c6831eae6983736f3ddc1694cf9e2a7b5de7ae4cd9893e.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "IM" + } + ], + "image_footnote": [] + }, + "bbox": [ + 86, + 92, + 243, + 348 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/f8ef2c30199fc58a342f7a58868c1c866353e25dbd178c8afbdde2e0bacd980c.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "QuadriFlow" + } + ], + "image_footnote": [] + }, + "bbox": [ + 253, + 92, + 410, + 347 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/de59dc2aca23a57eec2683f60b7f1b52cd128a449350af0692087b743987e366.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "QuadWild" + } + ], + "image_footnote": [] + }, + "bbox": [ + 419, + 92, + 573, + 347 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/e17009ff1b7da345b7a8166963a66727e4a7d1a544fa97b9096c62d02576a39a.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "MIQ" + } + ], + "image_footnote": [] + }, + "bbox": [ + 584, + 92, + 741, + 347 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/29c4f30a1150810fba89f4d08559ab15b11f482c74c84b6f6244d48b7e6d2317.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "NeurCross (Ours)" + } + ], + "image_footnote": [] + }, + "bbox": [ + 750, + 92, + 906, + 347 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/82282e58612d24db85d424cbd4f9ace54d12c5adc061f798b70f69955fbbbdeb.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "Fig. 21. Comparison of quad meshes generated by various methods for some challenging models, i.e. with high genus, thin shells, and non-orientable rings Across all tests, the quad meshes generated by NeurCross consistently exhibit higher quality compared to those produced by other methods." + }, + { + "type": "text", + "content": "(a) Open boundaries (b) Feature lines (c) Free-form model" + }, + { + "type": "text", + "content": "Fig. 22. Quad meshes extracted by NeurCross using diferent mesh extraction methods for various models: (a) A garment with open boundaries; (b) A CAD model with feature lines; and (c) A free-form model. The results are presented for each extraction method with or without the localized patching mechanism (LPM)." + } + ], + "image_footnote": [] + }, + "bbox": [ + 81, + 411, + 472, + 728 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "the quad meshes generated by our method and other methods on sev eral geometrically complex models. The visualization results show that our method’s performance on the unoriented ring model is comparable to that of IM [Jakob et al. 2015] and QuadriFlow [Huang et al. 2018]. However, for the other two models, only our method consistently produces high-quality quad meshes. Specifically, on the model with a thin shell (the leaf model), only our method and MIQ [Bommes et al. 2009] managed to avoid surface damage. While MIQ produced distorted quadrilaterals at the boundary of the thin shell, our method maintained good overall consistency in the quadrilateral meshes. Fig. 26 shows more results generated by our Neur-Cros on challenging models." + } + ] + }, + "bbox": [ + 78, + 834, + 483, + 876 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/8cb9e9130675bfac20d29de5b46d07fa94de2c1b0193f562e6b31251ae567eab.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "(a) w/o " + }, + { + "type": "equation_inline", + "content": "\\mathcal { L } _ { \\mathbf { A P } }" + }, + { + "type": "text", + "content": "(b) w/o " + }, + { + "type": "equation_inline", + "content": "\\mathcal { L } _ { \\pmb { s } }" + }, + { + "type": "text", + "content": "(c) w/o " + }, + { + "type": "equation_inline", + "content": "\\mathcal { L } _ { \\mathbf { A P } }" + }, + { + "type": "text", + "content": "& " + }, + { + "type": "equation_inline", + "content": "\\mathcal { L } _ { \\pmb { S } }" + }, + { + "type": "text", + "content": "(d) Ours" + }, + { + "type": "text", + "content": "Fig. 23. The quad meshes and cross fields generated by our NeurCross using various loss term combinations: (a) without the alignment with principa directions loss term (w/o L ); (b) without the smoothness loss term (w/o " + }, + { + "type": "equation_inline", + "content": "\\mathcal { L } _ { \\mathbb { S } } ) ;" + }, + { + "type": "text", + "content": "(c) without both (w/o L & " + }, + { + "type": "equation_inline", + "content": "\\mathcal { L } _ { \\mathbb { S } } ) ;" + }, + { + "type": "text", + "content": "and (d) with both (Ours)." + } + ], + "image_footnote": [] + }, + "bbox": [ + 522, + 411, + 906, + 635 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 513, + 750, + 916, + 876 + ] + }, + { + "type": "page_header", + "content": { + "page_header_content": [ + { + "type": "text", + "content": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation" + } + ] + }, + "bbox": [ + 470, + 68, + 879, + 80 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "• 13" + } + ] + }, + "bbox": [ + 885, + 69, + 915, + 78 + ] + }, + { + "type": "page_footer", + "content": { + "page_footer_content": [ + { + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025." + } + ] + }, + "bbox": [ + 676, + 893, + 915, + 905 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/ab4084d217d8303fbd00db4e658d66f92537fbc607146b7a4a86caba029e47b0.jpg" + }, + "content": "Grid-based 3D wireframe models of human figures and objects, no text or symbols present", + "image_caption": [ + { + "type": "text", + "content": "Fig. 24. Quad meshes generated by our NeurCross at diferent resolutions. The low-resolution models contain fewer than 1,000 vertices, while the high resolution models consist of over 5,000 vertices." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 111, + 95, + 880, + 305 + ] + }, + { + "type": "table", + "content": { + "image_source": { + "path": "images/75062270809ee0a2c949ba87ccf162c377c8f4a2dd17d1c8e5c034ad7f75c253.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 4. Ablation studies on the alignment with principal directions loss term " + }, + { + "type": "equation_inline", + "content": "\\mathcal { L } _ { \\mathsf { A P } }" + }, + { + "type": "text", + "content": "and the smoothness loss term " + }, + { + "type": "equation_inline", + "content": "\\mathcal { L } _ { S }" + } + ], + "table_footnote": [], + "html": "
Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
ShapeNet[Chang et al. 2015]w/o $\\mathcal{L}_{\\text{AP}}$ 1.5911.9689.968.050.75
w/o $\\mathcal{L}_{\\text{S}}$ 1.9615.12113.288.090.71
w/o $\\mathcal{L}_{\\text{AP}}$ & $\\mathcal{L}_{\\text{S}}$ 2.2520.73238.718.150.55
NeurCross (Ours)1.489.8585.328.030.78
Thingi10K[Zhou and Jacobson 2016]w/o $\\mathcal{L}_{\\text{AP}}$ 1.4811.8973.798.250.79
w/o $\\mathcal{L}_{\\text{S}}$ 1.8715.03105.378.290.73
w/o $\\mathcal{L}_{\\text{AP}}$ & $\\mathcal{L}_{\\text{S}}$ 2.2120.67225.188.310.58
NeurCross (Ours)1.339.6868.968.220.81
", + "table_type": "complex_table", + "table_nest_level": 1 + }, + "bbox": [ + 86, + 407, + 475, + 512 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "5 ABLATION STUDIES" + } + ], + "level": 2 + }, + "bbox": [ + 78, + 532, + 250, + 546 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "5.1 Extraction Methods" + } + ], + "level": 2 + }, + "bbox": [ + 78, + 551, + 253, + 564 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "As discussed in Section 4.1, the global parameterization techniques in libigl [Jacobson et al. 2017] fail to align parameterized lines with sharp feature lines. To address this, we adopt QuadWild [Pietroni et al. 2021], leveraging the marked sharp features from Sec. 3.3 to divide the surface into patches using the localized patching mecha nism (LPM) [Pietroni et al. 2021], and using our cross field to guide the patch tessellation process." + } + ] + }, + "bbox": [ + 78, + 569, + 482, + 666 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "As illustrated in the bottom row of Fig. 22, NeurCross can successfully generate feature-aligned quadrilateral meshes, which is particularly beneficial for CAD models. For free-form models, the localized patching mechanism (LPM) [Pietroni et al. 2021] introduces singularities at the junctions of adjacent patches and even produces malformed quadrilaterals. Therefore, we generally rely on the global parameterization methods from libigl [Jacobson et al. 2017], unless the user explicitly requires the alignment of parameterized lines with sharp feature lines, in which case we employ the localized patching mechanism (LPM) [Pietroni et al. 2021]." + } + ] + }, + "bbox": [ + 78, + 666, + 482, + 805 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "5.2 Cross Field Loss Terms" + } + ], + "level": 2 + }, + "bbox": [ + 78, + 816, + 272, + 830 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "To further highlight the eficacy of our cross field loss terms in quad mesh generation, we conducted a comparative analysis by disabling these loss terms. We used the ShapeNet [Chang et al. 2015] and Thingi10K [Zhou and Jacobson 2016] datasets for testing and comparison, setting the weight " + }, + { + "type": "equation_inline", + "content": "\\lambda _ { \\mathrm { A P } }" + }, + { + "type": "text", + "content": "of the alignment with principal directions loss term, the weight " + }, + { + "type": "equation_inline", + "content": "\\lambda _ { \\mathrm { { S } } }" + }, + { + "type": "text", + "content": "of the smoothness loss term, or both, to zero, while keeping other settings unchanged." + } + ] + }, + "bbox": [ + 78, + 834, + 480, + 876 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 511, + 367, + 916, + 422 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Fig. 23 illustrates the quadrilateral meshes and cross field generated by our method under various loss term combinations. The results show that our method produces the highest quality quadrilateral meshes. Disabling the alignment with principal directions term " + }, + { + "type": "equation_inline", + "content": "\\mathcal { L } _ { \\mathrm { A P } }" + }, + { + "type": "text", + "content": "maintains only local correlation and lacks overall consistency. Although the mesh generated without the smoothness term " + }, + { + "type": "equation_inline", + "content": "\\mathcal { L } _ { S }" + }, + { + "type": "text", + "content": "shows some degree of overall consistency, it is prone to producing singular points due to the absence of constraints on the local cross field. Without constraints from neither " + }, + { + "type": "equation_inline", + "content": "\\mathcal { L } _ { \\mathrm { A P } }" + }, + { + "type": "text", + "content": "nor " + }, + { + "type": "equation_inline", + "content": "\\mathcal { L } _ { \\mathrm { S } } ," + }, + { + "type": "text", + "content": "the resulting quadrilateral mesh exhibits both aforementioned defects. The quantitative results presented in Tab. 4 align with the qualitative findings in Fig. 23, further demonstrating the superiority of our method in generating quadrilateral meshes." + } + ] + }, + "bbox": [ + 511, + 422, + 918, + 603 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "5.3 Resolution of Quad Mesh" + } + ], + "level": 2 + }, + "bbox": [ + 514, + 625, + 725, + 638 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In real-world applications, selecting the appropriate resolution for quad mesh extraction depends on the specific requirements of different tasks. In Fig. 24, we use the same cross field for both lowand high-resolution quad meshes, ensuring consistent placement of singular points. Interestingly, the low-resolution mesh better high lights the positioning of these singular points. Fig. 24 demonstrates that, in our approach, most singular points are strategically located in regions with high curvature rather than in flat areas." + } + ] + }, + "bbox": [ + 511, + 641, + 916, + 753 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "6 LIMITATION" + } + ], + "level": 2 + }, + "bbox": [ + 514, + 773, + 632, + 787 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "A significant limitation of the self-supervised optimization is its substantial time requirement. For a triangular mesh input with 50,000 faces, each iteration takes 68.34 ms, with a default setting of 10,000 iterations. However, for geometrically simple and regular shapes, NeurCross typically converges in fewer iterations to produce highquality quadrilateral meshes (see the top row of Fig. 25), whereas complex shapes may require additional iterations to achieve comparable results (see the bottom row of Fig. 25)." + } + ] + }, + "bbox": [ + 511, + 792, + 916, + 876 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "14" + } + ] + }, + "bbox": [ + 81, + 69, + 94, + 78 + ] + }, + { + "type": "page_header", + "content": { + "page_header_content": [ + { + "type": "text", + "content": "• Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang" + } + ] + }, + "bbox": [ + 104, + 68, + 720, + 80 + ] + }, + { + "type": "page_footnote", + "content": { + "page_footnote_content": [ + { + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025." + } + ] + }, + "bbox": [ + 81, + 893, + 321, + 905 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/6a649330551fcd77dfaed364df6f9c80b06ebe0f637b6cf540fb6808abd13a3c.jpg" + }, + "content": "Grid-based 3D model of a human figure with labeled iteration counts (500, 1k, 5k, 10k), no text or symbols present.", + "image_caption": [ + { + "type": "text", + "content": "Fig. 25. Trend of convergence. Quad meshes generated by our NeurCross with diferent numbers of iterations (#iter)." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 81, + 97, + 480, + 286 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 78, + 353, + 482, + 380 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "A promising future direction is to leverage this approach to gen erate ample training data for feeding generative models, such as MeshGPT [Siddiqui et al. 2024]. This would enable users to obtain high-quality quad meshing outcomes instantly." + } + ] + }, + "bbox": [ + 78, + 380, + 483, + 436 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "7 CONCLUSION" + } + ], + "level": 2 + }, + "bbox": [ + 80, + 450, + 210, + 462 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In this paper, we propose a self-supervised neural representation of the cross field for quadrilateral mesh generation. To the best of our knowledge, this is the first self-supervised approach for this task. Our network, named NeurCross, consists of two modules: one to fit the SDF and another to predict the cross field. The design of our loss function addresses three key aspects: surface approximation quality, alignment with principal directions, and the spatial smooth ness of the cross field. Leveraging our network, the SDF and cross field are optimized simultaneously, achieving a desirable balance between approximation accuracy and cross field smoothness. Experimental results consistently validate improvements in singular point placement and in the approximation accuracy between the input triangular surface and the output quad mesh." + } + ] + }, + "bbox": [ + 78, + 467, + 483, + 648 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "ACKNOWLEDGMENTS" + } + ], + "level": 2 + }, + "bbox": [ + 80, + 661, + 248, + 674 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the National Key R&D Program of China (2022YFB3303200), the Na tional Natural Science Foundation of China (U23A20312, 62272277, 62102380), the Shandong Provincial Natural Science Foundation (ZR2024MF083), the Innovation and Technology Commission of the HKSAR Government under the InnoHK initiative (TransGP project) and the ITSP-Platform grant (Ref: ITS/335/23FP), and the Research Grants Council of Hong Kong (Ref: 17210222)." + } + ] + }, + "bbox": [ + 78, + 679, + 483, + 804 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "REFERENCES" + } + ], + "level": 2 + }, + "bbox": [ + 81, + 816, + 179, + 829 + ] + }, + { + "type": "list", + "content": { + "list_type": "reference_list", + "list_items": [ + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "Yizhak Ben-Shabat, Chamin Hewa Koneputugodage, and Stephen Gould. 2022. 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Our joint op-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 602, + 560, + 609 + ], + "spans": [ + { + "bbox": [ + 317, + 602, + 560, + 609 + ], + "type": "text", + "content": "timization is guided by three factors: faithful approximation of the optimized", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 612, + 560, + 620 + ], + "spans": [ + { + "bbox": [ + 317, + 612, + 560, + 620 + ], + "type": "text", + "content": "SDF surface to the input surface, alignment between the cross field and the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 622, + 561, + 629 + ], + "spans": [ + { + "bbox": [ + 317, + 622, + 561, + 629 + ], + "type": "text", + "content": "principal curvature field derived from the SDF surface, and smoothness of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 632, + 560, + 640 + ], + "spans": [ + { + "bbox": [ + 317, + 632, + 560, + 640 + ], + "type": "text", + "content": "the cross field. 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Second, we leverage the Hessian matrix of the neural SDF to implicitly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 672, + 561, + 680 + ], + "spans": [ + { + "bbox": [ + 317, + 672, + 561, + 680 + ], + "type": "text", + "content": "enforce cross field alignment with principal curvature directions, thus elim-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 681, + 559, + 689 + ], + "spans": [ + { + "bbox": [ + 317, + 681, + 559, + 689 + ], + "type": "text", + "content": "inating the need for explicit curvature extraction. Extensive experiments", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 14, + 206, + 37, + 555 + ], + "type": "aside_text", + "angle": 270, + "lines": [ + { + "bbox": [ + 14, + 206, + 37, + 555 + ], + "spans": [ + { + "bbox": [ + 14, + 206, + 37, + 555 + ], + "type": "text", + "content": "arXiv:2405.13745v3 [cs.CV] 9 May 2025" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 582, + 156, + 592 + ], + "type": "page_footnote", + "angle": 0, + "index": 16, + "lines": [ + { + "bbox": [ + 52, + 584, + 155, + 591 + ], + "spans": [ + { + "bbox": [ + 52, + 584, + 155, + 591 + ], + "type": "text", + "content": "∗Corresponding author: Shiqing Xin.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 48, + 604, + 295, + 693 + ], + "type": "page_footnote", + "angle": 0, + "index": 17, + "lines": [ + { + "bbox": [ + 51, + 605, + 294, + 613 + ], + "spans": [ + { + "bbox": [ + 51, + 605, + 294, + 613 + ], + "type": "text", + "content": "Authors’ addresses: Qiujie Dong, Shandong University, Qingdao, Shandong, China and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 613, + 294, + 620 + ], + "spans": [ + { + "bbox": [ + 50, + 613, + 294, + 620 + ], + "type": "text", + "content": "The University of Hong Kong, Hong Kong, China and TransGP, Hong Kong, China,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 621, + 294, + 629 + ], + "spans": [ + { + "bbox": [ + 51, + 621, + 294, + 629 + ], + "type": "text", + "content": "qiujie.jay.dong@gmail.com; Huibiao Wen, Shandong University, Qingdao, Shandong,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 630, + 294, + 637 + ], + "spans": [ + { + "bbox": [ + 51, + 630, + 294, + 637 + ], + "type": "text", + "content": "China, ericvein@163.com; Rui Xu, The University of Hong Kong, Hong Kong, China,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 638, + 294, + 645 + ], + "spans": [ + { + "bbox": [ + 50, + 638, + 294, + 645 + ], + "type": "text", + "content": "xrvitd@163.com; Shuangmin Chen, Qingdao University of Science and Technology,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 52, + 647, + 294, + 652 + ], + "spans": [ + { + "bbox": [ + 52, + 647, + 294, + 652 + ], + "type": "text", + "content": "Qingdao, Shandong, China, csmqq@163.com; Jiaran Zhou, Ocean University of China,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 52, + 654, + 294, + 660 + ], + "spans": [ + { + "bbox": [ + 52, + 654, + 294, + 660 + ], + "type": "text", + "content": "Qingdao, Shandong, China, zhoujiaran@ouc.edu.cn; Shiqing Xin, Shandong University,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 662, + 294, + 669 + ], + "spans": [ + { + "bbox": [ + 51, + 662, + 294, + 669 + ], + "type": "text", + "content": "Qingdao, Shandong, China, xinshiqing@sdu.edu.cn; Changhe Tu, Shandong University,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 670, + 294, + 677 + ], + "spans": [ + { + "bbox": [ + 51, + 670, + 294, + 677 + ], + "type": "text", + "content": "Qingdao, Shandong, China, chtu@sdu.edu.cn; Taku Komura, The University of Hong", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 678, + 294, + 685 + ], + "spans": [ + { + "bbox": [ + 51, + 678, + 294, + 685 + ], + "type": "text", + "content": "Kong, Hong Kong, China, taku@cs.hku.hk; Wenping Wang, Texas A&M University,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 685, + 204, + 693 + ], + "spans": [ + { + "bbox": [ + 50, + 685, + 204, + 693 + ], + "type": "text", + "content": "Texas, United States of America, wenping@tamu.edu.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 414, + 708, + 561, + 717 + ], + "type": "footer", + "angle": 0, + "index": 18, + "lines": [ + { + "bbox": [ + 414, + 709, + 559, + 716 + ], + "spans": [ + { + "bbox": [ + 414, + 709, + 559, + 716 + ], + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0, + "para_blocks": [ + { + "bbox": [ + 48, + 75, + 533, + 113 + ], + "type": "title", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 51, + 76, + 533, + 94 + ], + "spans": [ + { + "bbox": [ + 51, + 76, + 533, + 94 + ], + "type": "text", + "content": "NeurCross: A Neural Approach to Computing Cross Fields for Quad", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 97, + 175, + 113 + ], + "spans": [ + { + "bbox": [ + 51, + 97, + 175, + 113 + ], + "type": "text", + "content": "Mesh Generation", + "score": 1.0 + } + ] + } + ], + "level": 1 + }, + { + "bbox": [ + 48, + 119, + 487, + 133 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 51, + 121, + 486, + 133 + ], + "spans": [ + { + "bbox": [ + 51, + 121, + 486, + 133 + ], + "type": "text", + "content": "QIUJIE DONG, Shandong University, China, The University of Hong Kong, China, and TransGP, China", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 50, + 133, + 250, + 146 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 51, + 134, + 249, + 146 + ], + "spans": [ + { + "bbox": [ + 51, + 134, + 249, + 146 + ], + "type": "text", + "content": "HUIBIAO WEN, Shandong University, China", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 50, + 148, + 244, + 160 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 51, + 148, + 243, + 160 + ], + "spans": [ + { + "bbox": [ + 51, + 148, + 243, + 160 + ], + "type": "text", + "content": "RUI XU, The University of Hong Kong, China", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 50, + 162, + 383, + 175 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 50, + 162, + 383, + 175 + ], + "spans": [ + { + "bbox": [ + 50, + 162, + 383, + 175 + ], + "type": "text", + "content": "SHUANGMIN CHEN, Qingdao University of Science and Technology, China", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 50, + 175, + 270, + 188 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 50, + 177, + 269, + 187 + ], + "spans": [ + { + "bbox": [ + 50, + 177, + 269, + 187 + ], + "type": "text", + "content": "JIARAN ZHOU, Ocean University of China, China", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 50, + 190, + 246, + 202 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 51, + 190, + 246, + 201 + ], + "spans": [ + { + "bbox": [ + 51, + 190, + 246, + 201 + ], + "type": "text", + "content": "SHIQING XIN∗, Shandong University, China", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 50, + 203, + 247, + 216 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 51, + 204, + 247, + 216 + ], + "spans": [ + { + "bbox": [ + 51, + 204, + 247, + 216 + ], + "type": "text", + "content": "CHANGHE TU, Shandong University, China", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 50, + 217, + 288, + 230 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 51, + 218, + 288, + 230 + ], + "spans": [ + { + "bbox": [ + 51, + 218, + 288, + 230 + ], + "type": "text", + "content": "TAKU KOMURA, The University of Hong Kong, China", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 50, + 232, + 347, + 243 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 50, + 232, + 347, + 243 + ], + "spans": [ + { + "bbox": [ + 50, + 232, + 347, + 243 + ], + "type": "text", + "content": "WENPING WANG, Texas A&M University, United States of America", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "image", + "bbox": [ + 50, + 254, + 561, + 459 + ], + "blocks": [ + { + "bbox": [ + 50, + 254, + 561, + 459 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 254, + 561, + 459 + ], + "spans": [ + { + "bbox": [ + 50, + 254, + 561, + 459 + ], + "type": "image", + "content": "3D wireframe models of various 3D geometric structures, including human figures and torus-like forms (no text or symbols)", + "image_path": "ec5c189df3d8309359b7cb1e9ef73d98ec4ded9f2d1c1f1a4a5200bff5643d0d.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 48, + 464, + 561, + 495 + ], + "type": "image_caption", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 51, + 466, + 559, + 473 + ], + "spans": [ + { + "bbox": [ + 51, + 466, + 559, + 473 + ], + "type": "text", + "content": "Fig. 1. Gallery of quad meshes generated with our NeurCros method. NeurCross excels in computing cross field for generating high-quality quad meshes. Its", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 475, + 559, + 483 + ], + "spans": [ + { + "bbox": [ + 51, + 475, + 559, + 483 + ], + "type": "text", + "content": "advantages include optimized singular point placement, insensitivity to surface noise and minor surface undulations, and faithful alignment with principa", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 486, + 201, + 493 + ], + "spans": [ + { + "bbox": [ + 50, + 486, + 201, + 493 + ], + "type": "text", + "content": "curvature directions and sharp feature curves.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 11, + "sub_type": "natural_image" + }, + { + "bbox": [ + 48, + 501, + 295, + 571 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 51, + 502, + 294, + 510 + ], + "spans": [ + { + "bbox": [ + 51, + 502, + 294, + 510 + ], + "type": "text", + "content": "Quadrilateral mesh generation plays a crucial role in numerical simulations", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 512, + 294, + 520 + ], + "spans": [ + { + "bbox": [ + 50, + 512, + 294, + 520 + ], + "type": "text", + "content": "within Computer-Aided Design and Engineering (CAD/E). 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Existing methods generally involve first com-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 512, + 560, + 520 + ], + "spans": [ + { + "bbox": [ + 316, + 512, + 560, + 520 + ], + "type": "text", + "content": "puting a regular cross field to represent quad element orientations across", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 522, + 560, + 530 + ], + "spans": [ + { + "bbox": [ + 317, + 522, + 560, + 530 + ], + "type": "text", + "content": "the surface, followed by extracting a quadrilateral mesh aligned closely with", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 533, + 559, + 540 + ], + "spans": [ + { + "bbox": [ + 317, + 533, + 559, + 540 + ], + "type": "text", + "content": "this cross field. A primary challenge with this approach is balancing the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 542, + 560, + 550 + ], + "spans": [ + { + "bbox": [ + 317, + 542, + 560, + 550 + ], + "type": "text", + "content": "smoothness of the cross field with its alignment to pre-computed principal", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 552, + 559, + 559 + ], + "spans": [ + { + "bbox": [ + 317, + 552, + 559, + 559 + ], + "type": "text", + "content": "curvature directions, which are sensitive to small surface perturbations and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 562, + 468, + 570 + ], + "spans": [ + { + "bbox": [ + 317, + 562, + 468, + 570 + ], + "type": "text", + "content": "often ill-defined in spherical or planar regions.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 313, + 501, + 561, + 570 + ], + "type": "text", + "angle": 0, + "index": 14, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 313, + 571, + 561, + 691 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 326, + 571, + 560, + 580 + ], + "spans": [ + { + "bbox": [ + 326, + 571, + 560, + 580 + ], + "type": "text", + "content": "To tackle this challenge, we propose NeurCross, a novel framework that", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 582, + 560, + 590 + ], + "spans": [ + { + "bbox": [ + 317, + 582, + 560, + 590 + ], + "type": "text", + "content": "simultaneously optimizes a cross field and a neural signed distance function", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 591, + 561, + 601 + ], + "spans": [ + { + "bbox": [ + 317, + 591, + 561, + 601 + ], + "type": "text", + "content": "(SDF), whose zero-level set serves as a proxy of the input shape. Our joint op-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 602, + 560, + 609 + ], + "spans": [ + { + "bbox": [ + 317, + 602, + 560, + 609 + ], + "type": "text", + "content": "timization is guided by three factors: faithful approximation of the optimized", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 612, + 560, + 620 + ], + "spans": [ + { + "bbox": [ + 317, + 612, + 560, + 620 + ], + "type": "text", + "content": "SDF surface to the input surface, alignment between the cross field and the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 622, + 561, + 629 + ], + "spans": [ + { + "bbox": [ + 317, + 622, + 561, + 629 + ], + "type": "text", + "content": "principal curvature field derived from the SDF surface, and smoothness of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 632, + 560, + 640 + ], + "spans": [ + { + "bbox": [ + 317, + 632, + 560, + 640 + ], + "type": "text", + "content": "the cross field. Acting as an intermediary, the neural SDF contributes in", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 641, + 559, + 649 + ], + "spans": [ + { + "bbox": [ + 317, + 641, + 559, + 649 + ], + "type": "text", + "content": "two essential ways. First, it provides an alternative, optimizable base surface", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 653, + 559, + 659 + ], + "spans": [ + { + "bbox": [ + 317, + 653, + 559, + 659 + ], + "type": "text", + "content": "exhibiting more regular principal curvature directions for guiding the cross", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 662, + 559, + 670 + ], + "spans": [ + { + "bbox": [ + 317, + 662, + 559, + 670 + ], + "type": "text", + "content": "field. Second, we leverage the Hessian matrix of the neural SDF to implicitly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 672, + 561, + 680 + ], + "spans": [ + { + "bbox": [ + 317, + 672, + 561, + 680 + ], + "type": "text", + "content": "enforce cross field alignment with principal curvature directions, thus elim-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 681, + 559, + 689 + ], + "spans": [ + { + "bbox": [ + 317, + 681, + 559, + 689 + ], + "type": "text", + "content": "inating the need for explicit curvature extraction. Extensive experiments", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 82, + 294, + 90 + ], + "spans": [ + { + "bbox": [ + 51, + 82, + 294, + 90 + ], + "type": "text", + "content": "demonstrate that NeurCross outperforms the state-of-the-art methods in", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 50, + 92, + 294, + 100 + ], + "spans": [ + { + "bbox": [ + 50, + 92, + 294, + 100 + ], + "type": "text", + "content": "terms of singular point placement, robustness against surface noise and", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 51, + 102, + 294, + 110 + ], + "spans": [ + { + "bbox": [ + 51, + 102, + 294, + 110 + ], + "type": "text", + "content": "surface undulations, and alignment with principal curvature directions and", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 50, + 111, + 119, + 121 + ], + "spans": [ + { + "bbox": [ + 50, + 111, + 119, + 121 + ], + "type": "text", + "content": "sharp feature curves.", + "score": 1.0, + "cross_page": true + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "bbox": [ + 48, + 80, + 294, + 121 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 51, + 82, + 294, + 90 + ], + "spans": [ + { + "bbox": [ + 51, + 82, + 294, + 90 + ], + "type": "text", + "content": "demonstrate that NeurCross outperforms the state-of-the-art methods in", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 92, + 294, + 100 + ], + "spans": [ + { + "bbox": [ + 50, + 92, + 294, + 100 + ], + "type": "text", + "content": "terms of singular point placement, robustness against surface noise and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 102, + 294, + 110 + ], + "spans": [ + { + "bbox": [ + 51, + 102, + 294, + 110 + ], + "type": "text", + "content": "surface undulations, and alignment with principal curvature directions and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 111, + 119, + 121 + ], + "spans": [ + { + "bbox": [ + 50, + 111, + 119, + 121 + ], + "type": "text", + "content": "sharp feature curves.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 126, + 294, + 148 + ], + "type": "title", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 51, + 128, + 293, + 137 + ], + "spans": [ + { + "bbox": [ + 51, + 128, + 293, + 137 + ], + "type": "text", + "content": "CCS Concepts: • Computing methodologies → Shape analysis; Mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 138, + 115, + 146 + ], + "spans": [ + { + "bbox": [ + 50, + 138, + 115, + 146 + ], + "type": "text", + "content": "geometry models.", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 48, + 152, + 294, + 174 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 51, + 154, + 294, + 163 + ], + "spans": [ + { + "bbox": [ + 51, + 154, + 294, + 163 + ], + "type": "text", + "content": "Additional Key Words and Phrases: quadrangulation, neural network, cross", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 164, + 215, + 172 + ], + "spans": [ + { + "bbox": [ + 50, + 164, + 215, + 172 + ], + "type": "text", + "content": "field, signed distance function, principal curvature", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 49, + 186, + 140, + 197 + ], + "type": "title", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 50, + 187, + 139, + 198 + ], + "spans": [ + { + "bbox": [ + 50, + 187, + 139, + 198 + ], + "type": "text", + "content": "1 INTRODUCTION", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 48, + 200, + 294, + 266 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 51, + 202, + 293, + 211 + ], + "spans": [ + { + "bbox": [ + 51, + 202, + 293, + 211 + ], + "type": "text", + "content": "Quadrangulation is fundamental in both Computer-Aided Design", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 213, + 295, + 222 + ], + "spans": [ + { + "bbox": [ + 50, + 213, + 295, + 222 + ], + "type": "text", + "content": "(CAD) and Computer-Aided Engineering (CAE) [Bommes et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 224, + 294, + 233 + ], + "spans": [ + { + "bbox": [ + 51, + 224, + 294, + 233 + ], + "type": "text", + "content": "2013b; Vaxman et al. 2016], with significant applications in finite", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 235, + 294, + 243 + ], + "spans": [ + { + "bbox": [ + 51, + 235, + 294, + 243 + ], + "type": "text", + "content": "element analysis, isogeometric analysis, character animation, and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 246, + 294, + 255 + ], + "spans": [ + { + "bbox": [ + 50, + 246, + 294, + 255 + ], + "type": "text", + "content": "physics simulations [Bommes et al. 2013a, 2009; Campen et al. 2015a;", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 257, + 170, + 265 + ], + "spans": [ + { + "bbox": [ + 50, + 257, + 170, + 265 + ], + "type": "text", + "content": "Jakob et al. 2015; Mu et al. 2023].", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 266, + 295, + 419 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 58, + 267, + 294, + 277 + ], + "spans": [ + { + "bbox": [ + 58, + 267, + 294, + 277 + ], + "type": "text", + "content": "Existing approaches typically first compute a reliable cross field", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 278, + 294, + 287 + ], + "spans": [ + { + "bbox": [ + 50, + 278, + 294, + 287 + ], + "type": "text", + "content": "to represent quad element orientations across the surface, followed", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 290, + 294, + 298 + ], + "spans": [ + { + "bbox": [ + 51, + 290, + 294, + 298 + ], + "type": "text", + "content": "by extracting quad meshes aligned closely with the computed field", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 300, + 294, + 309 + ], + "spans": [ + { + "bbox": [ + 51, + 300, + 294, + 309 + ], + "type": "text", + "content": "[Bommes et al. 2013a, 2009; Huang et al. 2018; Jakob et al. 2015;", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 312, + 294, + 320 + ], + "spans": [ + { + "bbox": [ + 51, + 312, + 294, + 320 + ], + "type": "text", + "content": "Zhang et al. 2020]. Most methods require principal curvature di", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 323, + 294, + 331 + ], + "spans": [ + { + "bbox": [ + 50, + 323, + 294, + 331 + ], + "type": "text", + "content": "rections as input. However, computing a desired cross field from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 334, + 294, + 342 + ], + "spans": [ + { + "bbox": [ + 51, + 334, + 294, + 342 + ], + "type": "text", + "content": "principal curvature directions entails meeting four key requirements:", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 345, + 294, + 353 + ], + "spans": [ + { + "bbox": [ + 50, + 345, + 294, + 353 + ], + "type": "text", + "content": "First, the quadrilateral mesh should align closely with principal cur", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 355, + 294, + 364 + ], + "spans": [ + { + "bbox": [ + 50, + 355, + 294, + 364 + ], + "type": "text", + "content": "vature directions. 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These challenges are", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 399, + 294, + 407 + ], + "spans": [ + { + "bbox": [ + 50, + 399, + 294, + 407 + ], + "type": "text", + "content": "particularly pronounced in geometrically or topologically complex", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 411, + 78, + 419 + ], + "spans": [ + { + "bbox": [ + 50, + 411, + 78, + 419 + ], + "type": "text", + "content": "shapes.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 420, + 294, + 507 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 59, + 421, + 294, + 430 + ], + "spans": [ + { + "bbox": [ + 59, + 421, + 294, + 430 + ], + "type": "text", + "content": "Fig. 2 shows quadrangulation results of some existing methods.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 432, + 293, + 441 + ], + "spans": [ + { + "bbox": [ + 50, + 432, + 293, + 441 + ], + "type": "text", + "content": "As shown, for instance, QuadWild [Pietroni et al. 2021] fails to align", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 443, + 294, + 452 + ], + "spans": [ + { + "bbox": [ + 50, + 443, + 294, + 452 + ], + "type": "text", + "content": "properly with principal curvature directions due to an overemphasis", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 453, + 294, + 463 + ], + "spans": [ + { + "bbox": [ + 50, + 453, + 294, + 463 + ], + "type": "text", + "content": "on the smoothness of the cross field. Although principal curvature", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 465, + 293, + 473 + ], + "spans": [ + { + "bbox": [ + 51, + 465, + 293, + 473 + ], + "type": "text", + "content": "directions provide useful geometric clues, precisely controlling their", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 476, + 293, + 484 + ], + "spans": [ + { + "bbox": [ + 50, + 476, + 293, + 484 + ], + "type": "text", + "content": "influence on the inferred cross field is dificult, especially in nearly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 487, + 294, + 495 + ], + "spans": [ + { + "bbox": [ + 51, + 487, + 294, + 495 + ], + "type": "text", + "content": "spherical or planar regions, or on a surface with small undulations,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 498, + 250, + 506 + ], + "spans": [ + { + "bbox": [ + 50, + 498, + 250, + 506 + ], + "type": "text", + "content": "where principal curvature directions become unstable.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 508, + 295, + 694 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 59, + 509, + 294, + 517 + ], + "spans": [ + { + "bbox": [ + 59, + 509, + 294, + 517 + ], + "type": "text", + "content": "We introduce an optimizable neural signed distance function", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 519, + 294, + 529 + ], + "spans": [ + { + "bbox": [ + 51, + 519, + 294, + 529 + ], + "type": "text", + "content": "(SDF) as the underlying shape representation to infer the desired", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 530, + 294, + 540 + ], + "spans": [ + { + "bbox": [ + 50, + 530, + 294, + 540 + ], + "type": "text", + "content": "cross field. 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While some methods, such as Dual Marching Cubes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 531, + 560, + 539 + ], + "spans": [ + { + "bbox": [ + 317, + 531, + 560, + 539 + ], + "type": "text", + "content": "(DMC) [Nielson 2004], can directly extract quad facets without", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 541, + 560, + 550 + ], + "spans": [ + { + "bbox": [ + 317, + 541, + 560, + 550 + ], + "type": "text", + "content": "relying on direction fields, the resulting meshes often lack quality,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 553, + 561, + 561 + ], + "spans": [ + { + "bbox": [ + 317, + 553, + 561, + 561 + ], + "type": "text", + "content": "particularly in aligning with principal directions. Most state-of-the-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 564, + 561, + 572 + ], + "spans": [ + { + "bbox": [ + 317, + 564, + 561, + 572 + ], + "type": "text", + "content": "art approaches rely on a cross field [Lai et al. 2010; Palmer et al. 2021;", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 574, + 561, + 583 + ], + "spans": [ + { + "bbox": [ + 317, + 574, + 561, + 583 + ], + "type": "text", + "content": "Ray et al. 2008] to guide the generation of high-quality quad meshes,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 586, + 560, + 594 + ], + "spans": [ + { + "bbox": [ + 317, + 586, + 560, + 594 + ], + "type": "text", + "content": "as it ensures edge alignment and proper placement of irregular", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 597, + 560, + 605 + ], + "spans": [ + { + "bbox": [ + 317, + 597, + 560, + 605 + ], + "type": "text", + "content": "vertices. 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Although", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 641, + 560, + 649 + ], + "spans": [ + { + "bbox": [ + 317, + 641, + 560, + 649 + ], + "type": "text", + "content": "several robust quadrangulation methods [Dong et al. 2006; Gurung", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 651, + 561, + 660 + ], + "spans": [ + { + "bbox": [ + 317, + 651, + 561, + 660 + ], + "type": "text", + "content": "et al. 2011; Ling et al. 2014; Owen et al. 1999; Remacle et al. 2012;", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 662, + 560, + 671 + ], + "spans": [ + { + "bbox": [ + 317, + 662, + 560, + 671 + ], + "type": "text", + "content": "Velho and Zorin 2001; Zhang et al. 2010] operate independently of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 673, + 560, + 681 + ], + "spans": [ + { + "bbox": [ + 317, + 673, + 560, + 681 + ], + "type": "text", + "content": "direction fields, they often fail to achieve global smoothness. Below,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 684, + 476, + 693 + ], + "spans": [ + { + "bbox": [ + 317, + 684, + 476, + 693 + ], + "type": "text", + "content": "we review related works on direction fields.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 50, + 55, + 56, + 62 + ], + "type": "page_number", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 51, + 56, + 55, + 63 + ], + "spans": [ + { + "bbox": [ + 51, + 56, + 55, + 63 + ], + "type": "text", + "content": "2", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 69, + 54, + 438, + 64 + ], + "type": "header", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 70, + 54, + 438, + 64 + ], + "spans": [ + { + "bbox": [ + 70, + 54, + 438, + 64 + ], + "type": "text", + "content": "Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 50, + 708, + 197, + 717 + ], + "type": "footer", + "angle": 0, + "index": 22, + "lines": [ + { + "bbox": [ + 51, + 710, + 195, + 716 + ], + "spans": [ + { + "bbox": [ + 51, + 710, + 195, + 716 + ], + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1, + "para_blocks": [ + { + "bbox": [ + 48, + 80, + 294, + 121 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 48, + 126, + 294, + 148 + ], + "type": "title", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 51, + 128, + 293, + 137 + ], + "spans": [ + { + "bbox": [ + 51, + 128, + 293, + 137 + ], + "type": "text", + "content": "CCS Concepts: • Computing methodologies → Shape analysis; Mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 138, + 115, + 146 + ], + "spans": [ + { + "bbox": [ + 50, + 138, + 115, + 146 + ], + "type": "text", + "content": "geometry models.", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 48, + 152, + 294, + 174 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 51, + 154, + 294, + 163 + ], + "spans": [ + { + "bbox": [ + 51, + 154, + 294, + 163 + ], + "type": "text", + "content": "Additional Key Words and Phrases: quadrangulation, neural network, cross", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 164, + 215, + 172 + ], + "spans": [ + { + "bbox": [ + 50, + 164, + 215, + 172 + ], + "type": "text", + "content": "field, signed distance function, principal curvature", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 49, + 186, + 140, + 197 + ], + "type": "title", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 50, + 187, + 139, + 198 + ], + "spans": [ + { + "bbox": [ + 50, + 187, + 139, + 198 + ], + "type": "text", + "content": "1 INTRODUCTION", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 48, + 200, + 294, + 266 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 51, + 202, + 293, + 211 + ], + "spans": [ + { + "bbox": [ + 51, + 202, + 293, + 211 + ], + "type": "text", + "content": "Quadrangulation is fundamental in both Computer-Aided Design", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 213, + 295, + 222 + ], + "spans": [ + { + "bbox": [ + 50, + 213, + 295, + 222 + ], + "type": "text", + "content": "(CAD) and Computer-Aided Engineering (CAE) [Bommes et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 224, + 294, + 233 + ], + "spans": [ + { + "bbox": [ + 51, + 224, + 294, + 233 + ], + "type": "text", + "content": "2013b; Vaxman et al. 2016], with significant applications in finite", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 235, + 294, + 243 + ], + "spans": [ + { + "bbox": [ + 51, + 235, + 294, + 243 + ], + "type": "text", + "content": "element analysis, isogeometric analysis, character animation, and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 246, + 294, + 255 + ], + "spans": [ + { + "bbox": [ + 50, + 246, + 294, + 255 + ], + "type": "text", + "content": "physics simulations [Bommes et al. 2013a, 2009; Campen et al. 2015a;", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 257, + 170, + 265 + ], + "spans": [ + { + "bbox": [ + 50, + 257, + 170, + 265 + ], + "type": "text", + "content": "Jakob et al. 2015; Mu et al. 2023].", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 266, + 295, + 419 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 58, + 267, + 294, + 277 + ], + "spans": [ + { + "bbox": [ + 58, + 267, + 294, + 277 + ], + "type": "text", + "content": "Existing approaches typically first compute a reliable cross field", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 278, + 294, + 287 + ], + "spans": [ + { + "bbox": [ + 50, + 278, + 294, + 287 + ], + "type": "text", + "content": "to represent quad element orientations across the surface, followed", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 290, + 294, + 298 + ], + "spans": [ + { + "bbox": [ + 51, + 290, + 294, + 298 + ], + "type": "text", + "content": "by extracting quad meshes aligned closely with the computed field", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 300, + 294, + 309 + ], + "spans": [ + { + "bbox": [ + 51, + 300, + 294, + 309 + ], + "type": "text", + "content": "[Bommes et al. 2013a, 2009; Huang et al. 2018; Jakob et al. 2015;", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 312, + 294, + 320 + ], + "spans": [ + { + "bbox": [ + 51, + 312, + 294, + 320 + ], + "type": "text", + "content": "Zhang et al. 2020]. Most methods require principal curvature di", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 323, + 294, + 331 + ], + "spans": [ + { + "bbox": [ + 50, + 323, + 294, + 331 + ], + "type": "text", + "content": "rections as input. However, computing a desired cross field from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 334, + 294, + 342 + ], + "spans": [ + { + "bbox": [ + 51, + 334, + 294, + 342 + ], + "type": "text", + "content": "principal curvature directions entails meeting four key requirements:", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 345, + 294, + 353 + ], + "spans": [ + { + "bbox": [ + 50, + 345, + 294, + 353 + ], + "type": "text", + "content": "First, the quadrilateral mesh should align closely with principal cur", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 355, + 294, + 364 + ], + "spans": [ + { + "bbox": [ + 50, + 355, + 294, + 364 + ], + "type": "text", + "content": "vature directions. 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Although principal curvature", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 465, + 293, + 473 + ], + "spans": [ + { + "bbox": [ + 51, + 465, + 293, + 473 + ], + "type": "text", + "content": "directions provide useful geometric clues, precisely controlling their", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 476, + 293, + 484 + ], + "spans": [ + { + "bbox": [ + 50, + 476, + 293, + 484 + ], + "type": "text", + "content": "influence on the inferred cross field is dificult, especially in nearly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 487, + 294, + 495 + ], + "spans": [ + { + "bbox": [ + 51, + 487, + 294, + 495 + ], + "type": "text", + "content": "spherical or planar regions, or on a surface with small undulations,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 498, + 250, + 506 + ], + "spans": [ + { + "bbox": [ + 50, + 498, + 250, + 506 + ], + "type": "text", + "content": "where principal curvature directions become unstable.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 508, + 295, + 694 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 59, + 509, + 294, + 517 + ], + "spans": [ + { + "bbox": [ + 59, + 509, + 294, + 517 + ], + "type": "text", + "content": "We introduce an optimizable neural signed distance function", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 519, + 294, + 529 + ], + "spans": [ + { + "bbox": [ + 51, + 519, + 294, + 529 + ], + "type": "text", + "content": "(SDF) as the underlying shape representation to infer the desired", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 530, + 294, + 540 + ], + "spans": [ + { + "bbox": [ + 50, + 530, + 294, + 540 + ], + "type": "text", + "content": "cross field. 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Fig. 3 illustrates our method’s success on a dimpled el", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 662, + 294, + 671 + ], + "spans": [ + { + "bbox": [ + 50, + 662, + 294, + 671 + ], + "type": "text", + "content": "lipsoid with irregular curvature directions, compared to a naïve", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 673, + 294, + 682 + ], + "spans": [ + { + "bbox": [ + 51, + 673, + 294, + 682 + ], + "type": "text", + "content": "two-stage approach that first optimizes an SDF to properly fit the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 685, + 293, + 693 + ], + "spans": [ + { + "bbox": [ + 51, + 685, + 293, + 693 + ], + "type": "text", + "content": "input shape and then uses the curvature field of this fixed SDF to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 81, + 560, + 90 + ], + "spans": [ + { + "bbox": [ + 317, + 81, + 560, + 90 + ], + "type": "text", + "content": "guide the generation of the cross field. 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Extensive experiments validate Neur-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 289, + 559, + 298 + ], + "spans": [ + { + "bbox": [ + 317, + 289, + 559, + 298 + ], + "type": "text", + "content": "Cross’s efectiveness, demonstrating improvements in singular point", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 300, + 561, + 309 + ], + "spans": [ + { + "bbox": [ + 317, + 300, + 561, + 309 + ], + "type": "text", + "content": "placement, robustness to noise and geometric variations, and ap-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 312, + 508, + 320 + ], + "spans": [ + { + "bbox": [ + 317, + 312, + 508, + 320 + ], + "type": "text", + "content": "proximation accuracy, as shown in the teaser figure.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 324, + 322, + 495, + 331 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 326, + 323, + 493, + 331 + ], + "spans": [ + { + "bbox": [ + 326, + 323, + 493, + 331 + ], + "type": "text", + "content": "Our contributions are summarized as follows:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 331, + 332, + 561, + 419 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 331, + 332, + 561, + 354 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 334, + 334, + 561, + 342 + ], + "spans": [ + { + "bbox": [ + 334, + 334, + 561, + 342 + ], + "type": "text", + "content": "- We propose NeurCross, the first self-supervised neural net-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 340, + 344, + 449, + 353 + ], + "spans": [ + { + "bbox": [ + 340, + 344, + 449, + 353 + ], + "type": "text", + "content": "work for learning cross fields.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 331, + 354, + 561, + 387 + ], + "type": "text", + "angle": 0, + "index": 16, + "lines": [ + { + "bbox": [ + 334, + 355, + 561, + 364 + ], + "spans": [ + { + "bbox": [ + 334, + 355, + 561, + 364 + ], + "type": "text", + "content": "- We implicitly enforce cross field alignment with principal cur-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 339, + 365, + 560, + 376 + ], + "spans": [ + { + "bbox": [ + 339, + 365, + 560, + 376 + ], + "type": "text", + "content": "vature directions via an SDF-based shape operator, naturally", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 340, + 377, + 455, + 387 + ], + "spans": [ + { + "bbox": [ + 340, + 377, + 455, + 387 + ], + "type": "text", + "content": "addressing potential ambiguity.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 331, + 387, + 561, + 418 + ], + "type": "text", + "angle": 0, + "index": 17, + "lines": [ + { + "bbox": [ + 332, + 388, + 562, + 398 + ], + "spans": [ + { + "bbox": [ + 332, + 388, + 562, + 398 + ], + "type": "text", + "content": "- We leverage an optimizable neural SDF as an underlying repre-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 339, + 399, + 560, + 408 + ], + "spans": [ + { + "bbox": [ + 339, + 399, + 560, + 408 + ], + "type": "text", + "content": "sentation to coordinate requirements, dynamically adjusting", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 339, + 410, + 441, + 418 + ], + "spans": [ + { + "bbox": [ + 339, + 410, + 441, + 418 + ], + "type": "text", + "content": "to minor surface variations.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 315, + 430, + 404, + 441 + ], + "type": "title", + "angle": 0, + "index": 18, + "lines": [ + { + "bbox": [ + 315, + 431, + 404, + 441 + ], + "spans": [ + { + "bbox": [ + 315, + 431, + 404, + 441 + ], + "type": "text", + "content": "2 RELATED WORK", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 314, + 445, + 561, + 488 + ], + "type": "text", + "angle": 0, + "index": 19, + "lines": [ + { + "bbox": [ + 317, + 445, + 560, + 455 + ], + "spans": [ + { + "bbox": [ + 317, + 445, + 560, + 455 + ], + "type": "text", + "content": "This paper focuses on developing a neural representation of the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 457, + 560, + 466 + ], + "spans": [ + { + "bbox": [ + 317, + 457, + 560, + 466 + ], + "type": "text", + "content": "cross field for quadrilateral mesh generation. 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While some methods, such as Dual Marching Cubes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 531, + 560, + 539 + ], + "spans": [ + { + "bbox": [ + 317, + 531, + 560, + 539 + ], + "type": "text", + "content": "(DMC) [Nielson 2004], can directly extract quad facets without", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 541, + 560, + 550 + ], + "spans": [ + { + "bbox": [ + 317, + 541, + 560, + 550 + ], + "type": "text", + "content": "relying on direction fields, the resulting meshes often lack quality,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 553, + 561, + 561 + ], + "spans": [ + { + "bbox": [ + 317, + 553, + 561, + 561 + ], + "type": "text", + "content": "particularly in aligning with principal directions. 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All these methods leverage neural networks to approximate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 404, + 82, + 413 + ], + "spans": [ + { + "bbox": [ + 50, + 404, + 82, + 413 + ], + "type": "text", + "content": "the SDF.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 414, + 295, + 448 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 59, + 416, + 294, + 424 + ], + "spans": [ + { + "bbox": [ + 59, + 416, + 294, + 424 + ], + "type": "text", + "content": "In this paper, SDFs play a central role in quad mesh generation,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 426, + 294, + 435 + ], + "spans": [ + { + "bbox": [ + 51, + 426, + 294, + 435 + ], + "type": "text", + "content": "as the Hessian of the SDF fully encodes principal curvatures and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 437, + 241, + 446 + ], + "spans": [ + { + "bbox": [ + 51, + 437, + 241, + 446 + ], + "type": "text", + "content": "their directions [Dong et al. 2024; Wang et al. 2023].", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 49, + 460, + 140, + 471 + ], + "type": "title", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 50, + 462, + 139, + 471 + ], + "spans": [ + { + "bbox": [ + 50, + 462, + 139, + 471 + ], + "type": "text", + "content": "3 OUR APPROACH", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 49, + 475, + 113, + 485 + ], + "type": "title", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 50, + 476, + 112, + 487 + ], + "spans": [ + { + "bbox": [ + 50, + 476, + 112, + 487 + ], + "type": "text", + "content": "3.1 Overview", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 48, + 489, + 296, + 588 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 50, + 491, + 294, + 499 + ], + "spans": [ + { + "bbox": [ + 50, + 491, + 294, + 499 + ], + "type": "text", + "content": "The core idea of NeurCross is to leverage the optimizable neural", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 502, + 294, + 510 + ], + "spans": [ + { + "bbox": [ + 51, + 502, + 294, + 510 + ], + "type": "text", + "content": "Signed Distance Function (SDF) as an underlying representation to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 513, + 294, + 521 + ], + "spans": [ + { + "bbox": [ + 51, + 513, + 294, + 521 + ], + "type": "text", + "content": "coordinate various requirements. 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Neural-Singular-Hessian [Wang et al. 2023] ensures", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 339, + 295, + 347 + ], + "spans": [ + { + "bbox": [ + 51, + 339, + 295, + 347 + ], + "type": "text", + "content": "that the Hessian of the neural implicit function has a zero deter-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 350, + 294, + 358 + ], + "spans": [ + { + "bbox": [ + 51, + 350, + 294, + 358 + ], + "type": "text", + "content": "minant for points near the surface, which is particularly useful for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 361, + 294, + 369 + ], + "spans": [ + { + "bbox": [ + 50, + 361, + 294, + 369 + ], + "type": "text", + "content": "recovering details from unoriented point clouds. Additionally, Dong", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 372, + 294, + 380 + ], + "spans": [ + { + "bbox": [ + 51, + 372, + 294, + 380 + ], + "type": "text", + "content": "et al. [2024] proposed a zero Gaussian curvature constraint for re", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 383, + 294, + 392 + ], + "spans": [ + { + "bbox": [ + 51, + 383, + 294, + 392 + ], + "type": "text", + "content": "constructing CAD-type surfaces from low-quality unoriented point", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 393, + 294, + 403 + ], + "spans": [ + { + "bbox": [ + 50, + 393, + 294, + 403 + ], + "type": "text", + "content": "clouds. All these methods leverage neural networks to approximate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 404, + 82, + 413 + ], + "spans": [ + { + "bbox": [ + 50, + 404, + 82, + 413 + ], + "type": "text", + "content": "the SDF.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 414, + 295, + 448 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 59, + 416, + 294, + 424 + ], + "spans": [ + { + "bbox": [ + 59, + 416, + 294, + 424 + ], + "type": "text", + "content": "In this paper, SDFs play a central role in quad mesh generation,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 426, + 294, + 435 + ], + "spans": [ + { + "bbox": [ + 51, + 426, + 294, + 435 + ], + "type": "text", + "content": "as the Hessian of the SDF fully encodes principal curvatures and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 437, + 241, + 446 + ], + "spans": [ + { + "bbox": [ + 51, + 437, + 241, + 446 + ], + "type": "text", + "content": "their directions [Dong et al. 2024; Wang et al. 2023].", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 49, + 460, + 140, + 471 + ], + "type": "title", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 50, + 462, + 139, + 471 + ], + "spans": [ + { + "bbox": [ + 50, + 462, + 139, + 471 + ], + "type": "text", + "content": "3 OUR APPROACH", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 49, + 475, + 113, + 485 + ], + "type": "title", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 50, + 476, + 112, + 487 + ], + "spans": [ + { + "bbox": [ + 50, + 476, + 112, + 487 + ], + "type": "text", + "content": "3.1 Overview", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 48, + 489, + 296, + 588 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 50, + 491, + 294, + 499 + ], + "spans": [ + { + "bbox": [ + 50, + 491, + 294, + 499 + ], + "type": "text", + "content": "The core idea of NeurCross is to leverage the optimizable neural", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 502, + 294, + 510 + ], + "spans": [ + { + "bbox": [ + 51, + 502, + 294, + 510 + ], + "type": "text", + "content": "Signed Distance Function (SDF) as an underlying representation to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 513, + 294, + 521 + ], + "spans": [ + { + "bbox": [ + 51, + 513, + 294, + 521 + ], + "type": "text", + "content": "coordinate various requirements. 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To address this limitation, we adopt an implicit alignment", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 374, + 560, + 382 + ], + "spans": [ + { + "bbox": [ + 317, + 374, + 560, + 382 + ], + "type": "text", + "content": "strategy by evaluating the compatibility between the cross field and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 385, + 388, + 394 + ], + "spans": [ + { + "bbox": [ + 317, + 385, + 388, + 394 + ], + "type": "text", + "content": "the shape operator.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 314, + 394, + 561, + 437 + ], + "type": "text", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 325, + 395, + 560, + 405 + ], + "spans": [ + { + "bbox": [ + 325, + 395, + 560, + 405 + ], + "type": "text", + "content": "To align the cross field with the principal directions, we encourage", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 406, + 561, + 417 + ], + "spans": [ + { + "bbox": [ + 317, + 407, + 329, + 416 + ], + "type": "inline_equation", + "content": "\\alpha _ { p }", + "score": 0.8806 + }, + { + "bbox": [ + 330, + 406, + 345, + 415 + ], + "type": "text", + "content": "and", + "score": 1.0 + }, + { + "bbox": [ + 346, + 406, + 358, + 417 + ], + "type": "inline_equation", + "content": "\\beta _ { p }", + "score": 0.8867 + }, + { + "bbox": [ + 358, + 406, + 519, + 415 + ], + "type": "text", + "content": "to coincide with two of the eigenvectors of", + "score": 1.0 + }, + { + "bbox": [ + 520, + 406, + 534, + 416 + ], + "type": "inline_equation", + "content": "H _ { p } .", + "score": 0.86 + }, + { + "bbox": [ + 534, + 406, + 561, + 415 + ], + "type": "text", + "content": ". To en-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 417, + 560, + 428 + ], + "spans": [ + { + "bbox": [ + 317, + 417, + 411, + 426 + ], + "type": "text", + "content": "force collinearity between", + "score": 1.0 + }, + { + "bbox": [ + 413, + 417, + 437, + 428 + ], + "type": "inline_equation", + "content": "H _ { P } \\alpha _ { P }", + "score": 0.9056 + }, + { + "bbox": [ + 438, + 417, + 454, + 427 + ], + "type": "text", + "content": "and", + "score": 1.0 + }, + { + "bbox": [ + 455, + 418, + 468, + 428 + ], + "type": "inline_equation", + "content": "\\alpha _ { p }", + "score": 0.8783 + }, + { + "bbox": [ + 468, + 417, + 560, + 427 + ], + "type": "text", + "content": ", we impose the following", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 429, + 354, + 437 + ], + "spans": [ + { + "bbox": [ + 317, + 429, + 354, + 437 + ], + "type": "text", + "content": "condition:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 405, + 441, + 561, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 405, + 441, + 561, + 453 + ], + "spans": [ + { + "bbox": [ + 405, + 441, + 561, + 453 + ], + "type": "interline_equation", + "content": "H _ {p} \\alpha_ {p} \\times \\alpha_ {p} = 0. \\tag {5}", + "image_path": "ba223402a3f0f5675424b75d93b1d18b33179e644082143138ea3174fcee21cb.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 456, + 397, + 468 + ], + "type": "text", + "angle": 0, + "index": 16, + "lines": [ + { + "bbox": [ + 317, + 457, + 395, + 467 + ], + "spans": [ + { + "bbox": [ + 317, + 457, + 395, + 467 + ], + "type": "text", + "content": "Similarly, we require:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 406, + 474, + 561, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 406, + 474, + 561, + 488 + ], + "spans": [ + { + "bbox": [ + 406, + 474, + 561, + 488 + ], + "type": "interline_equation", + "content": "H _ {p} \\boldsymbol {\\beta} _ {p} \\times \\boldsymbol {\\beta} _ {p} = 0. \\tag {6}", + "image_path": "d2f2996bd0e982450b135a0a04c0b28e5bf469fed517ae49ea407c1673c8b758.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 314, + 492, + 561, + 513 + ], + "type": "text", + "angle": 0, + "index": 18, + "lines": [ + { + "bbox": [ + 316, + 493, + 560, + 502 + ], + "spans": [ + { + "bbox": [ + 316, + 493, + 560, + 502 + ], + "type": "text", + "content": "We define the loss term to measure alignment with the principal", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 503, + 395, + 513 + ], + "spans": [ + { + "bbox": [ + 317, + 503, + 395, + 513 + ], + "type": "text", + "content": "directions as follows:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 348, + 517, + 561, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 517, + 561, + 540 + ], + "spans": [ + { + "bbox": [ + 348, + 517, + 561, + 540 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm{AP}} ^ {(1)} = \\frac {1}{| \\mathcal {P} |} \\int_ {\\mathcal {P}} \\left| H _ {p} \\boldsymbol {\\alpha} _ {p} \\times \\boldsymbol {\\alpha} _ {p} \\right| + \\left| H _ {p} \\boldsymbol {\\beta} _ {p} \\times \\boldsymbol {\\beta} _ {p} \\right| \\mathrm{d} p. \\tag {7}", + "image_path": "466e06c66c3646a5156b3c2252276d8c6e594d88dd0560bdd2250ef0a3b704dd.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 314, + 544, + 561, + 589 + ], + "type": "text", + "angle": 0, + "index": 20, + "lines": [ + { + "bbox": [ + 325, + 545, + 560, + 555 + ], + "spans": [ + { + "bbox": [ + 325, + 545, + 560, + 555 + ], + "type": "text", + "content": "Smoothness ofthe Cross Field. Consider two pairs of orthogonal", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 556, + 560, + 567 + ], + "spans": [ + { + "bbox": [ + 317, + 558, + 446, + 566 + ], + "type": "text", + "content": "unit vectors in a plane, denoted as", + "score": 1.0 + }, + { + "bbox": [ + 447, + 556, + 478, + 567 + ], + "type": "inline_equation", + "content": "( \\pmb { \\alpha } _ { 1 } , \\pmb { \\beta } _ { 1 } )", + "score": 0.9067 + }, + { + "bbox": [ + 480, + 556, + 496, + 567 + ], + "type": "text", + "content": "and", + "score": 1.0 + }, + { + "bbox": [ + 497, + 556, + 528, + 567 + ], + "type": "inline_equation", + "content": "( \\alpha _ { 2 } , \\beta _ { 2 } )", + "score": 0.9112 + }, + { + "bbox": [ + 528, + 558, + 560, + 566 + ], + "type": "text", + "content": ". We say", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 566, + 561, + 578 + ], + "spans": [ + { + "bbox": [ + 317, + 567, + 364, + 577 + ], + "type": "text", + "content": "that the pair", + "score": 1.0 + }, + { + "bbox": [ + 364, + 567, + 394, + 578 + ], + "type": "inline_equation", + "content": "( \\alpha _ { 1 } , \\beta _ { 1 } )", + "score": 0.8962 + }, + { + "bbox": [ + 395, + 568, + 440, + 577 + ], + "type": "text", + "content": "aligns with", + "score": 1.0 + }, + { + "bbox": [ + 441, + 568, + 471, + 578 + ], + "type": "inline_equation", + "content": "( \\alpha _ { 2 } , \\beta _ { 2 } )", + "score": 0.8886 + }, + { + "bbox": [ + 472, + 566, + 504, + 578 + ], + "type": "text", + "content": "if either", + "score": 1.0 + }, + { + "bbox": [ + 505, + 569, + 517, + 578 + ], + "type": "inline_equation", + "content": "\\pmb { \\alpha } _ { 1 }", + "score": 0.788 + }, + { + "bbox": [ + 517, + 566, + 534, + 578 + ], + "type": "text", + "content": "and", + "score": 1.0 + }, + { + "bbox": [ + 534, + 569, + 546, + 578 + ], + "type": "inline_equation", + "content": "\\pmb { \\alpha } _ { 2 }", + "score": 0.8506 + }, + { + "bbox": [ + 547, + 566, + 561, + 578 + ], + "type": "text", + "content": "are", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 578, + 446, + 589 + ], + "spans": [ + { + "bbox": [ + 317, + 578, + 359, + 587 + ], + "type": "text", + "content": "colinear, or", + "score": 1.0 + }, + { + "bbox": [ + 360, + 579, + 370, + 588 + ], + "type": "inline_equation", + "content": "\\pmb { \\alpha } _ { 1 }", + "score": 0.5822 + }, + { + "bbox": [ + 371, + 578, + 388, + 587 + ], + "type": "text", + "content": "and", + "score": 1.0 + }, + { + "bbox": [ + 389, + 578, + 400, + 589 + ], + "type": "inline_equation", + "content": "\\beta _ { 2 }", + "score": 0.8759 + }, + { + "bbox": [ + 400, + 578, + 446, + 587 + ], + "type": "text", + "content": "are colinear.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 314, + 589, + 560, + 611 + ], + "type": "text", + "angle": 0, + "index": 21, + "lines": [ + { + "bbox": [ + 326, + 590, + 559, + 600 + ], + "spans": [ + { + "bbox": [ + 326, + 590, + 525, + 599 + ], + "type": "text", + "content": "Based on the above definition, it can be proved that", + "score": 1.0 + }, + { + "bbox": [ + 528, + 590, + 559, + 600 + ], + "type": "inline_equation", + "content": "( \\alpha _ { 1 } , \\beta _ { 1 } )", + "score": 0.9087 + } + ] + }, + { + "bbox": [ + 316, + 600, + 441, + 611 + ], + "spans": [ + { + "bbox": [ + 316, + 601, + 359, + 610 + ], + "type": "text", + "content": "aligns with", + "score": 1.0 + }, + { + "bbox": [ + 360, + 601, + 391, + 611 + ], + "type": "inline_equation", + "content": "( \\alpha _ { 2 } , \\beta _ { 2 } )", + "score": 0.8998 + }, + { + "bbox": [ + 392, + 600, + 441, + 609 + ], + "type": "text", + "content": "if and only if", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 359, + 616, + 561, + 630 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 616, + 561, + 630 + ], + "spans": [ + { + "bbox": [ + 359, + 616, + 561, + 630 + ], + "type": "interline_equation", + "content": "\\left| \\boldsymbol {\\alpha} _ {1} \\cdot \\boldsymbol {\\alpha} _ {2} \\right| + \\left| \\boldsymbol {\\alpha} _ {1} \\cdot \\boldsymbol {\\beta} _ {2} \\right| + \\left| \\boldsymbol {\\beta} _ {1} \\cdot \\boldsymbol {\\alpha} _ {2} \\right| + \\left| \\boldsymbol {\\beta} _ {1} \\cdot \\boldsymbol {\\beta} _ {2} \\right| \\tag {8}", + "image_path": "f01737464d818fdeb13928a3cd61be66ab023b2108355b601995436cee35d53d.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 314, + 635, + 562, + 669 + ], + "type": "text", + "angle": 0, + "index": 23, + "lines": [ + { + "bbox": [ + 317, + 636, + 561, + 645 + ], + "spans": [ + { + "bbox": [ + 317, + 636, + 561, + 645 + ], + "type": "text", + "content": "achieves the minimum. We explain the correctness as follows. With-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 646, + 561, + 657 + ], + "spans": [ + { + "bbox": [ + 317, + 647, + 459, + 656 + ], + "type": "text", + "content": "out loss of generality, we assume that", + "score": 1.0 + }, + { + "bbox": [ + 459, + 646, + 500, + 656 + ], + "type": "inline_equation", + "content": "\\pmb { \\alpha } _ { 1 } = ( 1 , 0 )", + "score": 0.9012 + }, + { + "bbox": [ + 502, + 647, + 518, + 656 + ], + "type": "text", + "content": "and", + "score": 1.0 + }, + { + "bbox": [ + 518, + 646, + 558, + 657 + ], + "type": "inline_equation", + "content": "\\beta _ { 1 } = ( 0 , 1 )", + "score": 0.9219 + }, + { + "bbox": [ + 558, + 649, + 561, + 654 + ], + "type": "text", + "content": ".", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 658, + 537, + 667 + ], + "spans": [ + { + "bbox": [ + 317, + 658, + 364, + 667 + ], + "type": "text", + "content": "By denoting", + "score": 1.0 + }, + { + "bbox": [ + 364, + 658, + 376, + 667 + ], + "type": "inline_equation", + "content": "\\alpha _ { 2 }", + "score": 0.7516 + }, + { + "bbox": [ + 376, + 658, + 537, + 667 + ], + "type": "text", + "content": "as (cos �, sin �), the above sum simplifies to", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 400, + 673, + 561, + 686 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 400, + 673, + 561, + 686 + ], + "spans": [ + { + "bbox": [ + 400, + 673, + 561, + 686 + ], + "type": "interline_equation", + "content": "2 (| \\cos \\theta | + | \\sin \\theta |). \\tag {9}", + "image_path": "0f8780af8a8d312f9ed5760bf3b5bccc8611c984dba8c2a44dcd8fa4e70d286c.jpg" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 291, + 54, + 540, + 64 + ], + "type": "header", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 293, + 56, + 540, + 63 + ], + "spans": [ + { + "bbox": [ + 293, + 56, + 540, + 63 + ], + "type": "text", + "content": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 555, + 55, + 560, + 62 + ], + "type": "page_number", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 556, + 56, + 559, + 62 + ], + "spans": [ + { + "bbox": [ + 556, + 56, + 559, + 62 + ], + "type": "text", + "content": "5", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 414, + 708, + 560, + 717 + ], + "type": "footer", + "angle": 0, + "index": 25, + "lines": [ + { + "bbox": [ + 414, + 710, + 559, + 716 + ], + "spans": [ + { + "bbox": [ + 414, + 710, + 559, + 716 + ], + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4, + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 74, + 556, + 243 + ], + "blocks": [ + { + "bbox": [ + 53, + 74, + 556, + 243 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 74, + 556, + 243 + ], + "spans": [ + { + "bbox": [ + 53, + 74, + 556, + 243 + ], + "type": "image", + "content": "```mermaid\ngraph LR\n A[\"Input Image\"] --> B[\"Image with Scatter Plot\"]\n B --> C[\"P\"]\n C --> D[\"SDF fitting module\"]\n D --> E[\"Feature Output\"]\n F[\"MLP\"] --> G[\"θ\"]\n G --> H[\"μ, ν\"]\n H --> I[\"⊕\"]\n J[\"L_SDF\"] --> K[\"min L\"]\n K --> L[\"L_CrossField\"]\n L --> M[\"Output Image\"]\n N[\"α = μcosθ + vsinθ\\nβ = vcosθ - μsinθ\"] --> I\n E --> O[\"H\"]\n O --> P[\"⊕\"]\n P --> Q[\"Output Image\"]\n```", + "image_path": "de77e6dbc3e8b40ddf3fe821e9c18bcdc2eb8f2daed28bf5505c5cbc863228c1.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 248, + 561, + 281 + ], + "type": "image_caption", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 51, + 250, + 559, + 257 + ], + "spans": [ + { + "bbox": [ + 51, + 250, + 559, + 257 + ], + "type": "text", + "content": "Fig. 5. Our self-supervised network pipeline for representing cross fields in quad mesh generation. All layers in the network are implemented as multi-layer", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 258, + 559, + 267 + ], + "spans": [ + { + "bbox": [ + 50, + 260, + 433, + 267 + ], + "type": "text", + "content": "perceptrons (MLPs), with the SDF fiting module utilizing the SIREN [Sitzmann et al. 2020] architecture. The circled", + "score": 1.0 + }, + { + "bbox": [ + 433, + 258, + 445, + 267 + ], + "type": "inline_equation", + "content": "^ { 6 } + \\prime", + "score": 0.4847 + }, + { + "bbox": [ + 445, + 260, + 559, + 267 + ], + "type": "text", + "content": "symbol denotes a data-combining", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 270, + 85, + 277 + ], + "spans": [ + { + "bbox": [ + 50, + 270, + 85, + 277 + ], + "type": "text", + "content": "operation.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 2, + "sub_type": "flowchart" + }, + { + "bbox": [ + 48, + 295, + 295, + 352 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 147, + 357, + 295, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 147, + 357, + 295, + 369 + ], + "spans": [ + { + "bbox": [ + 147, + 357, + 295, + 369 + ], + "type": "interline_equation", + "content": "H _ {p} \\cdot n _ {p} = 0. \\tag {2}", + "image_path": "1f752ff95ef86055b54cee891bd0db5d6f17ccf9d1cffa97fcdd85379c89aadd.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 376, + 296, + 398 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 50, + 377, + 295, + 388 + ], + "spans": [ + { + "bbox": [ + 50, + 377, + 295, + 388 + ], + "type": "text", + "content": "The overall alignment with predefined surface normals can be quan-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 388, + 83, + 397 + ], + "spans": [ + { + "bbox": [ + 50, + 388, + 83, + 397 + ], + "type": "text", + "content": "tified as:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 118, + 401, + 295, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 401, + 295, + 425 + ], + "spans": [ + { + "bbox": [ + 118, + 401, + 295, + 425 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm{AN}} = \\frac {1}{| \\mathcal {P} |} \\int_ {\\mathcal {P}} \\left| H _ {\\boldsymbol {p}} \\cdot \\boldsymbol {n} _ {\\boldsymbol {p}} \\right| \\mathrm{d} \\boldsymbol {p}. \\tag {3}", + "image_path": "b2e7b8b162da66c4314c04c7a7fe8c7288f21d2a176b6139b1a3984453319dd8.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 49, + 434, + 164, + 445 + ], + "type": "title", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 50, + 435, + 162, + 445 + ], + "spans": [ + { + "bbox": [ + 50, + 435, + 162, + 445 + ], + "type": "text", + "content": "3.3 Cross Field Prediction", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 48, + 449, + 173, + 569 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 59, + 450, + 172, + 459 + ], + "spans": [ + { + "bbox": [ + 59, + 450, + 172, + 459 + ], + "type": "text", + "content": "Local Coordinate System. Re-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 460, + 173, + 470 + ], + "spans": [ + { + "bbox": [ + 51, + 461, + 126, + 469 + ], + "type": "text", + "content": "call that each point", + "score": 1.0 + }, + { + "bbox": [ + 127, + 460, + 154, + 470 + ], + "type": "inline_equation", + "content": "\\pmb { p } \\in \\mathcal { P }", + "score": 0.8764 + }, + { + "bbox": [ + 156, + 461, + 173, + 470 + ], + "type": "text", + "content": "cor-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 472, + 172, + 481 + ], + "spans": [ + { + "bbox": [ + 50, + 472, + 172, + 481 + ], + "type": "text", + "content": "responds to the centroid of a tri-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 483, + 172, + 492 + ], + "spans": [ + { + "bbox": [ + 51, + 483, + 172, + 492 + ], + "type": "text", + "content": "angular face. 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An explicit approach", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 308, + 561, + 316 + ], + "spans": [ + { + "bbox": [ + 317, + 308, + 561, + 316 + ], + "type": "text", + "content": "to implementing alignment with principal directions involves com-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 319, + 561, + 328 + ], + "spans": [ + { + "bbox": [ + 317, + 319, + 561, + 328 + ], + "type": "text", + "content": "paring the cross field with pre-extracted principal directions. How-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 330, + 561, + 338 + ], + "spans": [ + { + "bbox": [ + 317, + 330, + 561, + 338 + ], + "type": "text", + "content": "ever, most existing methods for extracting principal directions heav-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 341, + 560, + 350 + ], + "spans": [ + { + "bbox": [ + 317, + 341, + 560, + 350 + ], + "type": "text", + "content": "ily rely on local shape variations, which can lead to instability,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 352, + 560, + 361 + ], + "spans": [ + { + "bbox": [ + 317, + 352, + 560, + 361 + ], + "type": "text", + "content": "particularly when the local geometry is approximately planar or", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 363, + 560, + 372 + ], + "spans": [ + { + "bbox": [ + 317, + 363, + 560, + 372 + ], + "type": "text", + "content": "spherical. 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To en-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 417, + 560, + 428 + ], + "spans": [ + { + "bbox": [ + 317, + 417, + 411, + 426 + ], + "type": "text", + "content": "force collinearity between", + "score": 1.0 + }, + { + "bbox": [ + 413, + 417, + 437, + 428 + ], + "type": "inline_equation", + "content": "H _ { P } \\alpha _ { P }", + "score": 0.9056 + }, + { + "bbox": [ + 438, + 417, + 454, + 427 + ], + "type": "text", + "content": "and", + "score": 1.0 + }, + { + "bbox": [ + 455, + 418, + 468, + 428 + ], + "type": "inline_equation", + "content": "\\alpha _ { p }", + "score": 0.8783 + }, + { + "bbox": [ + 468, + 417, + 560, + 427 + ], + "type": "text", + "content": ", we impose the following", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 429, + 354, + 437 + ], + "spans": [ + { + "bbox": [ + 317, + 429, + 354, + 437 + ], + "type": "text", + "content": "condition:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 405, + 441, + 561, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 405, + 441, + 561, + 453 + ], + "spans": [ + { + "bbox": [ + 405, + 441, + 561, + 453 + ], + "type": "interline_equation", + "content": "H _ {p} \\alpha_ {p} \\times \\alpha_ {p} = 0. \\tag {5}", + "image_path": "ba223402a3f0f5675424b75d93b1d18b33179e644082143138ea3174fcee21cb.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 456, + 397, + 468 + ], + "type": "text", + "angle": 0, + "index": 16, + "lines": [ + { + "bbox": [ + 317, + 457, + 395, + 467 + ], + "spans": [ + { + "bbox": [ + 317, + 457, + 395, + 467 + ], + "type": "text", + "content": "Similarly, we require:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 406, + 474, + 561, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 406, + 474, + 561, + 488 + ], + "spans": [ + { + "bbox": [ + 406, + 474, + 561, + 488 + ], + "type": "interline_equation", + "content": "H _ {p} \\boldsymbol {\\beta} _ {p} \\times \\boldsymbol {\\beta} _ {p} = 0. \\tag {6}", + "image_path": "d2f2996bd0e982450b135a0a04c0b28e5bf469fed517ae49ea407c1673c8b758.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 314, + 492, + 561, + 513 + ], + "type": "text", + "angle": 0, + "index": 18, + "lines": [ + { + "bbox": [ + 316, + 493, + 560, + 502 + ], + "spans": [ + { + "bbox": [ + 316, + 493, + 560, + 502 + ], + "type": "text", + "content": "We define the loss term to measure alignment with the principal", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 503, + 395, + 513 + ], + "spans": [ + { + "bbox": [ + 317, + 503, + 395, + 513 + ], + "type": "text", + "content": "directions as follows:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 348, + 517, + 561, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 517, + 561, + 540 + ], + "spans": [ + { + "bbox": [ + 348, + 517, + 561, + 540 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm{AP}} ^ {(1)} = \\frac {1}{| \\mathcal {P} |} \\int_ {\\mathcal {P}} \\left| H _ {p} \\boldsymbol {\\alpha} _ {p} \\times \\boldsymbol {\\alpha} _ {p} \\right| + \\left| H _ {p} \\boldsymbol {\\beta} _ {p} \\times \\boldsymbol {\\beta} _ {p} \\right| \\mathrm{d} p. \\tag {7}", + "image_path": "466e06c66c3646a5156b3c2252276d8c6e594d88dd0560bdd2250ef0a3b704dd.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 314, + 544, + 561, + 589 + ], + "type": "text", + "angle": 0, + "index": 20, + "lines": [ + { + "bbox": [ + 325, + 545, + 560, + 555 + ], + "spans": [ + { + "bbox": [ + 325, + 545, + 560, + 555 + ], + "type": "text", + "content": "Smoothness ofthe Cross Field. 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At", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 520, + 294, + 529 + ], + "spans": [ + { + "bbox": [ + 51, + 520, + 294, + 529 + ], + "type": "text", + "content": "each point on such a surface, the principal curvature directions are", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 530, + 294, + 539 + ], + "spans": [ + { + "bbox": [ + 50, + 530, + 294, + 539 + ], + "type": "text", + "content": "not unique. In this case, the smoothness constraint of the cross field", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 542, + 294, + 550 + ], + "spans": [ + { + "bbox": [ + 50, + 542, + 294, + 550 + ], + "type": "text", + "content": "plays a crucial role in better controlling the distribution of singular", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 553, + 294, + 562 + ], + "spans": [ + { + "bbox": [ + 51, + 553, + 294, + 562 + ], + "type": "text", + "content": "ity points. 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At", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 520, + 294, + 529 + ], + "spans": [ + { + "bbox": [ + 51, + 520, + 294, + 529 + ], + "type": "text", + "content": "each point on such a surface, the principal curvature directions are", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 530, + 294, + 539 + ], + "spans": [ + { + "bbox": [ + 50, + 530, + 294, + 539 + ], + "type": "text", + "content": "not unique. In this case, the smoothness constraint of the cross field", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 542, + 294, + 550 + ], + "spans": [ + { + "bbox": [ + 50, + 542, + 294, + 550 + ], + "type": "text", + "content": "plays a crucial role in better controlling the distribution of singular", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 553, + 294, + 562 + ], + "spans": [ + { + "bbox": [ + 51, + 553, + 294, + 562 + ], + "type": "text", + "content": "ity points. 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For this module, we initialize the orien", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 491, + 294, + 500 + ], + "spans": [ + { + "bbox": [ + 50, + 491, + 294, + 500 + ], + "type": "text", + "content": "tation at a point � using a normal distribution with a mean of 0 and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 502, + 149, + 510 + ], + "spans": [ + { + "bbox": [ + 50, + 502, + 149, + 510 + ], + "type": "text", + "content": "a standard deviation of 0.2.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 49, + 526, + 235, + 537 + ], + "type": "title", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 50, + 526, + 235, + 537 + ], + "spans": [ + { + "bbox": [ + 50, + 526, + 235, + 537 + ], + "type": "text", + "content": "3.4 SDF and Cross Field Joint Optimization", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 48, + 540, + 295, + 605 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 51, + 542, + 294, + 551 + ], + "spans": [ + { + "bbox": [ + 51, + 542, + 294, + 551 + ], + "type": "text", + "content": "One challenge in quad meshing is balancing the overall simplicity of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 552, + 293, + 561 + ], + "spans": [ + { + "bbox": [ + 51, + 552, + 293, + 561 + ], + "type": "text", + "content": "the cross field with alignment to the principal directions, a dificulty", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 564, + 293, + 573 + ], + "spans": [ + { + "bbox": [ + 51, + 564, + 293, + 573 + ], + "type": "text", + "content": "that becomes more pronounced for geometrically or topologically", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 574, + 294, + 583 + ], + "spans": [ + { + "bbox": [ + 51, + 574, + 294, + 583 + ], + "type": "text", + "content": "complex shapes. In this paper, we address this challenge by using an", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 586, + 294, + 594 + ], + "spans": [ + { + "bbox": [ + 51, + 586, + 294, + 594 + ], + "type": "text", + "content": "optimizable neural SDF as a bridge to achieve this balance. Notably,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 596, + 286, + 605 + ], + "spans": [ + { + "bbox": [ + 50, + 596, + 286, + 605 + ], + "type": "text", + "content": "the neural SDF and the cross field are optimized simultaneously.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 606, + 296, + 693 + ], + "type": "text", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 60, + 607, + 294, + 616 + ], + "spans": [ + { + "bbox": [ + 60, + 607, + 294, + 616 + ], + "type": "text", + "content": "An alternative approach is to first fully optimize the SDF to accu", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 619, + 294, + 627 + ], + "spans": [ + { + "bbox": [ + 51, + 619, + 294, + 627 + ], + "type": "text", + "content": "rately represent the input shape and then keep it fixed. 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As shown in Fig. 9, the fixed SDF, while providing an accu-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 662, + 294, + 672 + ], + "spans": [ + { + "bbox": [ + 50, + 662, + 294, + 672 + ], + "type": "text", + "content": "rate representation, may introduce overly complex curvature lines,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 673, + 294, + 681 + ], + "spans": [ + { + "bbox": [ + 50, + 673, + 294, + 681 + ], + "type": "text", + "content": "leading to an excessive number of singular points in the final cross", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 684, + 70, + 693 + ], + "spans": [ + { + "bbox": [ + 50, + 684, + 70, + 693 + ], + "type": "text", + "content": "field.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "image", + "bbox": [ + 320, + 76, + 560, + 273 + ], + "blocks": [ + { + "bbox": [ + 320, + 76, + 560, + 273 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 76, + 560, + 273 + ], + "spans": [ + { + "bbox": [ + 320, + 76, + 560, + 273 + ], + "type": "image", + "content": "3D modeling visualization of two humanoid figures with meshed surfaces and color-coded heatmaps (no text or symbols)", + "image_path": "08575997b0e24ff7c2d0e51a07d30705fcf0f1763876fb57050444dad618e6c4.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 326, + 275, + 377, + 285 + ], + "type": "image_caption", + "angle": 0, + "index": 16, + "lines": [ + { + "bbox": [ + 326, + 277, + 378, + 285 + ], + "spans": [ + { + "bbox": [ + 326, + 277, + 378, + 285 + ], + "type": "text", + "content": "(a) Cross field", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 381, + 275, + 435, + 285 + ], + "type": "image_caption", + "angle": 0, + "index": 17, + "lines": [ + { + "bbox": [ + 381, + 277, + 435, + 285 + ], + "spans": [ + { + "bbox": [ + 381, + 277, + 435, + 285 + ], + "type": "text", + "content": "(b) Quad mesh", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 441, + 275, + 492, + 285 + ], + "type": "image_caption", + "angle": 0, + "index": 18, + "lines": [ + { + "bbox": [ + 441, + 275, + 492, + 287 + ], + "spans": [ + { + "bbox": [ + 441, + 275, + 492, + 287 + ], + "type": "text", + "content": "(c) SDF fitting", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 496, + 275, + 554, + 285 + ], + "type": "image_caption", + "angle": 0, + "index": 19, + "lines": [ + { + "bbox": [ + 497, + 277, + 553, + 286 + ], + "spans": [ + { + "bbox": [ + 497, + 277, + 553, + 286 + ], + "type": "text", + "content": "(d) Fitting error", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 314, + 291, + 561, + 361 + ], + "type": "image_caption", + "angle": 0, + "index": 20, + "lines": [ + { + "bbox": [ + 317, + 293, + 560, + 300 + ], + "spans": [ + { + "bbox": [ + 317, + 293, + 560, + 300 + ], + "type": "text", + "content": "Fig. 9. Comparison between the two-step method (top row) and our joint", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 302, + 560, + 311 + ], + "spans": [ + { + "bbox": [ + 317, + 302, + 560, + 311 + ], + "type": "text", + "content": "optimization strategy (botom row). (a) Cross field; (b) Quad mesh; (c) The", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 312, + 560, + 320 + ], + "spans": [ + { + "bbox": [ + 317, + 312, + 560, + 320 + ], + "type": "text", + "content": "underlying SDF surface; (d) Fiting error between the SDF and the input", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 323, + 560, + 330 + ], + "spans": [ + { + "bbox": [ + 317, + 323, + 560, + 330 + ], + "type": "text", + "content": "triangular mesh. 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The loss terms used to regularize the SDF in-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 411, + 561, + 419 + ], + "spans": [ + { + "bbox": [ + 317, + 411, + 561, + 419 + ], + "type": "text", + "content": "clude the Eikonal condition [Gropp et al. 2020], the Dirichlet condi-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 422, + 561, + 430 + ], + "spans": [ + { + "bbox": [ + 317, + 422, + 561, + 430 + ], + "type": "text", + "content": "tion [Lipman 2021], and the alignment condition [Wang et al. 2024,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 434, + 559, + 441 + ], + "spans": [ + { + "bbox": [ + 317, + 434, + 559, + 441 + ], + "type": "text", + "content": "2023]. For further details on these loss terms, we refer readers to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 444, + 552, + 453 + ], + "spans": [ + { + "bbox": [ + 317, + 444, + 552, + 453 + ], + "type": "text", + "content": "the existing literature [Dong et al. 2024; Wang et al. 2024, 2023].", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 313, + 464, + 561, + 571 + ], + "type": "text", + "angle": 0, + "index": 23, + "lines": [ + { + "bbox": [ + 326, + 464, + 560, + 474 + ], + "spans": [ + { + "bbox": [ + 326, + 464, + 560, + 474 + ], + "type": "text", + "content": "Sampling Strategy. A neural SDF is employed to approximate the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 475, + 560, + 484 + ], + "spans": [ + { + "bbox": [ + 317, + 475, + 560, + 484 + ], + "type": "text", + "content": "base surface, with regularization at sample points, as detailed in", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 487, + 561, + 495 + ], + "spans": [ + { + "bbox": [ + 317, + 487, + 561, + 495 + ], + "type": "text", + "content": "previous works [Ben-Shabat et al. 2022; Boulch and Marlet 2022;", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 498, + 561, + 506 + ], + "spans": [ + { + "bbox": [ + 317, + 498, + 561, + 506 + ], + "type": "text", + "content": "Dong et al. 2024; Gropp et al. 2020; Hou et al. 2022; Huang et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 509, + 561, + 518 + ], + "spans": [ + { + "bbox": [ + 317, + 509, + 561, + 518 + ], + "type": "text", + "content": "2022; Kazhdan and Hoppe 2013; Ma et al. 2021; Sitzmann et al. 2020;", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 520, + 560, + 529 + ], + "spans": [ + { + "bbox": [ + 317, + 520, + 560, + 529 + ], + "type": "text", + "content": "Wang et al. 2024, 2023; Xu et al. 2022]. We extract centroids from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 530, + 560, + 540 + ], + "spans": [ + { + "bbox": [ + 317, + 530, + 560, + 540 + ], + "type": "text", + "content": "all triangles in the mesh to define the sample set P, chosen for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 541, + 558, + 551 + ], + "spans": [ + { + "bbox": [ + 317, + 542, + 532, + 550 + ], + "type": "text", + "content": "their representative nature of the surface. 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The loss terms used to regularize the SDF in-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 411, + 561, + 419 + ], + "spans": [ + { + "bbox": [ + 317, + 411, + 561, + 419 + ], + "type": "text", + "content": "clude the Eikonal condition [Gropp et al. 2020], the Dirichlet condi-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 422, + 561, + 430 + ], + "spans": [ + { + "bbox": [ + 317, + 422, + 561, + 430 + ], + "type": "text", + "content": "tion [Lipman 2021], and the alignment condition [Wang et al. 2024,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 434, + 559, + 441 + ], + "spans": [ + { + "bbox": [ + 317, + 434, + 559, + 441 + ], + "type": "text", + "content": "2023]. 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The sizes of the building blocks within our U-Net-based module.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 89, + 561, + 97 + ], + "spans": [ + { + "bbox": [ + 316, + 89, + 561, + 97 + ], + "type": "text", + "content": "�b l k denotes the number of botleneck layers within each ResNet block.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 99, + 561, + 107 + ], + "spans": [ + { + "bbox": [ + 316, + 99, + 561, + 107 + ], + "type": "text", + "content": "From the 1st to the 7th block, the values of �b l k are set to 3, 4, 6, 3, 3,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 315, + 108, + 387, + 118 + ], + "spans": [ + { + "bbox": [ + 315, + 108, + 387, + 118 + ], + "type": "text", + "content": "4, and 6, respectively.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 330, + 130, + 549, + 244 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 130, + 549, + 244 + ], + "spans": [ + { + "bbox": [ + 330, + 130, + 549, + 244 + ], + "type": "table", + "html": "
Layer NameLayer ArchitectureOutput Size
1 \\times 1, input\\_size=12256
ResNets #1, #2, #3\\begin{bmatrix} 1 \\times 1, 256 \\\\ 1 \\times 1, 64 \\\\ 1 \\times 1, 64 \\end{bmatrix} \\times n_{bottleneck}256
ResNets #4, #5, #6, #7\\begin{bmatrix} 1 \\times 1, 512 \\\\ 1 \\times 1, 128 \\\\ 1 \\times 1, 128 \\end{bmatrix} \\times n_{bottleneck}512
1 \\times 1, 51232
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The sizes of the building blocks within our U-Net-based module.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 89, + 561, + 97 + ], + "spans": [ + { + "bbox": [ + 316, + 89, + 561, + 97 + ], + "type": "text", + "content": "�b l k denotes the number of botleneck layers within each ResNet block.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 99, + 561, + 107 + ], + "spans": [ + { + "bbox": [ + 316, + 99, + 561, + 107 + ], + "type": "text", + "content": "From the 1st to the 7th block, the values of �b l k are set to 3, 4, 6, 3, 3,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 315, + 108, + 387, + 118 + ], + "spans": [ + { + "bbox": [ + 315, + 108, + 387, + 118 + ], + "type": "text", + "content": "4, and 6, respectively.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 330, + 130, + 549, + 244 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 130, + 549, + 244 + ], + "spans": [ + { + "bbox": [ + 330, + 130, + 549, + 244 + ], + "type": "table", + "html": "
Layer NameLayer ArchitectureOutput Size
1 \\times 1, input\\_size=12256
ResNets #1, #2, #3\\begin{bmatrix} 1 \\times 1, 256 \\\\ 1 \\times 1, 64 \\\\ 1 \\times 1, 64 \\end{bmatrix} \\times n_{bottleneck}256
ResNets #4, #5, #6, #7\\begin{bmatrix} 1 \\times 1, 512 \\\\ 1 \\times 1, 128 \\\\ 1 \\times 1, 128 \\end{bmatrix} \\times n_{bottleneck}512
1 \\times 1, 51232
1 \\times 1, 321
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The annealing factor � remains", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 478, + 559, + 487 + ], + "spans": [ + { + "bbox": [ + 317, + 478, + 559, + 487 + ], + "type": "text", + "content": "1 during the initial 20% of iterations, then linearly decreases to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 487, + 560, + 498 + ], + "spans": [ + { + "bbox": [ + 316, + 487, + 349, + 498 + ], + "type": "inline_equation", + "content": "3 \\times 1 0 ^ { - 4 }", + "score": 0.8495 + }, + { + "bbox": [ + 350, + 488, + 560, + 498 + ], + "type": "text", + "content": "from 20% to 40% of the iteration span, and finally drops", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 499, + 560, + 510 + ], + "spans": [ + { + "bbox": [ + 316, + 499, + 560, + 510 + ], + "type": "text", + "content": "to 0 towards the end. 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In implementation, we", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 594, + 561, + 603 + ], + "spans": [ + { + "bbox": [ + 317, + 594, + 561, + 603 + ], + "type": "text", + "content": "utilize the global-seamless parametrization technique from libigl [Ja-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 605, + 561, + 614 + ], + "spans": [ + { + "bbox": [ + 317, + 605, + 561, + 614 + ], + "type": "text", + "content": "cobson et al. 2017] to align the parametrization with our cross field.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 616, + 559, + 625 + ], + "spans": [ + { + "bbox": [ + 317, + 616, + 559, + 625 + ], + "type": "text", + "content": "Subsequently, we employ libQEx [Ebke et al. 2013] to extract the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 628, + 459, + 636 + ], + "spans": [ + { + "bbox": [ + 317, + 628, + 459, + 636 + ], + "type": "text", + "content": "quad mesh from this parameterization.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 315, + 647, + 397, + 657 + ], + "type": "title", + "angle": 0, + "index": 20, + "lines": [ + { + "bbox": [ + 317, + 648, + 395, + 657 + ], + "spans": [ + { + "bbox": [ + 317, + 648, + 395, + 657 + ], + "type": "text", + "content": "4 EXPERIMENTS", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 314, + 661, + 562, + 694 + ], + "type": "text", + "angle": 0, + "index": 21, + "lines": [ + { + "bbox": [ + 326, + 662, + 559, + 671 + ], + "spans": [ + { + "bbox": [ + 326, + 662, + 559, + 671 + ], + "type": "text", + "content": "Evaluation Metrics and Platform. To evaluate the accuracy of the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 673, + 560, + 681 + ], + "spans": [ + { + "bbox": [ + 317, + 673, + 560, + 681 + ], + "type": "text", + "content": "quad mesh, we utilize four primary metrics [Huang et al. 2018;", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 684, + 561, + 693 + ], + "spans": [ + { + "bbox": [ + 317, + 684, + 561, + 693 + ], + "type": "text", + "content": "Wang et al. 2023]: area distortion (Area), angle distortion (Angle),", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 206, + 294, + 215 + ], + "spans": [ + { + "bbox": [ + 51, + 206, + 294, + 215 + ], + "type": "text", + "content": "the number of singularities (# of Sings), chamfer distance (CD), and", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 50, + 217, + 294, + 226 + ], + "spans": [ + { + "bbox": [ + 50, + 217, + 294, + 226 + ], + "type": "text", + "content": "Jacobian Ratio (JR). 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For the three methods, namely Instant", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 503, + 294, + 512 + ], + "spans": [ + { + "bbox": [ + 50, + 503, + 294, + 512 + ], + "type": "text", + "content": "Meshes (IM) [Jakob et al. 2015], QuadriFlow [Huang et al. 2018], and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 514, + 294, + 523 + ], + "spans": [ + { + "bbox": [ + 51, + 514, + 294, + 523 + ], + "type": "text", + "content": "QuadWild [Pietroni et al. 2021], we employed the open-source imple", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 525, + 294, + 534 + ], + "spans": [ + { + "bbox": [ + 50, + 525, + 294, + 534 + ], + "type": "text", + "content": "mentations that are readily available. It is worth noting that Quad", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 536, + 294, + 544 + ], + "spans": [ + { + "bbox": [ + 51, + 536, + 294, + 544 + ], + "type": "text", + "content": "Wild [Pietroni et al. 2021] is primarily a quadrangulation method", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 548, + 294, + 555 + ], + "spans": [ + { + "bbox": [ + 50, + 548, + 294, + 555 + ], + "type": "text", + "content": "rather than a cross field generation approach. The Mixed-Integer", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 558, + 294, + 567 + ], + "spans": [ + { + "bbox": [ + 51, + 558, + 294, + 567 + ], + "type": "text", + "content": "Quadrangulation (MIQ) method [Bommes et al. 2009] does not re", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 569, + 294, + 578 + ], + "spans": [ + { + "bbox": [ + 50, + 569, + 294, + 578 + ], + "type": "text", + "content": "lease its source code; therefore, we use the implementation provided", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 580, + 295, + 589 + ], + "spans": [ + { + "bbox": [ + 51, + 580, + 295, + 589 + ], + "type": "text", + "content": "by libigl [Jacobson et al. 2017]. However, the available implementa-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 591, + 294, + 600 + ], + "spans": [ + { + "bbox": [ + 51, + 591, + 294, + 600 + ], + "type": "text", + "content": "tion does not support the feature alignment constraint. For a fair", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 601, + 294, + 610 + ], + "spans": [ + { + "bbox": [ + 50, + 601, + 294, + 610 + ], + "type": "text", + "content": "comparison with MIQ, we employ the same parameterization and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 613, + 294, + 622 + ], + "spans": [ + { + "bbox": [ + 51, + 613, + 294, + 622 + ], + "type": "text", + "content": "extraction techniques, namely global-seamless parameterization", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 624, + 159, + 632 + ], + "spans": [ + { + "bbox": [ + 51, + 624, + 159, + 632 + ], + "type": "text", + "content": "and libQEx [Ebke et al. 2013].", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 639, + 296, + 694 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 60, + 641, + 294, + 649 + ], + "spans": [ + { + "bbox": [ + 60, + 641, + 294, + 649 + ], + "type": "text", + "content": "ShapeNet Dataset. The ShapeNet dataset [Chang et al. 2015] con", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 651, + 294, + 660 + ], + "spans": [ + { + "bbox": [ + 51, + 651, + 294, + 660 + ], + "type": "text", + "content": "sists of a diverse range of human-made models. As the global", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 662, + 294, + 671 + ], + "spans": [ + { + "bbox": [ + 51, + 662, + 294, + 671 + ], + "type": "text", + "content": "seamless parametrization from libigl [Jacobson et al. 2017] cannot", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 673, + 294, + 682 + ], + "spans": [ + { + "bbox": [ + 50, + 673, + 294, + 682 + ], + "type": "text", + "content": "handle non-manifold meshes, we use manifold ShapeNet meshes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 684, + 294, + 693 + ], + "spans": [ + { + "bbox": [ + 50, + 684, + 294, + 693 + ], + "type": "text", + "content": "repaired with DualOctreeGNN [Wang et al. 2022a]. We apply our", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "table", + "bbox": [ + 319, + 268, + 556, + 338 + ], + "blocks": [ + { + "bbox": [ + 314, + 206, + 561, + 257 + ], + "type": "table_caption", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 317, + 209, + 561, + 216 + ], + "spans": [ + { + "bbox": [ + 317, + 209, + 561, + 216 + ], + "type": "text", + "content": "Table 2. Quantitative comparison on the ShapeNet dataset [Chang et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 218, + 560, + 226 + ], + "spans": [ + { + "bbox": [ + 317, + 218, + 560, + 226 + ], + "type": "text", + "content": "2015]. Within each column, the best scores are emphasized with bold and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 228, + 560, + 236 + ], + "spans": [ + { + "bbox": [ + 317, + 228, + 560, + 236 + ], + "type": "text", + "content": "underlining (best), whereas the second-best scores are highlighted in bold", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 238, + 560, + 246 + ], + "spans": [ + { + "bbox": [ + 317, + 238, + 560, + 246 + ], + "type": "text", + "content": "(second best). The quad mesh generated by all the methods comprises an", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 248, + 454, + 256 + ], + "spans": [ + { + "bbox": [ + 317, + 248, + 454, + 256 + ], + "type": "text", + "content": "average of 6,000 vertices and 12,000 faces.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 319, + 268, + 556, + 338 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 268, + 556, + 338 + ], + "spans": [ + { + "bbox": [ + 319, + 268, + 556, + 338 + ], + "type": "table", + "html": "
Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
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MIQ [Bommes et al. 2009]5.2312.89\\underline{82.12}8.250.58
NeurCross (Ours)\\underline{1.48}\\underline{9.85}85.32\\underline{8.03}\\underline{0.78}
", + "image_path": "24c7c2967125183d50cc64176184088cf2ff50f3419dd3e40231b5b82b8bffb8.jpg" + } + ] + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 319, + 409, + 556, + 479 + ], + "blocks": [ + { + "bbox": [ + 314, + 347, + 561, + 398 + ], + "type": "table_caption", + "angle": 0, + "index": 16, + "lines": [ + { + "bbox": [ + 317, + 349, + 560, + 357 + ], + "spans": [ + { + "bbox": [ + 317, + 349, + 560, + 357 + ], + "type": "text", + "content": "Table 3. Quantitative comparison on the Thingi10K dataset [Zhou and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 359, + 560, + 367 + ], + "spans": [ + { + "bbox": [ + 316, + 359, + 560, + 367 + ], + "type": "text", + "content": "Jacobson 2016]. The quad mesh generated by all methods comprises an", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 369, + 560, + 377 + ], + "spans": [ + { + "bbox": [ + 317, + 369, + 560, + 377 + ], + "type": "text", + "content": "average of 10,000 vertices and 20,000 faces. Within each column, the best", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 380, + 561, + 388 + ], + "spans": [ + { + "bbox": [ + 317, + 380, + 561, + 388 + ], + "type": "text", + "content": "scores are emphasized with bold and underlining (best), whereas the second-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 389, + 504, + 396 + ], + "spans": [ + { + "bbox": [ + 317, + 389, + 504, + 396 + ], + "type": "text", + "content": "best scores are simply highlighted in bold (second best).", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 319, + 409, + 556, + 479 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 409, + 556, + 479 + ], + "spans": [ + { + "bbox": [ + 319, + 409, + 556, + 479 + ], + "type": "table", + "html": "
Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
IM [Jakob et al. 2015]1.4510.57397.189.830.75
QuadriFlow [Huang et al. 2018]1.5812.3978.3226.890.72
QuadWild [Pietroni et al. 2021]1.4010.1685.1128.120.77
MIQ [Bommes et al. 2009]1.389.8566.548.570.67
NeurCross (Ours)1.339.6868.968.220.81
", + "image_path": "c3f24835c59260fc54b3ad7d9e67f6ebb1a18570efa296567af9d56d199da364.jpg" + } + ] + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 490, + 561, + 533 + ], + "type": "text", + "angle": 0, + "index": 18, + "lines": [ + { + "bbox": [ + 317, + 491, + 561, + 500 + ], + "spans": [ + { + "bbox": [ + 317, + 491, + 561, + 500 + ], + "type": "text", + "content": "NeurCross to three randomly selected categories—airplane, bench,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 502, + 561, + 511 + ], + "spans": [ + { + "bbox": [ + 317, + 502, + 561, + 511 + ], + "type": "text", + "content": "and cabinet—which together contain 7433 models. For a fair com-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 514, + 560, + 522 + ], + "spans": [ + { + "bbox": [ + 316, + 514, + 560, + 522 + ], + "type": "text", + "content": "parison, all generated quad meshes are standardized to contain an", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 525, + 470, + 533 + ], + "spans": [ + { + "bbox": [ + 317, + 525, + 470, + 533 + ], + "type": "text", + "content": "average of 6,000 vertices and 12,000 faces.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 313, + 534, + 561, + 644 + ], + "type": "text", + "angle": 0, + "index": 19, + "lines": [ + { + "bbox": [ + 325, + 536, + 561, + 544 + ], + "spans": [ + { + "bbox": [ + 325, + 536, + 561, + 544 + ], + "type": "text", + "content": "In Fig. 11, we display the quad meshes generated by our Neur-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 547, + 560, + 555 + ], + "spans": [ + { + "bbox": [ + 317, + 547, + 560, + 555 + ], + "type": "text", + "content": "Cross alongside four other methods. For this example, although", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 558, + 560, + 566 + ], + "spans": [ + { + "bbox": [ + 317, + 558, + 560, + 566 + ], + "type": "text", + "content": "IM [Jakob et al. 2015] produces a regular quadrilateral mesh, the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 569, + 560, + 577 + ], + "spans": [ + { + "bbox": [ + 317, + 569, + 560, + 577 + ], + "type": "text", + "content": "outcome includes some triangular elements. More comparisons", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 579, + 561, + 588 + ], + "spans": [ + { + "bbox": [ + 317, + 579, + 561, + 588 + ], + "type": "text", + "content": "between IM and our method will be provided in Sec. 4.2. Quadri-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 590, + 561, + 599 + ], + "spans": [ + { + "bbox": [ + 317, + 590, + 561, + 599 + ], + "type": "text", + "content": "Flow [Huang et al. 2018], MIQ [Bommes et al. 2009], and Quad-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 601, + 561, + 610 + ], + "spans": [ + { + "bbox": [ + 317, + 601, + 561, + 610 + ], + "type": "text", + "content": "Wild [Pietroni et al. 2021] generate some misaligned quadrilateral el-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 613, + 560, + 621 + ], + "spans": [ + { + "bbox": [ + 317, + 613, + 560, + 621 + ], + "type": "text", + "content": "ements, as seen in the highlighted windows. In contrast, our method", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 624, + 560, + 632 + ], + "spans": [ + { + "bbox": [ + 317, + 624, + 560, + 632 + ], + "type": "text", + "content": "yields a better quadrilateral mesh. Tab. 2 shows the quantitative", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 635, + 520, + 643 + ], + "spans": [ + { + "bbox": [ + 317, + 635, + 520, + 643 + ], + "type": "text", + "content": "comparison of our method against the four approaches.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 314, + 649, + 561, + 694 + ], + "type": "text", + "angle": 0, + "index": 20, + "lines": [ + { + "bbox": [ + 327, + 651, + 560, + 660 + ], + "spans": [ + { + "bbox": [ + 327, + 651, + 560, + 660 + ], + "type": "text", + "content": "Thingi10K Dataset. 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Publication date: May 2025.", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8, + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 562, + 182 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 562, + 182 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 71, + 562, + 182 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 562, + 182 + ], + "type": "image", + "image_path": "d3234236f683909e2ffd9df3f83a583e3333e2acd52920c683db8773aa05bf28.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 80, + 183, + 528, + 194 + ], + "type": "image_caption", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 83, + 185, + 527, + 194 + ], + "spans": [ + { + "bbox": [ + 83, + 185, + 527, + 194 + ], + "type": "text", + "content": "Fig. 11. Quad meshes generated by NeurCross and four other methods on the table model in the ShapeNet dataset [Chang et al. 2015].", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 2, + "sub_images": [ + { + "type": "image", + "bbox": [ + 0.0, + 0.0, + 0.203, + 0.82 + ] + }, + { + "type": "image", + "bbox": [ + 0.205, + 0.009, + 0.398, + 0.811 + ] + }, + { + "type": "image", + "bbox": [ + 0.4, + 0.009, + 0.6, + 0.802 + ] + }, + { + "type": "image", + "bbox": [ + 0.604, + 0.009, + 0.799, + 0.802 + ] + }, + { + "type": "image", + "bbox": [ + 0.801, + 0.009, + 0.996, + 0.802 + ] + } + ] + }, + { + "bbox": [ + 48, + 205, + 296, + 376 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 48, + 380, + 294, + 435 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 59, + 382, + 294, + 390 + ], + "spans": [ + { + "bbox": [ + 59, + 382, + 294, + 390 + ], + "type": "text", + "content": "Datasets. We carry out quad mesh generation experiments on two", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 392, + 294, + 402 + ], + "spans": [ + { + "bbox": [ + 50, + 392, + 294, + 402 + ], + "type": "text", + "content": "popular datasets: ShapeNet [Chang et al. 2015] and Thingi10K [Zhou", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 403, + 294, + 413 + ], + "spans": [ + { + "bbox": [ + 50, + 403, + 294, + 413 + ], + "type": "text", + "content": "and Jacobson 2016]. To maintain uniformity in evaluation, all input", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 412, + 294, + 424 + ], + "spans": [ + { + "bbox": [ + 51, + 415, + 210, + 423 + ], + "type": "text", + "content": "meshes are scaled to fit within the range of", + "score": 1.0 + }, + { + "bbox": [ + 210, + 412, + 253, + 424 + ], + "type": "inline_equation", + "content": "[ - 0 . 5 , 0 . 5 ] ^ { 3 }", + "score": 0.567 + }, + { + "bbox": [ + 253, + 415, + 294, + 424 + ], + "type": "text", + "content": "ensuring a", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 426, + 267, + 434 + ], + "spans": [ + { + "bbox": [ + 50, + 426, + 267, + 434 + ], + "type": "text", + "content": "consistent and fair basis for comparison across all datasets.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 444, + 200, + 455 + ], + "type": "title", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 50, + 445, + 199, + 455 + ], + "spans": [ + { + "bbox": [ + 50, + 445, + 199, + 455 + ], + "type": "text", + "content": "4.1 Comparison on Open Datasets", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 48, + 457, + 295, + 634 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 50, + 459, + 294, + 468 + ], + "spans": [ + { + "bbox": [ + 50, + 459, + 294, + 468 + ], + "type": "text", + "content": "We assess the eficacy of our proposed method, NeurCross, by con", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 470, + 295, + 479 + ], + "spans": [ + { + "bbox": [ + 50, + 470, + 295, + 479 + ], + "type": "text", + "content": "ducting evaluations on two distinct datasets and comparing its per-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 482, + 294, + 491 + ], + "spans": [ + { + "bbox": [ + 50, + 482, + 294, + 491 + ], + "type": "text", + "content": "formance against four contemporary state-of-the-art quadrilateral", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 492, + 294, + 501 + ], + "spans": [ + { + "bbox": [ + 51, + 492, + 294, + 501 + ], + "type": "text", + "content": "mesh generation methods. For the three methods, namely Instant", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 503, + 294, + 512 + ], + "spans": [ + { + "bbox": [ + 50, + 503, + 294, + 512 + ], + "type": "text", + "content": "Meshes (IM) [Jakob et al. 2015], QuadriFlow [Huang et al. 2018], and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 514, + 294, + 523 + ], + "spans": [ + { + "bbox": [ + 51, + 514, + 294, + 523 + ], + "type": "text", + "content": "QuadWild [Pietroni et al. 2021], we employed the open-source imple", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 525, + 294, + 534 + ], + "spans": [ + { + "bbox": [ + 50, + 525, + 294, + 534 + ], + "type": "text", + "content": "mentations that are readily available. It is worth noting that Quad", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 536, + 294, + 544 + ], + "spans": [ + { + "bbox": [ + 51, + 536, + 294, + 544 + ], + "type": "text", + "content": "Wild [Pietroni et al. 2021] is primarily a quadrangulation method", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 548, + 294, + 555 + ], + "spans": [ + { + "bbox": [ + 50, + 548, + 294, + 555 + ], + "type": "text", + "content": "rather than a cross field generation approach. The Mixed-Integer", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 558, + 294, + 567 + ], + "spans": [ + { + "bbox": [ + 51, + 558, + 294, + 567 + ], + "type": "text", + "content": "Quadrangulation (MIQ) method [Bommes et al. 2009] does not re", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 569, + 294, + 578 + ], + "spans": [ + { + "bbox": [ + 50, + 569, + 294, + 578 + ], + "type": "text", + "content": "lease its source code; therefore, we use the implementation provided", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 580, + 295, + 589 + ], + "spans": [ + { + "bbox": [ + 51, + 580, + 295, + 589 + ], + "type": "text", + "content": "by libigl [Jacobson et al. 2017]. However, the available implementa-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 591, + 294, + 600 + ], + "spans": [ + { + "bbox": [ + 51, + 591, + 294, + 600 + ], + "type": "text", + "content": "tion does not support the feature alignment constraint. For a fair", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 601, + 294, + 610 + ], + "spans": [ + { + "bbox": [ + 50, + 601, + 294, + 610 + ], + "type": "text", + "content": "comparison with MIQ, we employ the same parameterization and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 613, + 294, + 622 + ], + "spans": [ + { + "bbox": [ + 51, + 613, + 294, + 622 + ], + "type": "text", + "content": "extraction techniques, namely global-seamless parameterization", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 624, + 159, + 632 + ], + "spans": [ + { + "bbox": [ + 51, + 624, + 159, + 632 + ], + "type": "text", + "content": "and libQEx [Ebke et al. 2013].", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 639, + 296, + 694 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 60, + 641, + 294, + 649 + ], + "spans": [ + { + "bbox": [ + 60, + 641, + 294, + 649 + ], + "type": "text", + "content": "ShapeNet Dataset. The ShapeNet dataset [Chang et al. 2015] con", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 651, + 294, + 660 + ], + "spans": [ + { + "bbox": [ + 51, + 651, + 294, + 660 + ], + "type": "text", + "content": "sists of a diverse range of human-made models. As the global", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 662, + 294, + 671 + ], + "spans": [ + { + "bbox": [ + 51, + 662, + 294, + 671 + ], + "type": "text", + "content": "seamless parametrization from libigl [Jacobson et al. 2017] cannot", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 673, + 294, + 682 + ], + "spans": [ + { + "bbox": [ + 50, + 673, + 294, + 682 + ], + "type": "text", + "content": "handle non-manifold meshes, we use manifold ShapeNet meshes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 684, + 294, + 693 + ], + "spans": [ + { + "bbox": [ + 50, + 684, + 294, + 693 + ], + "type": "text", + "content": "repaired with DualOctreeGNN [Wang et al. 2022a]. We apply our", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "table", + "bbox": [ + 319, + 268, + 556, + 338 + ], + "blocks": [ + { + "bbox": [ + 314, + 206, + 561, + 257 + ], + "type": "table_caption", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 317, + 209, + 561, + 216 + ], + "spans": [ + { + "bbox": [ + 317, + 209, + 561, + 216 + ], + "type": "text", + "content": "Table 2. Quantitative comparison on the ShapeNet dataset [Chang et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 218, + 560, + 226 + ], + "spans": [ + { + "bbox": [ + 317, + 218, + 560, + 226 + ], + "type": "text", + "content": "2015]. Within each column, the best scores are emphasized with bold and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 228, + 560, + 236 + ], + "spans": [ + { + "bbox": [ + 317, + 228, + 560, + 236 + ], + "type": "text", + "content": "underlining (best), whereas the second-best scores are highlighted in bold", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 238, + 560, + 246 + ], + "spans": [ + { + "bbox": [ + 317, + 238, + 560, + 246 + ], + "type": "text", + "content": "(second best). The quad mesh generated by all the methods comprises an", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 248, + 454, + 256 + ], + "spans": [ + { + "bbox": [ + 317, + 248, + 454, + 256 + ], + "type": "text", + "content": "average of 6,000 vertices and 12,000 faces.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 319, + 268, + 556, + 338 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 268, + 556, + 338 + ], + "spans": [ + { + "bbox": [ + 319, + 268, + 556, + 338 + ], + "type": "table", + "html": "
Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
IM [Jakob et al. 2015]1.5711.78200.528.970.70
QuadriFlow [Huang et al. 2018]2.2813.2491.5850.180.65
QuadWild [Pietroni et al. 2021]1.5211.0593.0410.340.73
MIQ [Bommes et al. 2009]5.2312.89\\underline{82.12}8.250.58
NeurCross (Ours)\\underline{1.48}\\underline{9.85}85.32\\underline{8.03}\\underline{0.78}
", + "image_path": "24c7c2967125183d50cc64176184088cf2ff50f3419dd3e40231b5b82b8bffb8.jpg" + } + ] + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 319, + 409, + 556, + 479 + ], + "blocks": [ + { + "bbox": [ + 314, + 347, + 561, + 398 + ], + "type": "table_caption", + "angle": 0, + "index": 16, + "lines": [ + { + "bbox": [ + 317, + 349, + 560, + 357 + ], + "spans": [ + { + "bbox": [ + 317, + 349, + 560, + 357 + ], + "type": "text", + "content": "Table 3. Quantitative comparison on the Thingi10K dataset [Zhou and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 359, + 560, + 367 + ], + "spans": [ + { + "bbox": [ + 316, + 359, + 560, + 367 + ], + "type": "text", + "content": "Jacobson 2016]. The quad mesh generated by all methods comprises an", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 369, + 560, + 377 + ], + "spans": [ + { + "bbox": [ + 317, + 369, + 560, + 377 + ], + "type": "text", + "content": "average of 10,000 vertices and 20,000 faces. Within each column, the best", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 380, + 561, + 388 + ], + "spans": [ + { + "bbox": [ + 317, + 380, + 561, + 388 + ], + "type": "text", + "content": "scores are emphasized with bold and underlining (best), whereas the second-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 389, + 504, + 396 + ], + "spans": [ + { + "bbox": [ + 317, + 389, + 504, + 396 + ], + "type": "text", + "content": "best scores are simply highlighted in bold (second best).", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 319, + 409, + 556, + 479 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 409, + 556, + 479 + ], + "spans": [ + { + "bbox": [ + 319, + 409, + 556, + 479 + ], + "type": "table", + "html": "
Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
IM [Jakob et al. 2015]1.4510.57397.189.830.75
QuadriFlow [Huang et al. 2018]1.5812.3978.3226.890.72
QuadWild [Pietroni et al. 2021]1.4010.1685.1128.120.77
MIQ [Bommes et al. 2009]1.389.8566.548.570.67
NeurCross (Ours)1.339.6868.968.220.81
", + "image_path": "c3f24835c59260fc54b3ad7d9e67f6ebb1a18570efa296567af9d56d199da364.jpg" + } + ] + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 490, + 561, + 533 + ], + "type": "text", + "angle": 0, + "index": 18, + "lines": [ + { + "bbox": [ + 317, + 491, + 561, + 500 + ], + "spans": [ + { + "bbox": [ + 317, + 491, + 561, + 500 + ], + "type": "text", + "content": "NeurCross to three randomly selected categories—airplane, bench,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 502, + 561, + 511 + ], + "spans": [ + { + "bbox": [ + 317, + 502, + 561, + 511 + ], + "type": "text", + "content": "and cabinet—which together contain 7433 models. For a fair com-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 514, + 560, + 522 + ], + "spans": [ + { + "bbox": [ + 316, + 514, + 560, + 522 + ], + "type": "text", + "content": "parison, all generated quad meshes are standardized to contain an", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 525, + 470, + 533 + ], + "spans": [ + { + "bbox": [ + 317, + 525, + 470, + 533 + ], + "type": "text", + "content": "average of 6,000 vertices and 12,000 faces.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 313, + 534, + 561, + 644 + ], + "type": "text", + "angle": 0, + "index": 19, + "lines": [ + { + "bbox": [ + 325, + 536, + 561, + 544 + ], + "spans": [ + { + "bbox": [ + 325, + 536, + 561, + 544 + ], + "type": "text", + "content": "In Fig. 11, we display the quad meshes generated by our Neur-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 547, + 560, + 555 + ], + "spans": [ + { + "bbox": [ + 317, + 547, + 560, + 555 + ], + "type": "text", + "content": "Cross alongside four other methods. For this example, although", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 558, + 560, + 566 + ], + "spans": [ + { + "bbox": [ + 317, + 558, + 560, + 566 + ], + "type": "text", + "content": "IM [Jakob et al. 2015] produces a regular quadrilateral mesh, the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 569, + 560, + 577 + ], + "spans": [ + { + "bbox": [ + 317, + 569, + 560, + 577 + ], + "type": "text", + "content": "outcome includes some triangular elements. More comparisons", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 579, + 561, + 588 + ], + "spans": [ + { + "bbox": [ + 317, + 579, + 561, + 588 + ], + "type": "text", + "content": "between IM and our method will be provided in Sec. 4.2. Quadri-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 590, + 561, + 599 + ], + "spans": [ + { + "bbox": [ + 317, + 590, + 561, + 599 + ], + "type": "text", + "content": "Flow [Huang et al. 2018], MIQ [Bommes et al. 2009], and Quad-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 601, + 561, + 610 + ], + "spans": [ + { + "bbox": [ + 317, + 601, + 561, + 610 + ], + "type": "text", + "content": "Wild [Pietroni et al. 2021] generate some misaligned quadrilateral el-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 613, + 560, + 621 + ], + "spans": [ + { + "bbox": [ + 317, + 613, + 560, + 621 + ], + "type": "text", + "content": "ements, as seen in the highlighted windows. In contrast, our method", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 624, + 560, + 632 + ], + "spans": [ + { + "bbox": [ + 317, + 624, + 560, + 632 + ], + "type": "text", + "content": "yields a better quadrilateral mesh. Tab. 2 shows the quantitative", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 635, + 520, + 643 + ], + "spans": [ + { + "bbox": [ + 317, + 635, + 520, + 643 + ], + "type": "text", + "content": "comparison of our method against the four approaches.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 314, + 649, + 561, + 694 + ], + "type": "text", + "angle": 0, + "index": 20, + "lines": [ + { + "bbox": [ + 327, + 651, + 560, + 660 + ], + "spans": [ + { + "bbox": [ + 327, + 651, + 560, + 660 + ], + "type": "text", + "content": "Thingi10K Dataset. The Thingi10K dataset [Zhou and Jacobson", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 662, + 561, + 670 + ], + "spans": [ + { + "bbox": [ + 317, + 662, + 561, + 670 + ], + "type": "text", + "content": "2016] features a variety of shapes with intricate geometric details.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 673, + 559, + 681 + ], + "spans": [ + { + "bbox": [ + 317, + 673, + 559, + 681 + ], + "type": "text", + "content": "For our analysis based on Thingi10K, we tested 1,000 randomly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 685, + 559, + 693 + ], + "spans": [ + { + "bbox": [ + 317, + 685, + 559, + 693 + ], + "type": "text", + "content": "selected triangle meshes from the dataset, which were also used as", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 530, + 294, + 539 + ], + "spans": [ + { + "bbox": [ + 51, + 530, + 294, + 539 + ], + "type": "text", + "content": "inputs for all comparative methods. 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Comparison with five state-of-the-art methods using data provided", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 475, + 151, + 483 + ], + "spans": [ + { + "bbox": [ + 51, + 475, + 151, + 483 + ], + "type": "text", + "content": "in IGM [Bommes et al. 2013a].", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 19, + "sub_type": "natural_image" + }, + { + "bbox": [ + 48, + 529, + 295, + 562 + ], + "type": "text", + "angle": 0, + "index": 22, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 48, + 563, + 295, + 694 + ], + "type": "text", + "angle": 0, + "index": 23, + "lines": [ + { + "bbox": [ + 59, + 563, + 294, + 572 + ], + "spans": [ + { + "bbox": [ + 59, + 563, + 294, + 572 + ], + "type": "text", + "content": "Quantitative comparison statistics are presented in Tab. 3. 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Quadwild [Pietroni et al. 2021] requires", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 641, + 294, + 649 + ], + "spans": [ + { + "bbox": [ + 51, + 641, + 294, + 649 + ], + "type": "text", + "content": "smoothing of the generated quad mesh, which compromises geo", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 651, + 294, + 660 + ], + "spans": [ + { + "bbox": [ + 50, + 651, + 294, + 660 + ], + "type": "text", + "content": "metric details and increases the Chamfer Distance (CD). 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Comparison of quad meshes generated by Power Fields [Knöppel", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 198, + 258, + 206 + ], + "spans": [ + { + "bbox": [ + 51, + 198, + 258, + 206 + ], + "type": "text", + "content": "et al. 2013], PolyVectors [Diamanti et al. 2014], and NeurCross.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 2, + "sub_type": "text_image" + }, + { + "type": "image", + "bbox": [ + 55, + 209, + 289, + 350 + ], + "blocks": [ + { + "bbox": [ + 55, + 209, + 289, + 350 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 209, + 289, + 350 + ], + "spans": [ + { + "bbox": [ + 55, + 209, + 289, + 350 + ], + "type": "image", + "content": "3D wireframe models of mechanical components with grid patterns, comparing IM and NeurCross (Ours) methods (no text or symbols on models)", + "image_path": "d50c48406bee2d709601f7f465d5f6fa5f4213fde40647fff6c37e264cb82ed2.jpg" + } + ] + } + ], + "index": 4 + } + ], + "index": 4, + "sub_type": "natural_image" + }, + { + "type": "image", + "bbox": [ + 55, + 395, + 287, + 531 + ], + "blocks": [ + { + "bbox": [ + 48, + 353, + 296, + 392 + ], + "type": "image_caption", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 51, + 354, + 293, + 361 + ], + "spans": [ + { + "bbox": [ + 51, + 354, + 293, + 361 + ], + "type": "text", + "content": "Fig. 16. Comparison with IM. Here, the same approach—applying globa", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 364, + 294, + 372 + ], + "spans": [ + { + "bbox": [ + 50, + 364, + 294, + 372 + ], + "type": "text", + "content": "seamless parameterization [Jacobson et al. 2017] and libQEx [Ebke et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 374, + 294, + 382 + ], + "spans": [ + { + "bbox": [ + 50, + 374, + 294, + 382 + ], + "type": "text", + "content": "2013]— is used to extract quadrilateral meshes from the respective cross", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 384, + 155, + 392 + ], + "spans": [ + { + "bbox": [ + 51, + 384, + 155, + 392 + ], + "type": "text", + "content": "fields of IM and our NeurCross.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 55, + 395, + 287, + 531 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 395, + 287, + 531 + ], + "spans": [ + { + "bbox": [ + 55, + 395, + 287, + 531 + ], + "type": "image", + "content": "Quad Remesher\nNeurCross (Ours)", + "image_path": "126bc8f58e5f3485846f850a50b2649ddfb2993725588b3f92a55d5c9b04b7bd.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 536, + 295, + 556 + ], + "type": "image_caption", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 50, + 536, + 294, + 546 + ], + "spans": [ + { + "bbox": [ + 50, + 536, + 294, + 546 + ], + "type": "text", + "content": "Fig. 17. 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Owing to a lack of required data, our comparison is limited", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 613, + 235, + 621 + ], + "spans": [ + { + "bbox": [ + 51, + 613, + 235, + 621 + ], + "type": "text", + "content": "to the model presented in their paper (see Fig. 14).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 628, + 296, + 694 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 60, + 629, + 295, + 638 + ], + "spans": [ + { + "bbox": [ + 60, + 629, + 295, + 638 + ], + "type": "text", + "content": "Comparison with PowerFields andPolyVectors. Power Fields [Knöp-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 640, + 294, + 649 + ], + "spans": [ + { + "bbox": [ + 50, + 640, + 294, + 649 + ], + "type": "text", + "content": "pel et al. 2013] eficiently constructs smooth n-direction fields on", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 651, + 294, + 660 + ], + "spans": [ + { + "bbox": [ + 51, + 651, + 294, + 660 + ], + "type": "text", + "content": "surfaces by solving a sparse eigenvalue problem, ensuring global", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 662, + 294, + 671 + ], + "spans": [ + { + "bbox": [ + 51, + 662, + 294, + 671 + ], + "type": "text", + "content": "optimality and high-quality results. PolyVectors [Diamanti et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 673, + 295, + 682 + ], + "spans": [ + { + "bbox": [ + 50, + 673, + 295, + 682 + ], + "type": "text", + "content": "2014] extends N-RoSy fields to N-PolyVector fields by relaxing or-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 685, + 294, + 693 + ], + "spans": [ + { + "bbox": [ + 50, + 685, + 294, + 693 + ], + "type": "text", + "content": "thogonality and symmetry constraints, enabling their computation", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "chart", + "bbox": [ + 329, + 75, + 555, + 265 + ], + "blocks": [ + { + "bbox": [ + 329, + 75, + 555, + 265 + ], + "type": "chart_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 75, + 555, + 265 + ], + "spans": [ + { + "bbox": [ + 329, + 75, + 555, + 265 + ], + "type": "chart", + "content": "| Method | Description |\n| --- | --- |\n| Input | White 3D model with a curved base structure. |\n| IM | Red 3D model with a curved base structure. |\n| QuadriFlow | Blue 3D model with a curved base structure. |\n| QuadWild | Red 3D model with a curved base structure. |\n| MIQ | Blue 3D model with a curved base structure. |\n| NeurCross (Ours) | Blue 3D model with a curved base structure. |", + "image_path": "c200ed43f6ebfd0324524a22617394ea94113b8b0a6584c9d0aa81ee90ce1d51.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 273, + 561, + 312 + ], + "type": "chart_caption", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 317, + 274, + 560, + 281 + ], + "spans": [ + { + "bbox": [ + 317, + 274, + 560, + 281 + ], + "type": "text", + "content": "Fig. 18. Approximation accuracy. Here we show the approximation errors", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 284, + 560, + 292 + ], + "spans": [ + { + "bbox": [ + 317, + 284, + 560, + 292 + ], + "type": "text", + "content": "between the input surface and the final quad meshes generated by diferent", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 293, + 560, + 301 + ], + "spans": [ + { + "bbox": [ + 317, + 293, + 560, + 301 + ], + "type": "text", + "content": "methods. The error is measured from each sampled point on the quad mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 304, + 383, + 312 + ], + "spans": [ + { + "bbox": [ + 317, + 304, + 383, + 312 + ], + "type": "text", + "content": "to the input surface.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 10, + "sub_type": "surface_3d" + }, + { + "bbox": [ + 314, + 316, + 561, + 392 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 317, + 317, + 561, + 325 + ], + "spans": [ + { + "bbox": [ + 317, + 317, + 561, + 325 + ], + "type": "text", + "content": "via a sparse linear system without integer variables. Both meth-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 328, + 560, + 336 + ], + "spans": [ + { + "bbox": [ + 317, + 328, + 560, + 336 + ], + "type": "text", + "content": "ods focus on eficient computation of directional fields, with Power", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 339, + 561, + 347 + ], + "spans": [ + { + "bbox": [ + 317, + 339, + 561, + 347 + ], + "type": "text", + "content": "Fields [Knöppel et al. 2013] optimizing smoothness and PolyVec-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 350, + 561, + 358 + ], + "spans": [ + { + "bbox": [ + 317, + 350, + 561, + 358 + ], + "type": "text", + "content": "tors [Diamanti et al. 2014] generalizing traditional field represen-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 361, + 559, + 369 + ], + "spans": [ + { + "bbox": [ + 317, + 361, + 559, + 369 + ], + "type": "text", + "content": "tations. Fig. 15 compares the quadrilateral meshes generated by", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 372, + 560, + 380 + ], + "spans": [ + { + "bbox": [ + 317, + 372, + 560, + 380 + ], + "type": "text", + "content": "our NeurCross and these methods. NeurCross not only aligns with", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 383, + 534, + 392 + ], + "spans": [ + { + "bbox": [ + 317, + 383, + 534, + 392 + ], + "type": "text", + "content": "principal curvatures but also preserves overall smoothness.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 314, + 397, + 561, + 486 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 327, + 399, + 559, + 407 + ], + "spans": [ + { + "bbox": [ + 327, + 399, + 559, + 407 + ], + "type": "text", + "content": "Comparison with IM. IM [Jakob et al. 2015] is an efective method", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 410, + 560, + 419 + ], + "spans": [ + { + "bbox": [ + 317, + 410, + 560, + 419 + ], + "type": "text", + "content": "for generating quad meshes. To facilitate a fair comparison between", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 422, + 561, + 430 + ], + "spans": [ + { + "bbox": [ + 317, + 422, + 561, + 430 + ], + "type": "text", + "content": "IM and our approach, we use the same global seamless parame-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 432, + 559, + 441 + ], + "spans": [ + { + "bbox": [ + 317, + 432, + 559, + 441 + ], + "type": "text", + "content": "terization and extraction technique (libQEx [Ebke et al. 2013]) to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 443, + 560, + 452 + ], + "spans": [ + { + "bbox": [ + 317, + 443, + 560, + 452 + ], + "type": "text", + "content": "extract the quad mesh. As shown in Fig. 16, our method produces", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 454, + 560, + 463 + ], + "spans": [ + { + "bbox": [ + 317, + 454, + 560, + 463 + ], + "type": "text", + "content": "fewer singularities than IM. Additionally, our method outperforms", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 465, + 560, + 474 + ], + "spans": [ + { + "bbox": [ + 317, + 465, + 560, + 474 + ], + "type": "text", + "content": "IM [Jakob et al. 2015] in terms of principal direction alignment and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 476, + 520, + 485 + ], + "spans": [ + { + "bbox": [ + 317, + 476, + 520, + 485 + ], + "type": "text", + "content": "structural integrity, as illustrated in the close-up views.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 314, + 491, + 561, + 579 + ], + "type": "text", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 326, + 492, + 560, + 502 + ], + "spans": [ + { + "bbox": [ + 326, + 492, + 560, + 502 + ], + "type": "text", + "content": "Comparison with Quad Remesher. 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How-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 548, + 559, + 556 + ], + "spans": [ + { + "bbox": [ + 317, + 548, + 559, + 556 + ], + "type": "text", + "content": "ever, its performance depends heavily on the quality of the input", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 558, + 560, + 567 + ], + "spans": [ + { + "bbox": [ + 317, + 558, + 560, + 567 + ], + "type": "text", + "content": "mesh, producing low-quality quadrilateral meshes when the input", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 570, + 474, + 578 + ], + "spans": [ + { + "bbox": [ + 317, + 570, + 474, + 578 + ], + "type": "text", + "content": "polygonal mesh is suboptimal (see Fig. 17).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 314, + 584, + 561, + 671 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 326, + 586, + 559, + 594 + ], + "spans": [ + { + "bbox": [ + 326, + 586, + 559, + 594 + ], + "type": "text", + "content": "Fidelity. In practical applications, when converting a shape from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 597, + 559, + 605 + ], + "spans": [ + { + "bbox": [ + 317, + 597, + 559, + 605 + ], + "type": "text", + "content": "a triangular mesh to a quadrilateral mesh representation, the goals", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 608, + 559, + 616 + ], + "spans": [ + { + "bbox": [ + 317, + 608, + 559, + 616 + ], + "type": "text", + "content": "extend beyond minimizing area distortion, angle distortion, and the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 619, + 559, + 627 + ], + "spans": [ + { + "bbox": [ + 317, + 619, + 559, + 627 + ], + "type": "text", + "content": "number of singular points; maintaining fidelity to the original shape", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 629, + 559, + 638 + ], + "spans": [ + { + "bbox": [ + 317, + 629, + 559, + 638 + ], + "type": "text", + "content": "is also crucial. 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The", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 288, + 54, + 538, + 63 + ], + "type": "header", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 290, + 57, + 536, + 62 + ], + "spans": [ + { + "bbox": [ + 290, + 57, + 536, + 62 + ], + "type": "text", + "content": "NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 542, + 55, + 560, + 62 + ], + "type": "page_number", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 543, + 54, + 561, + 64 + ], + "spans": [ + { + "bbox": [ + 543, + 54, + 561, + 64 + ], + "type": "text", + "content": "• 11", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 414, + 708, + 560, + 716 + ], + "type": "footer", + "angle": 0, + "index": 17, + "lines": [ + { + "bbox": [ + 414, + 709, + 559, + 716 + ], + "spans": [ + { + "bbox": [ + 414, + 709, + 559, + 716 + ], + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10, + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 76, + 289, + 182 + ], + "blocks": [ + { + "bbox": [ + 56, + 76, + 289, + 182 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 76, + 289, + 182 + ], + "spans": [ + { + "bbox": [ + 56, + 76, + 289, + 182 + ], + "type": "image", + "content": "Power Fields\nPolyVectors\nNeurCross (Ours)", + "image_path": "9a2a08412c7f36afe57072ddff0fe3f9e94217d7e42405da1bd0a41660d5d2e9.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 186, + 295, + 207 + ], + "type": "image_caption", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 51, + 189, + 294, + 197 + ], + "spans": [ + { + "bbox": [ + 51, + 189, + 294, + 197 + ], + "type": "text", + "content": "Fig. 15. Comparison of quad meshes generated by Power Fields [Knöppel", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 198, + 258, + 206 + ], + "spans": [ + { + "bbox": [ + 51, + 198, + 258, + 206 + ], + "type": "text", + "content": "et al. 2013], PolyVectors [Diamanti et al. 2014], and NeurCross.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 2, + "sub_type": "text_image" + }, + { + "type": "image", + "bbox": [ + 55, + 209, + 289, + 350 + ], + "blocks": [ + { + "bbox": [ + 55, + 209, + 289, + 350 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 209, + 289, + 350 + ], + "spans": [ + { + "bbox": [ + 55, + 209, + 289, + 350 + ], + "type": "image", + "content": "3D wireframe models of mechanical components with grid patterns, comparing IM and NeurCross (Ours) methods (no text or symbols on models)", + "image_path": "d50c48406bee2d709601f7f465d5f6fa5f4213fde40647fff6c37e264cb82ed2.jpg" + } + ] + } + ], + "index": 4 + } + ], + "index": 4, + "sub_type": "natural_image" + }, + { + "type": "image", + "bbox": [ + 55, + 395, + 287, + 531 + ], + "blocks": [ + { + "bbox": [ + 48, + 353, + 296, + 392 + ], + "type": "image_caption", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 51, + 354, + 293, + 361 + ], + "spans": [ + { + "bbox": [ + 51, + 354, + 293, + 361 + ], + "type": "text", + "content": "Fig. 16. Comparison with IM. Here, the same approach—applying globa", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 364, + 294, + 372 + ], + "spans": [ + { + "bbox": [ + 50, + 364, + 294, + 372 + ], + "type": "text", + "content": "seamless parameterization [Jacobson et al. 2017] and libQEx [Ebke et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 374, + 294, + 382 + ], + "spans": [ + { + "bbox": [ + 50, + 374, + 294, + 382 + ], + "type": "text", + "content": "2013]— is used to extract quadrilateral meshes from the respective cross", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 384, + 155, + 392 + ], + "spans": [ + { + "bbox": [ + 51, + 384, + 155, + 392 + ], + "type": "text", + "content": "fields of IM and our NeurCross.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 55, + 395, + 287, + 531 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 395, + 287, + 531 + ], + "spans": [ + { + "bbox": [ + 55, + 395, + 287, + 531 + ], + "type": "image", + "content": "Quad Remesher\nNeurCross (Ours)", + "image_path": "126bc8f58e5f3485846f850a50b2649ddfb2993725588b3f92a55d5c9b04b7bd.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 536, + 295, + 556 + ], + "type": "image_caption", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 50, + 536, + 294, + 546 + ], + "spans": [ + { + "bbox": [ + 50, + 536, + 294, + 546 + ], + "type": "text", + "content": "Fig. 17. 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Owing to a lack of required data, our comparison is limited", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 613, + 235, + 621 + ], + "spans": [ + { + "bbox": [ + 51, + 613, + 235, + 621 + ], + "type": "text", + "content": "to the model presented in their paper (see Fig. 14).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 628, + 296, + 694 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 60, + 629, + 295, + 638 + ], + "spans": [ + { + "bbox": [ + 60, + 629, + 295, + 638 + ], + "type": "text", + "content": "Comparison with PowerFields andPolyVectors. 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Both meth-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 328, + 560, + 336 + ], + "spans": [ + { + "bbox": [ + 317, + 328, + 560, + 336 + ], + "type": "text", + "content": "ods focus on eficient computation of directional fields, with Power", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 339, + 561, + 347 + ], + "spans": [ + { + "bbox": [ + 317, + 339, + 561, + 347 + ], + "type": "text", + "content": "Fields [Knöppel et al. 2013] optimizing smoothness and PolyVec-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 350, + 561, + 358 + ], + "spans": [ + { + "bbox": [ + 317, + 350, + 561, + 358 + ], + "type": "text", + "content": "tors [Diamanti et al. 2014] generalizing traditional field represen-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 361, + 559, + 369 + ], + "spans": [ + { + "bbox": [ + 317, + 361, + 559, + 369 + ], + "type": "text", + "content": "tations. Fig. 15 compares the quadrilateral meshes generated by", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 372, + 560, + 380 + ], + "spans": [ + { + "bbox": [ + 317, + 372, + 560, + 380 + ], + "type": "text", + "content": "our NeurCross and these methods. NeurCross not only aligns with", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 383, + 534, + 392 + ], + "spans": [ + { + "bbox": [ + 317, + 383, + 534, + 392 + ], + "type": "text", + "content": "principal curvatures but also preserves overall smoothness.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "chart", + "bbox": [ + 329, + 75, + 555, + 265 + ], + "blocks": [ + { + "bbox": [ + 329, + 75, + 555, + 265 + ], + "type": "chart_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 75, + 555, + 265 + ], + "spans": [ + { + "bbox": [ + 329, + 75, + 555, + 265 + ], + "type": "chart", + "content": "| Method | Description |\n| --- | --- |\n| Input | White 3D model with a curved base structure. |\n| IM | Red 3D model with a curved base structure. |\n| QuadriFlow | Blue 3D model with a curved base structure. |\n| QuadWild | Red 3D model with a curved base structure. |\n| MIQ | Blue 3D model with a curved base structure. |\n| NeurCross (Ours) | Blue 3D model with a curved base structure. |", + "image_path": "c200ed43f6ebfd0324524a22617394ea94113b8b0a6584c9d0aa81ee90ce1d51.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 273, + 561, + 312 + ], + "type": "chart_caption", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 317, + 274, + 560, + 281 + ], + "spans": [ + { + "bbox": [ + 317, + 274, + 560, + 281 + ], + "type": "text", + "content": "Fig. 18. Approximation accuracy. Here we show the approximation errors", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 284, + 560, + 292 + ], + "spans": [ + { + "bbox": [ + 317, + 284, + 560, + 292 + ], + "type": "text", + "content": "between the input surface and the final quad meshes generated by diferent", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 293, + 560, + 301 + ], + "spans": [ + { + "bbox": [ + 317, + 293, + 560, + 301 + ], + "type": "text", + "content": "methods. The error is measured from each sampled point on the quad mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 304, + 383, + 312 + ], + "spans": [ + { + "bbox": [ + 317, + 304, + 383, + 312 + ], + "type": "text", + "content": "to the input surface.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 10, + "sub_type": "surface_3d" + }, + { + "bbox": [ + 314, + 316, + 561, + 392 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 314, + 397, + 561, + 486 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 327, + 399, + 559, + 407 + ], + "spans": [ + { + "bbox": [ + 327, + 399, + 559, + 407 + ], + "type": "text", + "content": "Comparison with IM. IM [Jakob et al. 2015] is an efective method", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 410, + 560, + 419 + ], + "spans": [ + { + "bbox": [ + 317, + 410, + 560, + 419 + ], + "type": "text", + "content": "for generating quad meshes. To facilitate a fair comparison between", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 422, + 561, + 430 + ], + "spans": [ + { + "bbox": [ + 317, + 422, + 561, + 430 + ], + "type": "text", + "content": "IM and our approach, we use the same global seamless parame-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 432, + 559, + 441 + ], + "spans": [ + { + "bbox": [ + 317, + 432, + 559, + 441 + ], + "type": "text", + "content": "terization and extraction technique (libQEx [Ebke et al. 2013]) to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 443, + 560, + 452 + ], + "spans": [ + { + "bbox": [ + 317, + 443, + 560, + 452 + ], + "type": "text", + "content": "extract the quad mesh. As shown in Fig. 16, our method produces", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 454, + 560, + 463 + ], + "spans": [ + { + "bbox": [ + 317, + 454, + 560, + 463 + ], + "type": "text", + "content": "fewer singularities than IM. Additionally, our method outperforms", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 465, + 560, + 474 + ], + "spans": [ + { + "bbox": [ + 317, + 465, + 560, + 474 + ], + "type": "text", + "content": "IM [Jakob et al. 2015] in terms of principal direction alignment and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 476, + 520, + 485 + ], + "spans": [ + { + "bbox": [ + 317, + 476, + 520, + 485 + ], + "type": "text", + "content": "structural integrity, as illustrated in the close-up views.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 314, + 491, + 561, + 579 + ], + "type": "text", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 326, + 492, + 560, + 502 + ], + "spans": [ + { + "bbox": [ + 326, + 492, + 560, + 502 + ], + "type": "text", + "content": "Comparison with Quad Remesher. Quad Remesher [Remesher", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 503, + 560, + 512 + ], + "spans": [ + { + "bbox": [ + 317, + 503, + 560, + 512 + ], + "type": "text", + "content": "2019] excels at generating quadrilateral meshes and is available", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 514, + 561, + 523 + ], + "spans": [ + { + "bbox": [ + 316, + 514, + 561, + 523 + ], + "type": "text", + "content": "as a plugin for software like Blender. It is stable, eficient, and ef-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 315, + 525, + 560, + 534 + ], + "spans": [ + { + "bbox": [ + 315, + 525, + 560, + 534 + ], + "type": "text", + "content": "fective at preserving model features while maintaining topological", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 536, + 561, + 546 + ], + "spans": [ + { + "bbox": [ + 317, + 536, + 561, + 546 + ], + "type": "text", + "content": "uniformity, with our method achieving comparable results. How-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 548, + 559, + 556 + ], + "spans": [ + { + "bbox": [ + 317, + 548, + 559, + 556 + ], + "type": "text", + "content": "ever, its performance depends heavily on the quality of the input", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 558, + 560, + 567 + ], + "spans": [ + { + "bbox": [ + 317, + 558, + 560, + 567 + ], + "type": "text", + "content": "mesh, producing low-quality quadrilateral meshes when the input", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 570, + 474, + 578 + ], + "spans": [ + { + "bbox": [ + 317, + 570, + 474, + 578 + ], + "type": "text", + "content": "polygonal mesh is suboptimal (see Fig. 17).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 314, + 584, + 561, + 671 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 326, + 586, + 559, + 594 + ], + "spans": [ + { + "bbox": [ + 326, + 586, + 559, + 594 + ], + "type": "text", + "content": "Fidelity. 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The", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 457, + 294, + 466 + ], + "spans": [ + { + "bbox": [ + 51, + 457, + 294, + 466 + ], + "type": "text", + "content": "quad meshes generated by our NeurCross and MIQ [Bommes et al.", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 51, + 468, + 293, + 477 + ], + "spans": [ + { + "bbox": [ + 51, + 468, + 293, + 477 + ], + "type": "text", + "content": "2009] faithfully represent the original input. 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The top row shows the cross field generated by our method and four other methods on a noisy input mesh. The botom row shows the resulting quad", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 225, + 427, + 233 + ], + "spans": [ + { + "bbox": [ + 50, + 225, + 427, + 233 + ], + "type": "text", + "content": "meshes produced by each approach. Note that MIQ fails to produce a valid result for this input surface with noise.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 52, + 239, + 556, + 415 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 239, + 556, + 415 + ], + "spans": [ + { + "bbox": [ + 52, + 239, + 556, + 415 + ], + "type": "image", + "image_path": "16dee25d509d1d8d63202d824b6568049f1f82a746504f2fd3fac5ff3651bf64.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 48, + 418, + 560, + 439 + ], + "type": "image_caption", + "angle": 0, + "index": 34, + "lines": [ + { + "bbox": [ + 50, + 419, + 559, + 427 + ], + "spans": [ + { + "bbox": [ + 50, + 419, + 559, + 427 + ], + "type": "text", + "content": "Fig. 20. Quad meshes generated by all the methods on two models from ShapeNet [Chang et al. 2015] (the airplane model) and Thingi10K [Zhou and Jacobson", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 430, + 545, + 438 + ], + "spans": [ + { + "bbox": [ + 50, + 430, + 545, + 438 + ], + "type": "text", + "content": "2016] (the grayloc model). We also show the locations of singular points, where “# of Sings” denotes the number of singular points on each quad mesh.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 23, + "sub_images": [ + { + "type": "image", + "bbox": [ + 0.0, + 0.0, + 0.198, + 0.381 + ] + }, + { + "type": "image", + "bbox": [ + 0.204, + 0.0, + 0.399, + 0.381 + ] + }, + { + "type": "image", + "bbox": [ + 0.405, + 0.006, + 0.597, + 0.381 + ] + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.006, + 0.796, + 0.381 + ] + }, + { + "type": "image", + "bbox": [ + 0.802, + 0.006, + 0.996, + 0.381 + ] + }, + { + "type": "image", + "bbox": [ + 0.014, + 0.511, + 0.192, + 0.881 + ] + }, + { + "type": "image", + "bbox": [ + 0.216, + 0.517, + 0.393, + 0.881 + ] + }, + { + "type": "image", + "bbox": [ + 0.419, + 0.517, + 0.593, + 0.881 + ] + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.517, + 0.796, + 0.881 + ] + }, + { + "type": "image", + "bbox": [ + 0.819, + 0.523, + 0.994, + 0.881 + ] + } + ] + }, + { + "bbox": [ + 48, + 455, + 296, + 510 + ], + "type": "text", + "angle": 0, + "index": 35, + "lines": [ + { + "bbox": [ + 51, + 457, + 294, + 466 + ], + "spans": [ + { + "bbox": [ + 51, + 457, + 294, + 466 + ], + "type": "text", + "content": "quad meshes generated by our NeurCross and MIQ [Bommes et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 468, + 293, + 477 + ], + "spans": [ + { + "bbox": [ + 51, + 468, + 293, + 477 + ], + "type": "text", + "content": "2009] faithfully represent the original input. IM [Jakob et al. 2015]", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 479, + 294, + 487 + ], + "spans": [ + { + "bbox": [ + 51, + 479, + 294, + 487 + ], + "type": "text", + "content": "and QuadriFlow [Huang et al. 2018] exhibit minor shape distortions,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 491, + 294, + 499 + ], + "spans": [ + { + "bbox": [ + 50, + 491, + 294, + 499 + ], + "type": "text", + "content": "whereas QuadWild [Pietroni et al. 2021] produces a smoother result,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 501, + 143, + 509 + ], + "spans": [ + { + "bbox": [ + 50, + 501, + 143, + 509 + ], + "type": "text", + "content": "leading to a loss of detail.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 529, + 296, + 627 + ], + "type": "text", + "angle": 0, + "index": 36, + "lines": [ + { + "bbox": [ + 60, + 530, + 294, + 539 + ], + "spans": [ + { + "bbox": [ + 60, + 530, + 294, + 539 + ], + "type": "text", + "content": "Resistance to Noise. As noted in Wang et al. [2023], Wang et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 52, + 542, + 295, + 550 + ], + "spans": [ + { + "bbox": [ + 52, + 542, + 295, + 550 + ], + "type": "text", + "content": "[2024], and Dong et al. [2024], the Hessian matrix possesses in-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 553, + 294, + 561 + ], + "spans": [ + { + "bbox": [ + 51, + 553, + 294, + 561 + ], + "type": "text", + "content": "trinsic smoothing properties. Benefiting from this characteristic,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 564, + 294, + 572 + ], + "spans": [ + { + "bbox": [ + 51, + 564, + 294, + 572 + ], + "type": "text", + "content": "our method demonstrates inherent resistance to noise in cross field", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 574, + 295, + 583 + ], + "spans": [ + { + "bbox": [ + 51, + 574, + 295, + 583 + ], + "type": "text", + "content": "prediction. We used a baseline mesh with 15,000 vertices and in-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 586, + 294, + 594 + ], + "spans": [ + { + "bbox": [ + 51, + 586, + 294, + 594 + ], + "type": "text", + "content": "troduced Gaussian noise (i.e., 2% relative to the normal direction", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 597, + 294, + 605 + ], + "spans": [ + { + "bbox": [ + 51, + 597, + 294, + 605 + ], + "type": "text", + "content": "of each model) to test the noise immunity of our NeurCross. For a", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 608, + 293, + 615 + ], + "spans": [ + { + "bbox": [ + 50, + 608, + 293, + 615 + ], + "type": "text", + "content": "comprehensive comparison, we evaluated the four other methods", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 619, + 172, + 627 + ], + "spans": [ + { + "bbox": [ + 51, + 619, + 172, + 627 + ], + "type": "text", + "content": "under the same noise conditions.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 628, + 296, + 693 + ], + "type": "text", + "angle": 0, + "index": 37, + "lines": [ + { + "bbox": [ + 58, + 629, + 294, + 638 + ], + "spans": [ + { + "bbox": [ + 58, + 629, + 294, + 638 + ], + "type": "text", + "content": "In Fig. 19, we present the results of diferent methods under noisy", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 640, + 294, + 649 + ], + "spans": [ + { + "bbox": [ + 50, + 640, + 294, + 649 + ], + "type": "text", + "content": "input. Notably, our approach optimizes the SDF and the cross field", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 651, + 294, + 660 + ], + "spans": [ + { + "bbox": [ + 51, + 651, + 294, + 660 + ], + "type": "text", + "content": "simultaneously. As a result, during optimization, the underlying SDF", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 662, + 294, + 671 + ], + "spans": [ + { + "bbox": [ + 51, + 662, + 294, + 671 + ], + "type": "text", + "content": "naturally smooths out noise, leading to a more intuitive cross field.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 673, + 294, + 682 + ], + "spans": [ + { + "bbox": [ + 50, + 673, + 294, + 682 + ], + "type": "text", + "content": "In summary, our method demonstrates stronger noise resistance", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 685, + 171, + 693 + ], + "spans": [ + { + "bbox": [ + 51, + 685, + 171, + 693 + ], + "type": "text", + "content": "compared to four other methods.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 313, + 456, + 561, + 586 + ], + "type": "text", + "angle": 0, + "index": 38, + "lines": [ + { + "bbox": [ + 326, + 457, + 560, + 466 + ], + "spans": [ + { + "bbox": [ + 326, + 457, + 560, + 466 + ], + "type": "text", + "content": "Singular Points. It’s well acknowledged that a trade-of must be", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 468, + 561, + 477 + ], + "spans": [ + { + "bbox": [ + 317, + 468, + 561, + 477 + ], + "type": "text", + "content": "achieved between reducing singular points and aligning with prin-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 479, + 560, + 488 + ], + "spans": [ + { + "bbox": [ + 317, + 479, + 560, + 488 + ], + "type": "text", + "content": "cipal directions. Thus, it’s preferable to position singular points in", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 491, + 559, + 498 + ], + "spans": [ + { + "bbox": [ + 317, + 491, + 559, + 498 + ], + "type": "text", + "content": "regions with high curvature variation rather than in flatter areas. As", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 501, + 559, + 510 + ], + "spans": [ + { + "bbox": [ + 317, + 501, + 559, + 510 + ], + "type": "text", + "content": "observed in Tab. 2, Tab. 3, and Fig. 20, our method produces a slightly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 513, + 561, + 521 + ], + "spans": [ + { + "bbox": [ + 317, + 513, + 561, + 521 + ], + "type": "text", + "content": "higher number of singular points compared to MIQ [Bommes et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 523, + 561, + 532 + ], + "spans": [ + { + "bbox": [ + 317, + 523, + 561, + 532 + ], + "type": "text", + "content": "2009]. This occurrence can be attributed to MIQ’s tendency to pro-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 534, + 561, + 542 + ], + "spans": [ + { + "bbox": [ + 317, + 534, + 561, + 542 + ], + "type": "text", + "content": "duce distorted quadrilaterals, which consequently reduces the oc-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 545, + 561, + 554 + ], + "spans": [ + { + "bbox": [ + 317, + 545, + 561, + 554 + ], + "type": "text", + "content": "currence of singular points as well as area and angular distortions.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 556, + 560, + 564 + ], + "spans": [ + { + "bbox": [ + 317, + 556, + 560, + 564 + ], + "type": "text", + "content": "However, MIQ’s quad mesh lacks overall consistency and tends to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 567, + 559, + 575 + ], + "spans": [ + { + "bbox": [ + 317, + 567, + 559, + 575 + ], + "type": "text", + "content": "oversmooth areas with significant changes in the direction of the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 578, + 356, + 586 + ], + "spans": [ + { + "bbox": [ + 317, + 578, + 356, + 586 + ], + "type": "text", + "content": "cross field.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 314, + 587, + 561, + 642 + ], + "type": "text", + "angle": 0, + "index": 39, + "lines": [ + { + "bbox": [ + 324, + 588, + 560, + 598 + ], + "spans": [ + { + "bbox": [ + 324, + 588, + 560, + 598 + ], + "type": "text", + "content": "In Fig. 20, we visualize the locations of singular points in the quad", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 600, + 560, + 609 + ], + "spans": [ + { + "bbox": [ + 317, + 600, + 560, + 609 + ], + "type": "text", + "content": "meshes generated by all methods on two models. The placement", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 611, + 559, + 620 + ], + "spans": [ + { + "bbox": [ + 317, + 611, + 559, + 620 + ], + "type": "text", + "content": "of singular points in the quad mesh generated by our method is", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 621, + 560, + 631 + ], + "spans": [ + { + "bbox": [ + 316, + 621, + 560, + 631 + ], + "type": "text", + "content": "more reasonable, and the resulting quadrilateral mesh exhibits high", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 633, + 389, + 641 + ], + "spans": [ + { + "bbox": [ + 317, + 633, + 389, + 641 + ], + "type": "text", + "content": "overall consistency.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 314, + 661, + 562, + 694 + ], + "type": "text", + "angle": 0, + "index": 40, + "lines": [ + { + "bbox": [ + 326, + 662, + 561, + 671 + ], + "spans": [ + { + "bbox": [ + 326, + 662, + 561, + 671 + ], + "type": "text", + "content": "Geometrically Complex Models. Various complex geometric mod-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 673, + 561, + 681 + ], + "spans": [ + { + "bbox": [ + 317, + 673, + 561, + 681 + ], + "type": "text", + "content": "els, such as triangular meshes with high genus, thin shells, or non-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 684, + 559, + 693 + ], + "spans": [ + { + "bbox": [ + 317, + 684, + 559, + 693 + ], + "type": "text", + "content": "orientable surfaces, are common in many fields. In Fig. 21, we display", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 50, + 55, + 58, + 62 + ], + "type": "page_number", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 51, + 56, + 58, + 63 + ], + "spans": [ + { + "bbox": [ + 51, + 56, + 58, + 63 + ], + "type": "text", + "content": "12", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 64, + 54, + 441, + 64 + ], + "type": "header", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 64, + 54, + 441, + 64 + ], + "spans": [ + { + "bbox": [ + 64, + 54, + 441, + 64 + ], + "type": "text", + "content": "• Qiujie Dong, Huibiao Wen, Rui Xu, Shuangmin Chen, Jiaran Zhou, Shiqing Xin, Changhe Tu, Taku Komura, and Wenping Wang", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 50, + 708, + 196, + 717 + ], + "type": "footer", + "angle": 0, + "index": 41, + "lines": [ + { + "bbox": [ + 51, + 710, + 195, + 716 + ], + "spans": [ + { + "bbox": [ + 51, + 710, + 195, + 716 + ], + "type": "text", + "content": ", Vol. 1, No. 1, Article . Publication date: May 2025.", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11, + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 77, + 167, + 192 + ], + "blocks": [ + { + "bbox": [ + 62, + 77, + 167, + 192 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 77, + 167, + 192 + ], + "spans": [ + { + "bbox": [ + 62, + 77, + 167, + 192 + ], + "type": "image", + "image_path": "9af987df6afa7a322ff8f63778cc4ce9ec84c169acfdbe45be82b0cd71ba9017.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 110, + 198, + 123, + 207 + ], + "type": "image_caption", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 109, + 198, + 124, + 209 + ], + "spans": [ + { + "bbox": [ + 109, + 198, + 124, + 209 + ], + "type": "text", + "content": "IM", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 2, + "sub_images": [ + { + "type": "image", + "bbox": [ + 0.01, + 0.0, + 1.0, + 0.548 + ] + }, + { + "type": "image", + 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The top row shows the cross field generated by our method and four other methods on a noisy input mesh. The botom row shows the resulting quad", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 225, + 427, + 233 + ], + "spans": [ + { + "bbox": [ + 50, + 225, + 427, + 233 + ], + "type": "text", + "content": "meshes produced by each approach. Note that MIQ fails to produce a valid result for this input surface with noise.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 52, + 239, + 556, + 415 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 239, + 556, + 415 + ], + "spans": [ + { + "bbox": [ + 52, + 239, + 556, + 415 + ], + "type": "image", + "image_path": "16dee25d509d1d8d63202d824b6568049f1f82a746504f2fd3fac5ff3651bf64.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 48, + 418, + 560, + 439 + ], + "type": "image_caption", + "angle": 0, + "index": 34, + "lines": [ + { + "bbox": [ + 50, + 419, + 559, + 427 + ], + "spans": [ + { + "bbox": [ + 50, + 419, + 559, + 427 + ], + "type": "text", + "content": "Fig. 20. Quad meshes generated by all the methods on two models from ShapeNet [Chang et al. 2015] (the airplane model) and Thingi10K [Zhou and Jacobson", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 430, + 545, + 438 + ], + "spans": [ + { + "bbox": [ + 50, + 430, + 545, + 438 + ], + "type": "text", + "content": "2016] (the grayloc model). We also show the locations of singular points, where “# of Sings” denotes the number of singular points on each quad mesh.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 23, + "sub_images": [ + { + "type": "image", + "bbox": [ + 0.0, + 0.0, + 0.198, + 0.381 + ] + }, + { + "type": "image", + "bbox": [ + 0.204, + 0.0, + 0.399, + 0.381 + ] + }, + { + "type": "image", + "bbox": [ + 0.405, + 0.006, + 0.597, + 0.381 + ] + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.006, + 0.796, + 0.381 + ] + }, + { + "type": "image", + "bbox": [ + 0.802, + 0.006, + 0.996, + 0.381 + ] + }, + { + "type": "image", + "bbox": [ + 0.014, + 0.511, + 0.192, + 0.881 + ] + }, + { + "type": "image", + "bbox": [ + 0.216, + 0.517, + 0.393, + 0.881 + ] + }, + { + "type": "image", + "bbox": [ + 0.419, + 0.517, + 0.593, + 0.881 + ] + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.517, + 0.796, + 0.881 + ] + }, + { + "type": "image", + "bbox": [ + 0.819, + 0.523, + 0.994, + 0.881 + ] + } + ] + }, + { + "bbox": [ + 48, + 455, + 296, + 510 + ], + "type": "text", + "angle": 0, + "index": 35, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 48, + 529, + 296, + 627 + ], + "type": "text", + "angle": 0, + "index": 36, + "lines": [ + { + "bbox": [ + 60, + 530, + 294, + 539 + ], + "spans": [ + { + "bbox": [ + 60, + 530, + 294, + 539 + ], + "type": "text", + "content": "Resistance to Noise. As noted in Wang et al. [2023], Wang et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 52, + 542, + 295, + 550 + ], + "spans": [ + { + "bbox": [ + 52, + 542, + 295, + 550 + ], + "type": "text", + "content": "[2024], and Dong et al. [2024], the Hessian matrix possesses in-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 553, + 294, + 561 + ], + "spans": [ + { + "bbox": [ + 51, + 553, + 294, + 561 + ], + "type": "text", + "content": "trinsic smoothing properties. Benefiting from this characteristic,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 564, + 294, + 572 + ], + "spans": [ + { + "bbox": [ + 51, + 564, + 294, + 572 + ], + "type": "text", + "content": "our method demonstrates inherent resistance to noise in cross field", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 574, + 295, + 583 + ], + "spans": [ + { + "bbox": [ + 51, + 574, + 295, + 583 + ], + "type": "text", + "content": "prediction. We used a baseline mesh with 15,000 vertices and in-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 586, + 294, + 594 + ], + "spans": [ + { + "bbox": [ + 51, + 586, + 294, + 594 + ], + "type": "text", + "content": "troduced Gaussian noise (i.e., 2% relative to the normal direction", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 597, + 294, + 605 + ], + "spans": [ + { + "bbox": [ + 51, + 597, + 294, + 605 + ], + "type": "text", + "content": "of each model) to test the noise immunity of our NeurCross. For a", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 608, + 293, + 615 + ], + "spans": [ + { + "bbox": [ + 50, + 608, + 293, + 615 + ], + "type": "text", + "content": "comprehensive comparison, we evaluated the four other methods", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 619, + 172, + 627 + ], + "spans": [ + { + "bbox": [ + 51, + 619, + 172, + 627 + ], + "type": "text", + "content": "under the same noise conditions.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 628, + 296, + 693 + ], + "type": "text", + "angle": 0, + "index": 37, + "lines": [ + { + "bbox": [ + 58, + 629, + 294, + 638 + ], + "spans": [ + { + "bbox": [ + 58, + 629, + 294, + 638 + ], + "type": "text", + "content": "In Fig. 19, we present the results of diferent methods under noisy", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 640, + 294, + 649 + ], + "spans": [ + { + "bbox": [ + 50, + 640, + 294, + 649 + ], + "type": "text", + "content": "input. Notably, our approach optimizes the SDF and the cross field", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 651, + 294, + 660 + ], + "spans": [ + { + "bbox": [ + 51, + 651, + 294, + 660 + ], + "type": "text", + "content": "simultaneously. As a result, during optimization, the underlying SDF", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 662, + 294, + 671 + ], + "spans": [ + { + "bbox": [ + 51, + 662, + 294, + 671 + ], + "type": "text", + "content": "naturally smooths out noise, leading to a more intuitive cross field.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 673, + 294, + 682 + ], + "spans": [ + { + "bbox": [ + 50, + 673, + 294, + 682 + ], + "type": "text", + "content": "In summary, our method demonstrates stronger noise resistance", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 685, + 171, + 693 + ], + "spans": [ + { + "bbox": [ + 51, + 685, + 171, + 693 + ], + "type": "text", + "content": "compared to four other methods.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 313, + 456, + 561, + 586 + ], + "type": "text", + "angle": 0, + "index": 38, + "lines": [ + { + "bbox": [ + 326, + 457, + 560, + 466 + ], + "spans": [ + { + "bbox": [ + 326, + 457, + 560, + 466 + ], + "type": "text", + "content": "Singular Points. It’s well acknowledged that a trade-of must be", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 468, + 561, + 477 + ], + "spans": [ + { + "bbox": [ + 317, + 468, + 561, + 477 + ], + "type": "text", + "content": "achieved between reducing singular points and aligning with prin-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 479, + 560, + 488 + ], + "spans": [ + { + "bbox": [ + 317, + 479, + 560, + 488 + ], + "type": "text", + "content": "cipal directions. Thus, it’s preferable to position singular points in", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 491, + 559, + 498 + ], + "spans": [ + { + "bbox": [ + 317, + 491, + 559, + 498 + ], + "type": "text", + "content": "regions with high curvature variation rather than in flatter areas. As", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 501, + 559, + 510 + ], + "spans": [ + { + "bbox": [ + 317, + 501, + 559, + 510 + ], + "type": "text", + "content": "observed in Tab. 2, Tab. 3, and Fig. 20, our method produces a slightly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 513, + 561, + 521 + ], + "spans": [ + { + "bbox": [ + 317, + 513, + 561, + 521 + ], + "type": "text", + "content": "higher number of singular points compared to MIQ [Bommes et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 523, + 561, + 532 + ], + "spans": [ + { + "bbox": [ + 317, + 523, + 561, + 532 + ], + "type": "text", + "content": "2009]. This occurrence can be attributed to MIQ’s tendency to pro-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 534, + 561, + 542 + ], + "spans": [ + { + "bbox": [ + 317, + 534, + 561, + 542 + ], + "type": "text", + "content": "duce distorted quadrilaterals, which consequently reduces the oc-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 545, + 561, + 554 + ], + "spans": [ + { + "bbox": [ + 317, + 545, + 561, + 554 + ], + "type": "text", + "content": "currence of singular points as well as area and angular distortions.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 556, + 560, + 564 + ], + "spans": [ + { + "bbox": [ + 317, + 556, + 560, + 564 + ], + "type": "text", + "content": "However, MIQ’s quad mesh lacks overall consistency and tends to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 567, + 559, + 575 + ], + "spans": [ + { + "bbox": [ + 317, + 567, + 559, + 575 + ], + "type": "text", + "content": "oversmooth areas with significant changes in the direction of the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 578, + 356, + 586 + ], + "spans": [ + { + "bbox": [ + 317, + 578, + 356, + 586 + ], + "type": "text", + "content": "cross field.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 314, + 587, + 561, + 642 + ], + "type": "text", + "angle": 0, + "index": 39, + "lines": [ + { + "bbox": [ + 324, + 588, + 560, + 598 + ], + "spans": [ + { + "bbox": [ + 324, + 588, + 560, + 598 + ], + "type": "text", + "content": "In Fig. 20, we visualize the locations of singular points in the quad", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 600, + 560, + 609 + ], + "spans": [ + { + "bbox": [ + 317, + 600, + 560, + 609 + ], + "type": "text", + "content": "meshes generated by all methods on two models. The placement", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 611, + 559, + 620 + ], + "spans": [ + { + "bbox": [ + 317, + 611, + 559, + 620 + ], + "type": "text", + "content": "of singular points in the quad mesh generated by our method is", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 621, + 560, + 631 + ], + "spans": [ + { + "bbox": [ + 316, + 621, + 560, + 631 + ], + "type": "text", + "content": "more reasonable, and the resulting quadrilateral mesh exhibits high", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 633, + 389, + 641 + ], + "spans": [ + { + "bbox": [ + 317, + 633, + 389, + 641 + ], + "type": "text", + "content": "overall consistency.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 314, + 661, + 562, + 694 + ], + "type": "text", + "angle": 0, + "index": 40, + "lines": [ + { + "bbox": [ + 326, + 662, + 561, + 671 + ], + "spans": [ + { + "bbox": [ + 326, + 662, + 561, + 671 + ], + "type": "text", + "content": "Geometrically Complex Models. Various complex geometric mod-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 673, + 561, + 681 + ], + "spans": [ + { + "bbox": [ + 317, + 673, + 561, + 681 + ], + "type": "text", + "content": "els, such as triangular meshes with high genus, thin shells, or non-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 684, + 559, + 693 + ], + "spans": [ + { + "bbox": [ + 317, + 684, + 559, + 693 + ], + "type": "text", + "content": "orientable surfaces, are common in many fields. In Fig. 21, we display", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 73, + 149, + 276 + ], + "blocks": [ + { + "bbox": [ + 53, + 73, + 149, + 276 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 73, + 149, + 276 + ], + "spans": [ + { + "bbox": [ + 53, + 73, + 149, + 276 + ], + "type": "image", + "image_path": "dff8a0b78248ca6769c6831eae6983736f3ddc1694cf9e2a7b5de7ae4cd9893e.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 94, + 285, + 107, + 293 + ], + "type": "image_caption", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 94, + 285, + 107, + 295 + ], + "spans": [ + { + "bbox": [ + 94, + 285, + 107, + 295 + ], + "type": "text", + "content": "IM", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 2, + "sub_images": [ + { + "type": "image", + "bbox": [ + 0.0, + 0.0, + 1.0, + 0.591 + ] + }, + { + "type": "image", + "bbox": [ + 0.135, + 0.601, + 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Comparison of quad meshes generated by various methods for some challenging models, i.e. with high genus, thin shells, and non-orientable rings", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 312, + 512, + 319 + ], + "spans": [ + { + "bbox": [ + 50, + 312, + 512, + 319 + ], + "type": "text", + "content": "Across all tests, the quad meshes generated by NeurCross consistently exhibit higher quality compared to those produced by other methods.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 50, + 326, + 289, + 577 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 326, + 289, + 577 + ], + "spans": [ + { + "bbox": [ + 50, + 326, + 289, + 577 + ], + "type": "image", + "image_path": "82282e58612d24db85d424cbd4f9ace54d12c5adc061f798b70f69955fbbbdeb.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 51, + 582, + 291, + 594 + ], + "type": "image_caption", + "angle": 0, + "index": 30, + "lines": [ + { + "bbox": [ + 52, + 583, + 290, + 593 + ], + "spans": [ + { + "bbox": [ + 52, + 583, + 290, + 593 + ], + "type": "text", + "content": "(a) Open boundaries (b) Feature lines (c) Free-form model", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 48, + 600, + 295, + 651 + ], + "type": "image_caption", + "angle": 0, + "index": 31, + "lines": [ + { + "bbox": [ + 51, + 601, + 295, + 609 + ], + "spans": [ + { + "bbox": [ + 51, + 601, + 295, + 609 + ], + "type": "text", + "content": "Fig. 22. 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Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
ShapeNet[Chang et al. 2015]w/o \\mathcal{L}_{\\text{AP}}1.5911.9689.968.050.75
w/o \\mathcal{L}_{\\text{S}}1.9615.12113.288.090.71
w/o \\mathcal{L}_{\\text{AP}} & \\mathcal{L}_{\\text{S}}2.2520.73238.718.150.55
NeurCross (Ours)1.489.8585.328.030.78
Thingi10K[Zhou and Jacobson 2016]w/o \\mathcal{L}_{\\text{AP}}1.4811.8973.798.250.79
w/o \\mathcal{L}_{\\text{S}}1.8715.03105.378.290.73
w/o \\mathcal{L}_{\\text{AP}} & \\mathcal{L}_{\\text{S}}2.2120.67225.188.310.58
NeurCross (Ours)1.339.6868.968.220.81
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The", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 358, + 561, + 367 + ], + "spans": [ + { + "bbox": [ + 317, + 358, + 561, + 367 + ], + "type": "text", + "content": "results show that our method produces the highest quality quadrilat-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 369, + 560, + 378 + ], + "spans": [ + { + "bbox": [ + 317, + 369, + 560, + 378 + ], + "type": "text", + "content": "eral meshes. 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Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
ShapeNet[Chang et al. 2015]w/o \\mathcal{L}_{\\text{AP}}1.5911.9689.968.050.75
w/o \\mathcal{L}_{\\text{S}}1.9615.12113.288.090.71
w/o \\mathcal{L}_{\\text{AP}} & \\mathcal{L}_{\\text{S}}2.2520.73238.718.150.55
NeurCross (Ours)1.489.8585.328.030.78
Thingi10K[Zhou and Jacobson 2016]w/o \\mathcal{L}_{\\text{AP}}1.4811.8973.798.250.79
w/o \\mathcal{L}_{\\text{S}}1.8715.03105.378.290.73
w/o \\mathcal{L}_{\\text{AP}} & \\mathcal{L}_{\\text{S}}2.2120.67225.188.310.58
NeurCross (Ours)1.339.6868.968.220.81
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For free-form models, the lo-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 562, + 294, + 571 + ], + "spans": [ + { + "bbox": [ + 51, + 562, + 294, + 571 + ], + "type": "text", + "content": "calized patching mechanism (LPM) [Pietroni et al. 2021] introduces", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 574, + 294, + 582 + ], + "spans": [ + { + "bbox": [ + 51, + 574, + 294, + 582 + ], + "type": "text", + "content": "singularities at the junctions of adjacent patches and even produces", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 585, + 294, + 593 + ], + "spans": [ + { + "bbox": [ + 51, + 585, + 294, + 593 + ], + "type": "text", + "content": "malformed quadrilaterals. Therefore, we generally rely on the global", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 595, + 294, + 604 + ], + "spans": [ + { + "bbox": [ + 51, + 595, + 294, + 604 + ], + "type": "text", + "content": "parameterization methods from libigl [Jacobson et al. 2017], unless", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 606, + 294, + 614 + ], + "spans": [ + { + "bbox": [ + 51, + 606, + 294, + 614 + ], + "type": "text", + "content": "the user explicitly requires the alignment of parameterized lines", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 617, + 294, + 625 + ], + "spans": [ + { + "bbox": [ + 51, + 617, + 294, + 625 + ], + "type": "text", + "content": "with sharp feature lines, in which case we employ the localized", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 628, + 230, + 636 + ], + "spans": [ + { + "bbox": [ + 50, + 628, + 230, + 636 + ], + "type": "text", + "content": "patching mechanism (LPM) [Pietroni et al. 2021].", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 647, + 167, + 658 + ], + "type": "title", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 50, + 647, + 166, + 658 + ], + "spans": [ + { + "bbox": [ + 50, + 647, + 166, + 658 + ], + "type": "text", + "content": "5.2 Cross Field Loss Terms", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 48, + 661, + 294, + 694 + ], + "type": "text", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 51, + 662, + 294, + 671 + ], + "spans": [ + { + "bbox": [ + 51, + 662, + 294, + 671 + ], + "type": "text", + "content": "To further highlight the eficacy of our cross field loss terms in", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 673, + 293, + 682 + ], + "spans": [ + { + "bbox": [ + 51, + 673, + 293, + 682 + ], + "type": "text", + "content": "quad mesh generation, we conducted a comparative analysis by", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 684, + 294, + 693 + ], + "spans": [ + { + "bbox": [ + 51, + 684, + 294, + 693 + ], + "type": "text", + "content": "disabling these loss terms. 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The", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 358, + 561, + 367 + ], + "spans": [ + { + "bbox": [ + 317, + 358, + 561, + 367 + ], + "type": "text", + "content": "results show that our method produces the highest quality quadrilat-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 369, + 560, + 378 + ], + "spans": [ + { + "bbox": [ + 317, + 369, + 560, + 378 + ], + "type": "text", + "content": "eral meshes. Disabling the alignment with principal directions term", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 380, + 561, + 389 + ], + "spans": [ + { + "bbox": [ + 317, + 380, + 334, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal { L } _ { \\mathrm { A P } }", + "score": 0.7393 + }, + { + "bbox": [ + 335, + 380, + 561, + 388 + ], + "type": "text", + "content": "maintains only local correlation and lacks overall consistency.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 391, + 560, + 400 + ], + "spans": [ + { + "bbox": [ + 317, + 392, + 546, + 399 + ], + "type": "text", + "content": "Although the mesh generated without the smoothness term", + "score": 1.0 + }, + { + "bbox": [ + 548, + 391, + 560, + 400 + ], + "type": "inline_equation", + "content": "\\mathcal { L } _ { S }", + "score": 0.799 + } + ] + }, + { + "bbox": [ + 316, + 401, + 560, + 411 + ], + "spans": [ + { + "bbox": [ + 316, + 401, + 560, + 411 + ], + "type": "text", + "content": "shows some degree of overall consistency, it is prone to producing", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 413, + 560, + 422 + ], + "spans": [ + { + "bbox": [ + 317, + 413, + 560, + 422 + ], + "type": "text", + "content": "singular points due to the absence of constraints on the local cross", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 422, + 560, + 434 + ], + "spans": [ + { + "bbox": [ + 317, + 424, + 462, + 432 + ], + "type": "text", + "content": "field. Without constraints from neither", + "score": 1.0 + }, + { + "bbox": [ + 462, + 422, + 480, + 433 + ], + "type": "inline_equation", + "content": "\\mathcal { L } _ { \\mathrm { A P } }", + "score": 0.8218 + }, + { + "bbox": [ + 480, + 424, + 496, + 434 + ], + "type": "text", + "content": "nor", + "score": 1.0 + }, + { + "bbox": [ + 496, + 423, + 509, + 433 + ], + "type": "inline_equation", + "content": "\\mathcal { L } _ { \\mathrm { S } } ,", + "score": 0.8103 + }, + { + "bbox": [ + 510, + 424, + 560, + 434 + ], + "type": "text", + "content": "the resulting", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 435, + 561, + 443 + ], + "spans": [ + { + "bbox": [ + 317, + 435, + 561, + 443 + ], + "type": "text", + "content": "quadrilateral mesh exhibits both aforementioned defects. The quan-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 446, + 559, + 455 + ], + "spans": [ + { + "bbox": [ + 317, + 446, + 559, + 455 + ], + "type": "text", + "content": "titative results presented in Tab. 4 align with the qualitative findings", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 457, + 559, + 465 + ], + "spans": [ + { + "bbox": [ + 317, + 457, + 559, + 465 + ], + "type": "text", + "content": "in Fig. 23, further demonstrating the superiority of our method in", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 468, + 437, + 476 + ], + "spans": [ + { + "bbox": [ + 317, + 468, + 437, + 476 + ], + "type": "text", + "content": "generating quadrilateral meshes.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 315, + 495, + 444, + 506 + ], + "type": "title", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 316, + 495, + 443, + 505 + ], + "spans": [ + { + "bbox": [ + 316, + 495, + 443, + 505 + ], + "type": "text", + "content": "5.3 Resolution of Quad Mesh", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 313, + 508, + 561, + 597 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 317, + 510, + 560, + 519 + ], + "spans": [ + { + "bbox": [ + 317, + 510, + 560, + 519 + ], + "type": "text", + "content": "In real-world applications, selecting the appropriate resolution for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 521, + 561, + 530 + ], + "spans": [ + { + "bbox": [ + 317, + 521, + 561, + 530 + ], + "type": "text", + "content": "quad mesh extraction depends on the specific requirements of dif-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 532, + 561, + 540 + ], + "spans": [ + { + "bbox": [ + 317, + 532, + 561, + 540 + ], + "type": "text", + "content": "ferent tasks. In Fig. 24, we use the same cross field for both low-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 543, + 561, + 552 + ], + "spans": [ + { + "bbox": [ + 317, + 543, + 561, + 552 + ], + "type": "text", + "content": "and high-resolution quad meshes, ensuring consistent placement of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 554, + 560, + 563 + ], + "spans": [ + { + "bbox": [ + 317, + 554, + 560, + 563 + ], + "type": "text", + "content": "singular points. Interestingly, the low-resolution mesh better high", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 566, + 560, + 574 + ], + "spans": [ + { + "bbox": [ + 317, + 566, + 560, + 574 + ], + "type": "text", + "content": "lights the positioning of these singular points. Fig. 24 demonstrates", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 576, + 560, + 584 + ], + "spans": [ + { + "bbox": [ + 317, + 576, + 560, + 584 + ], + "type": "text", + "content": "that, in our approach, most singular points are strategically located", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 587, + 520, + 595 + ], + "spans": [ + { + "bbox": [ + 317, + 587, + 520, + 595 + ], + "type": "text", + "content": "in regions with high curvature rather than in flat areas.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 315, + 613, + 387, + 624 + ], + "type": "title", + "angle": 0, + "index": 16, + "lines": [ + { + "bbox": [ + 316, + 615, + 386, + 624 + ], + "spans": [ + { + "bbox": [ + 316, + 615, + 386, + 624 + ], + "type": "text", + "content": "6 LIMITATION", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 313, + 628, + 561, + 694 + ], + "type": "text", + "angle": 0, + "index": 17, + "lines": [ + { + "bbox": [ + 317, + 629, + 561, + 638 + ], + "spans": [ + { + "bbox": [ + 317, + 629, + 561, + 638 + ], + "type": "text", + "content": "A significant limitation of the self-supervised optimization is its sub-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 641, + 560, + 649 + ], + "spans": [ + { + "bbox": [ + 317, + 641, + 560, + 649 + ], + "type": "text", + "content": "stantial time requirement. For a triangular mesh input with 50,000", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 317, + 651, + 560, + 660 + ], + "spans": [ + { + "bbox": [ + 317, + 651, + 560, + 660 + ], + "type": "text", + "content": "faces, each iteration takes 68.34 ms, with a default setting of 10,000", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 316, + 662, + 561, + 672 + ], + "spans": [ + { + "bbox": [ + 316, + 662, + 561, + 672 + ], + "type": "text", + "content": "iterations. 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Trend of convergence. Quad meshes generated by our NeurCross", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 245, + 192, + 253 + ], + "spans": [ + { + "bbox": [ + 50, + 245, + 192, + 253 + ], + "type": "text", + "content": "with diferent numbers of iterations (#iter).", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 2, + "sub_type": "natural_image" + }, + { + "bbox": [ + 48, + 280, + 295, + 301 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 51, + 281, + 295, + 290 + ], + "spans": [ + { + "bbox": [ + 51, + 281, + 295, + 290 + ], + "type": "text", + "content": "complex shapes may require additional iterations to achieve compa-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 50, + 292, + 211, + 300 + ], + "spans": [ + { + "bbox": [ + 50, + 292, + 211, + 300 + ], + "type": "text", + "content": "rable results (see the bottom row of Fig. 25).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 48, + 301, + 296, + 346 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 60, + 304, + 294, + 312 + ], + "spans": [ + { + "bbox": [ + 60, + 304, + 294, + 312 + ], + "type": "text", + "content": "A promising future direction is to leverage this approach to gen", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 315, + 294, + 323 + ], + "spans": [ + { + "bbox": [ + 51, + 315, + 294, + 323 + ], + "type": "text", + "content": "erate ample training data for feeding generative models, such as", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 51, + 325, + 294, + 333 + ], + "spans": [ + { + "bbox": [ + 51, + 325, + 294, + 333 + ], + "type": "text", + "content": "MeshGPT [Siddiqui et al. 2024]. 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], + [ + { + "type": "header", + "bbox": [ + 0.477, + 0.069, + 0.883, + 0.081 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.908, + 0.07, + 0.916, + 0.079 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.094, + 0.91, + 0.308 + ], + "angle": 0, + "content": "```mermaid\ngraph LR\n A[\"Input Image\"] --> B[\"Image with Scatter Plot\"]\n B --> C[\"P\"]\n C --> D[\"SDF fitting module\"]\n D --> E[\"Feature Output\"]\n F[\"MLP\"] --> G[\"θ\"]\n G --> H[\"μ, ν\"]\n H --> I[\"⊕\"]\n J[\"L_SDF\"] --> K[\"min L\"]\n K --> L[\"L_CrossField\"]\n L --> M[\"Output Image\"]\n N[\"α = μcosθ + vsinθ\\nβ = vcosθ - μsinθ\"] --> I\n E --> O[\"H\"]\n O --> P[\"⊕\"]\n P --> Q[\"Output Image\"]\n```", + "sub_type": "flowchart" + }, + { + "type": "image_caption", + "bbox": [ + 0.079, + 0.314, + 0.918, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.373, + 0.483, + 0.445 + ], + 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Layer NameLayer ArchitectureOutput Size
1 \\times 1, input\\_size=12256
ResNets #1, #2, #3\\begin{bmatrix} 1 \\times 1, 256 \\\\ 1 \\times 1, 64 \\\\ 1 \\times 1, 64 \\end{bmatrix} \\times n_{bottleneck}256
ResNets #4, #5, #6, #7\\begin{bmatrix} 1 \\times 1, 512 \\\\ 1 \\times 1, 128 \\\\ 1 \\times 1, 128 \\end{bmatrix} \\times n_{bottleneck}512
1 \\times 1, 51232
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Area ↓Angle ↓# of Sings ↓CD ↓JR ↑
ShapeNet[Chang et al. 2015]w/o \\mathcal{L}_{\\text{AP}}1.5911.9689.968.050.75
w/o \\mathcal{L}_{\\text{S}}1.9615.12113.288.090.71
w/o \\mathcal{L}_{\\text{AP}} & \\mathcal{L}_{\\text{S}}2.2520.73238.718.150.55
NeurCross (Ours)1.489.8585.328.030.78
Thingi10K[Zhou and Jacobson 2016]w/o \\mathcal{L}_{\\text{AP}}1.4811.8973.798.250.79
w/o \\mathcal{L}_{\\text{S}}1.8715.03105.378.290.73
w/o \\mathcal{L}_{\\text{AP}} & \\mathcal{L}_{\\text{S}}2.2120.67225.188.310.58
NeurCross (Ours)1.339.6868.968.220.81
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b/papers/markdown/2405.20853_MeshXL_Neural_Coordinate_Field_for_Generative_3D_Foundation_Models/hybrid_auto/2405.20853_MeshXL_Neural_Coordinate_Field_for_Generative_3D_Foundation_Models.md @@ -0,0 +1,415 @@ +![](images/1f8d1cd969800e902f0e3d13359bf240ad064db047501854dc33189a0c3f5546.jpg) + +# MeshXL: Neural Coordinate Field for Generative 3D Foundation Models + +Sijin Chen1,2,∗, Xin Chen2,†, Anqi Pang2, Xianfang Zeng2, Wei Cheng2, Yijun Fu2, Fukun Yin1,2 + +Yanru Wang2, Zhibin Wang2, Chi Zhang2, Jingyi Yu3, Gang Yu2, Bin Fu2, Tao Chen1,‡ + +https://github.com/OpenMeshLab/MeshXL + +1Fudan University 2Tencent PCG 3ShanghaiTech University + +† project lead ‡ corresponding author + +![](images/bad59a0dbcab584b56c1908c15cc14424b2c80d21846732b59f69d53796ee558.jpg) + +
+natural_image + +Collection of 3D wireframe models of various furniture and home items, including sofas, chairs, tables, and chairs (no text or symbols) +
+ +Figure 1: MeshXL can auto-regressively generate high-quality 3D meshes. We validate that Neural Coordinate Field (NeurCF), an explicit coordinate representation with implicit neural embeddings, is a simple-yet-effective sequence representation for large-scale mesh modelling. + +## Abstract + +The polygon mesh representation of 3D data exhibits great flexibility, fast rendering speed, and storage efficiency, which is widely preferred in various applications. However, given its unstructured graph representation, the direct generation of high-fidelity 3D meshes is challenging. Fortunately, with a pre-defined ordering strategy, 3D meshes can be represented as sequences, and the generation process can be seamlessly treated as an auto-regressive problem. In this paper, we validate the Neural Coordinate Field (NeurCF), an explicit coordinate representation with implicit neural embeddings, is a simple-yet-effective representation for largescale sequential mesh modeling. After that, we present MeshXL, a family of generative pre-trained auto-regressive models, which addresses the process of 3D mesh generation with modern large language model approaches. Extensive experiments show that MeshXL is able to generate high-quality 3D meshes, and can also serve as foundation models for various down-stream applications. + +## 1 Introduction + +The generation of high-quality 3D assets [61, 79, 29] is essential for various applications in video games, virtual reality, and robotics. Among existing 3D representations [51, 38, 57, 61], the 3D mesh represents the 3D data with graphs, which has the flexibility and accuracy for sharp edges as well as both flat and curved surfaces. However, the direct generation of high-quality 3D meshes is challenging, given 1) the unstructured graph representation and 2) the demand for accurate spatial locations and connectivity estimation within vertices. + +To generate 3D meshes, many works adopt an indirect way by first producing data in other 3D representations, including point clouds [99, 49, 54], SDF [90, 96], and multi-view images [46, 84, 30]. After that, re-meshing methods [37] are required for post-processing the generated geometries. There are also attempts towards the direct generation of 3D polynomial meshes. PolyGen [53] adopts two separate decoder-only transformers for vertices generation and connectivity prediction. MeshGPT [66] builds a mesh VQVAE to reconstruct the tokens generated by a GPT model [59] into 3D meshes. Meanwhile, PolyDiff [2] directly adopts discrete denoising diffusion [4] on the discretized mesh coordinates. + +Though these methods have achieved initial success in 3D assets generation, they suffer from certain limitations. To preserve high-frequency information, the point cloud and voxel representations will make dense samplings on the object surfaces, which inevitably lead to great redundancy when representing flat surfaces. The reconstruction-based methods [84, 30, 68], however, rely heavily on the quality of the multi-vew generation pipeline [46]. Additionally, the VQVAE-based 3D generation methods [90, 66] will inevitably result in cumulative errors when reconstructing the generated tokens into 3D structures. + +To tackle the above challenges and explore the potential of scaling up 3D generative pre-training, we introduce a simple-yet-effective way of 3D mesh representation, the Neural Coordinate Field (NeurCF). NeurCF represents the explicit 3D coordinates with implicit neural embeddings. We show that with a pre-defined ordering strategy, the generation of 3D meshes can be formulated as an auto-regressive problem. After that, we present MeshXL, a family of generative pre-trained transformers [95, 59], for the direct generation of high-fidelity 3D meshes. Without resorting to intermediate 3D representations, NeurCF facilitates an end-to-end learning pipeline for the direct pre-training on large-scale 3D mesh data. + +By organizing high-quality 3D assets from ShapeNet [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16], we achieve a collection of over 2.5 million 3D meshes to support large-scale generative pre-training. Extensive experiments demonstrate that the NeurCF representation facilitates MeshXL to generate higher-quality 3D meshes with an increased number of parameters and largescale pre-training data. By training on the collection of large-scale 3D mesh data, MeshXL can achieve better performance with larger numbers of parameters (Fig. 3 and Tab. 5), and surpass prior arts on multiple categories task of the ShapeNet dataset [9] (Tab. 3). + +In summary, our contributions can be summarized as follows: + +• We validate that Neural Coordinate Field is a simple-and-effective representation of 3D mesh, which is also friendly to large-scale auto-regressive pre-training. +• We present a family of MeshXLs that can be treated as strong base models for image-conditioned or text-conditioned 3D mesh generation tasks. +• We show that MeshXL surpasses state-of-the-art 3D mesh generation methods, and can produce delicate 3D meshes compatible with existing texturing methods. + +## 2 Related Work + +First, we present a concise review of existing 3D representations. Subsequently, we discuss related works on 3D generation and recent efforts in developing 3D foundation models. + +3D Representations. Researchers have long sought for accurate and efficient methods to represent 3D data. Point Cloud [54, 57, 58, 91] captures the spatial positions of discrete points in the Euclidean space, which is preferred by various 3D sensors [15, 89, 67, 3, 7]. Mesh [53, 2, 66, 12] represents the 3D structure with graphs. By connecting the vertices with edges, mesh can also be interpreted into a set of polygons in the 3D space. Similar to point clouds, 3D Gaussians [38, 69] also record the discrete Euclidean distribution in 3D space. However, each point is represented by a 3D Gaussian distribution function parameterized by its covariance matrix, color, and opacity. Given their fast convergence and rendering speed, 3D gaussians are often utilized for 3D reconstruction. Neural Radiance Field (NeRF) [51, 5] constructs a learnable volumetric function f using neural networks trained on multi-view images. Due to its derivability and flexibility, NeRF is also favored for 3D generative models [46, 101, 78, 56]. Additionally, there are other 3D representations such as multi-view images [76, 92, 102], voxel fields [61, 13, 45], and signed distance fields [96], among others [65, 90, 64]. In this paper, we consider the Neural Coordinate Field (NeurCF), an explicit spatial representation with implicit neural embeddings, and investigate its potential for scalable 3D asset generation. + +3D Generation. With the exploration of various 3D representations and the collection of large-scale 3D datasets [17, 9, 16], researchers have also put much effort exploring the generation of high-fidelity 3D assets [42, 39]. The Generative Adversarial Network (GAN) [25, 82, 1, 33] produces synthetic 3D data with a generator G, and train a discriminator network D to distinguish the generated and real data. Additionally, the potential of diffusion models [54, 28, 62] in the direct generation of 3D data is also widely explored [99, 2, 54, 50, 47]. The key idea behind diffusion is to transform the desired data distribution into a simpler distribution (e.g. gaussian) and learn a desnoising model for the reverse process. Besides, researchers have also explored the potential of diffusion models in generating multi-view images [46, 16, 84, 43], and reconstruct them into 3D structures. In this paper, we mainly explore the auto-regressive methods for 3D generation. AutoSDF [52] and MeshGPT [66] learn to generate discrete tokens and reconstruct them into 3D representations with a VQVAE model [73]. PolyGen [53] adopts two decoder-only transformers that predict the location and connectivity of vertices, sequentially. In this paper, we explore the potential of an explicit sequential modelling method for 3D meshes, and present a family of generative pre-trained transformers, MeshXL, for high-fidelity 3D mesh generation. + +3D Foundation Models. The collection of large-scale high-quality 3D data [17, 16, 9, 83, 72, 21, 22] builds up the foundation for various 3D-related tasks [85, 27, 10, 41]. To explore the scaling effects in 3D learning, researchers have made great endeavors in building 3D foundation models for 3D understanding [98, 44, 100, 87, 88, 94, 102], reconstruction [30, 80, 68, 46, 16, 86, 75], and generation [61, 29, 66, 8]. With the introduction of large-scale 3D data in both variety and granularity [34, 41, 16], existing 3D foundation models are capable of generalizing to unseen concepts [102, 88, 44], generating high-fidelity 3D assets [90, 36, 66], responding to complex instructions [31, 10, 32, 41], and generating actions that interacts with the 3D environments [20, 81, 97]. In this paper, we present a fully end-to-end 3D mesh generation pipeline, explore the scaling effect for large-scale pre-training, and test whether our method can serve as a well-trained foundation model for various down-stream tasks. + +## 3 Data + +Data Sources. We provide details on the 3D data collections we use to train and evaluate our models. The whole data collection is built upon four widely-acknowledged 3D mesh datasets, i.e. ShapeNet V2 [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16]. + +• ShapeNet V2 [9] collects about 51k 3D CAD models for 55 categories. We split the data in 9:1 for training and validation by each category. +• 3D-FUTURE [22] present about 10k high-quality 3D mesh data for indoor furniture. However, because of the delicate design, the objects contain many faces. Therefore, only a small proportion of the data can be used to train our MeshXL models. +• Objaverse [17] is a large 3D data collection with more than 800k 3D objects for about 21k categories collected from Sketchfab. We split the data in 99:1 for training and validation, respectively. +• Objaverse-XL [16] further expand Objaverse [17] into a dataset with more than 10M 3D objects with additional data collected from GitHub, Polycam, Thingiverse, and Smithsonian. We split the Github and Thingiverse part of the Objaverse-XL dataset into 99:1 for training and validation, respectively. + +Data collection and filtering. To organize existing datasets, we build up a filtering and pre-processing pipeline to ensure that the meshes met our demand. We first collect meshes with fewer than 800 faces, and ensure that they have corresponding UV maps for rendering. After that, we render the 3D meshes, and discard those are not center-aligned or occupying less than 10% of the frame. For those 3D meshes with more than 800 but less than 20,000 faces, we use planar decimation whether their meshes can be simplified. Finally, we achieve approximately 2.5 million pieces of data remained. + +Planar Decimation Pipeline. To ensure the quality of the decimated 3D meshes, we make sure either a lower Hausdorff distance $\delta _ { \mathrm { h a u s d o r f f } }$ [66] or a similar rendered views [11]. + +Collecting mesh-text pairs. We first render each 3D mesh with 12 different views, and concatenate them into one single image. Then, we annotate both the front view image and the fused multi-view image using CogVLM [77]. After that, we adopt the Mistral-7B-Instruct model [35] with few-shot in-context examples to extract information on category and geometry from the CogVLM annotations. We tag each 3D mesh with the resulting categories and 3 to 5 geometry descriptors. + +Collecting mesh-image pairs. To produce diverse image conditions for 3D mesh generation, we first generate images with multi-view image and depth rendering. After that, we use the sentences produced by CogVLM [77] as the prompt, and use a find-tuned Stable Diffusion model [63] to augment the rendered images for diverse textures and backgrounds. To ensure the quality of the generated images, we also adopt a manually cleansing procedure. + +Data Statistics. We present the data statistics of our large-scale 3D mesh collection in Tab. 1. After organizing and combing 3D assets from ShapeNet [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16], we could achieve a total of 2.5 million 3D meshes. + +Table 1: Statistics for the Training Data and Validation Data. After combining four data sources, our proposed MeshXL models are trained on approximately 2.5 million 3D meshes. + +
DatasetPre-trainingText-to-3D
TrainValTrainVal
ShapeNet [9]16,0011,75415,3841,728
3D-Future [22]1,603---
Objaverse [17]85,28285483,501820
Objaverse-XL [16]2,407,33715,2001,347,80213,579
Total2,510,22317,8081,446,67816,127
+ +## 4 Neural Coordinate Field + +Neural Coordinate Field (NeurCF) is an explicit representation with implicit neural embeddings. To be specific, for a Euclidean 3D coordinate system, we can partition the vertices coordinates into an $N ^ { 3 }$ grid. Then, each discretized coordinate $p = ( x , y , z )$ can be encoded with the coordinate embedding layer E, where $\mathcal { F } ( \boldsymbol { p } ) = ( \mathcal { E } ( \boldsymbol { x } ) , \mathcal { E } ( \boldsymbol { y } ) , \mathcal { E } ( \boldsymbol { z } ) )$ . Therefore, a k-sided polynomial face $f ^ { ( i ) }$ can be encoded with $\mathcal { E } _ { \mathrm { f a c e } } ( \boldsymbol { f } ^ { ( i ) } ) = ( \mathcal { F } ( \boldsymbol { p } _ { 1 } ^ { ( i ) } ) , \cdot \cdot \cdot , \mathcal { F } ( \boldsymbol { p } _ { k } ^ { ( i ) } ) )$ ). For simplicity, the learnable coordinate embeddings E are shared among axes. + +Ordering. Due to the graph representation, the order of the mesh vertices and the order of the edges between them are permutation-invariant. A pre-defined ordering strategy is essential to facilitate the sequence modelling in MeshXL. We employ the same ordering strategy as PolyGen [53] and MeshGPT [66]. The mesh coordinates are first normalized into a unit cube based on the mesh’s longest axis, and discretized into unsigned integers. Within each face, the vertices are cyclically permuted based their coordinates (z-y-x order, from lower to higher), which helps to preserve the direction of normal vectors. Then, we order these faces based on the permuted coordinates (lower to high). To this end, an n-faced 3D k-sided polynomial mesh can be represented as $\mathcal { M } \in \mathbb { Z } ^ { n \times k \times 3 }$ , and we can encode M with $\mathcal { E } _ { \mathrm { m e s h } } = ( \mathcal { E } _ { \mathrm { f a c e } } ( f ^ { ( 1 ) } ) , \cdot \cdot \cdot , \mathcal { E } _ { \mathrm { f a c e } } ( f ^ { ( n ) } ) )$ ). + +A Sequential Mesh Representation. One direct way to represent the 3D meshes is to directly reshape M into a vector with $( n \cdot k \cdot 3 )$ tokens. As a special case, an n-faced triangular mesh can be represented by a vector with 9n tokens. Meanwhile, our representation can also be expanded to hybrid polynomial mesh representations with the proper introduction of separate tokens. For example, we can generate triangles within “ · · · ” and quadrilaterals within “ · · · ”. To identify the start and end of a mesh sequence, we add a (“begin-of-sequence”) token before the mesh sequence and an (“end-of-sequence”) token after. + +![](images/a630cfe35c3ec609be24eeec3d723fe2b40be6f1211dbc75599c6cd0359ed5a8.jpg) + +
+flowchart + +```mermaid +graph LR + A["Coordinate Embeddings: ε"] --> B["p = (x,y,z)"] + B --> C["F(p) = (ε(x), ε(y), ε(z))"] + D["Face Embedding:\nε_face(f^(i)) = (F(p_1^(i)), ..., F(p_k^(i)))"] + E["Mesh Embedding:\nε_mesh(M) = (ε_face(f^(1)), ..., ε_face(f^(n)))"] +``` +
+ +(a) Neural Coordinate Field + +![](images/51c707d52655b90586d370683125db668549db2f46c0499de79259dea0e59432.jpg) + +
+text_image + +Next Coordinate Prediction +
+ +(b) Auto-regressive Mesh Generation +Figure 2: Mesh Representation. We present the Neural Coordinate Field (NeurCF) to encode the discretized coordinates in the Euclidean space. Benefiting from NeurCF and a pre-defined ordering strategy, our proposed MeshXL can directly generate the unstructured 3D mesh auto-regressively. + +Comparisons. Compared to other forms of 3D representations, NeurCF is a direct representation for 3D meshes. Since we represent each coordinate with learnable embeddings, NeurCF is an end-toend trainable representation for unstructured 3D meshes. Additionally, NeurCF is storage efficient comparing to voxel fields $( O ( N ^ { 3 } ) )$ ) and point clouds, since it can naturally model the flat surfaces with graph structures. + +## 5 Method + +We first present the architecture and training objective for MeshXL models. Then, we show that MeshXL models can take an additional modality as the condition for controllable 3D assets generation. After this, we investigate the effects of scaling. + +Architecture. In Sec. 4, we present a simple-yet-effective way to represent a 3D mesh into a sequence. Therefore, the learning of 3D mesh generation can be formulated into an auto-regressive problem, and can be seaminglessly addressed by modern Large Language Model (LLM) approaches. In our paper, we adopt the decoder-only transformers using the OPT [95] codebase as our base models. To adapt the pre-trained OPT models to our next-coordinate prediction setting, we fine-tune the whole model with newly-initialized coordinate and position embeddings. + +Generative Pre-Training. We use the standard next-token prediction loss to train our models. Given the trainable weights θ and an |s|-length sequence s, the generation loss is calculated as: + +$$ +\mathcal {L} _ {\mathrm{MeshXL}} \left(\theta\right) = - \sum_ {i = 1} ^ {| s |} \log P \left(s _ {[ i ]} | s _ {[ 1, \dots , i - 1 ]}; \theta\right). \tag {1} +$$ + +For each mesh sequence, we add a token before the mesh tokens, and an token after the mesh tokens to identify the ending of a 3D mesh. During inference, we adopt the top-k and top-p sampling strategy to produce diverse outputs. + +X-to-Mesh Generation. Here we mainly consider generating 3D meshes from images and texts. We adopt a pre-trained BERT [18] model for text feature encoding, and a pre-trained ViT [19] model for image feature encoding. To align the additional text/image feature with the mesh coordinate field, we adopt the Q-Former architecture [40] to compress the encoded feature into a fixed-length of 32 learnable tokens as the prefix of the MeshXL model. The overall training objective of the conditional mesh generation is shown in Eq. (2): + +$$ +\mathcal {L} _ {\mathcal {X} \text {-to - mesh}} (\theta) = - \sum_ {i = 1} ^ {| s |} \log P \left(s _ {[ i ]} | s _ {[ 1, \dots , i - 1 ]}; \mathcal {X}\right). \tag {2} +$$ + +During inference, the model predicts the mesh tokens after the fixed-length prefix. + +![](images/f5a493f49eb91e662a5f269332e0b435babbd67f87842f82cfe63479c24abc2f.jpg) +Figure 3: Training and Validation Perplexity (PPL) for MeshXL Models. We train all the models from scratch on 150 billion tokens. We observe that the performance grows with model sizes. + +Scaling Up. We present MeshXL in various sizes, including 125M, 350M, and 1.3B. The detailed hyperparameters for training different models can be found in Tab. 2. To better analyze the scaling effects, we train all models from scratch on 150 billion tokens. We provide both training curve and validation perplexity for different models in Fig. 3. One can see that as the number of parameters grows, the model achieves a lower validation perplexity, indicating a higher probability to produce the validation data. + +## 6 Experiments + +We first briefly introduce the data, metrics, and implementation details in Sec. 6.1. Then, we provide evaluations and comparisons on the generated meshes (cf. Sec. 6.2) and ablations (cf. Sec. 6.3). We also provide visualization results in Sec. 6.4. + +## 6.1 Data, Metrics, and Implementation Details + +Data. We pre-train the base model with 2.5 million 3D meshes collected from the combination of ShapeNet [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16]. We use planar decimation on meshes with more than 800 faces following MeshGPT [66] and RobustLowPoly [11]. More details on the data collection and processing pipeline can be found in the appendix. For generative mesh pre-training, we randomly rotate these meshes with degrees from (0◦, 90◦, 180◦, 270◦), and adopt random scaling along each axis within range [0.9, 1.1] for data augmentation. + +Metrics. We follow the standard evaluation protocols in MeshGPT [66] and PolyDiff [2] with the following metrics. Coverage (COV) is sensitive to mode dropping and is used to quantify the diversity of the generated meshes. However, COV does not assess the quality of the generated results. Minimum Matching Distance (MMD) calculates the average distance between the reference set and their closest neighbors in the generated set. However, MMD is not sensitive to low-quality results. The 1-Nearest Neighbor Accuracy (1-NNA) directly quantifies the quality and diversity between the generation set and the reference set. The optimal value of 1-NNA is 50%. We adopt the Jensen-Shannon Divergence (JSD) score to directly evaluate 3D meshes. We use Chamfer Distance to measure the similarity between two samples. We also adopt the Frechet Inception Distance (FID) and Kernel Inception Distance (KID) on the rendered images for feature-level evaluation. The MMD, JSD, and KID scores are multiplied by 103. + +Implementation. All experiments are conducted on a cluster consisting of 128 A100 GPUs. We train our models under bfloat16 and the ZeRO-2 strategy [60] using the AdamW [48] optimizer with a learning rate decaying from $1 0 ^ { - 4 } ~ \mathrm { t o } ~ 1 0 ^ { - 6 }$ and a weight decay of 0.1. The detailed hyperparameters for different models can be found in Tab. 2. To train our base models, we load the weights from the pre-trained OPT models [95] and initialize the word embeddings and positional embeddings from scratch. Without further specification, we generate 3D meshes with the top-k and top-p sampling strategy with k = 50 and p = 0.95. + +Table 2: Hyperparameters for different MeshXL Base Models. We present three MeshXL models with 125M, 350M, and 1.3B parameters, respectively. + +
HyperparametersMeshXL(125M)MeshXL(350M)MeshXL(1.3B)
# Layers122424
# Heads121632
$d_{model}$ 7681,0242,048
$d_{FFN}$ 3,0724,0968,192
OptimizerAdamW( $\beta_1$ =0.9, $\beta_2$ =0.999)
Learning rate $1.0 \times 10^{-4}$ $1.0 \times 10^{-4}$ $1.0 \times 10^{-4}$
LR schedulerCosineCosineCosine
Weight decay0.10.10.1
Gradient Clip1.01.01.0
Number of GPUs81632
# GPU hrs (A100)1,9446,00023,232
+ +## 6.2 Evaluations and Comparisons + +We provide quantitative as well as qualitative comparisons on both unconditional and conditional 3D mesh generation on public benchmarks + +Unconditional Generation. We evaluate MeshXL as well as other baseline methods using the ShapeNet [9] data in Tab. 3. We split the data by 9:1 for training and validation by each category. For evaluation, we fine-tune our pre-trained base model and sample 1,000 meshes for each category. Among the listed methods, we reproduce the MeshGPT [66] with a GPT2-medium model (355M) [59]. With a similar number of parameters, Mesh-XL (350M) out-performs MeshGPT by a large margin, showing a higher COV score, a lower MMD score, and a closer 1-NNA score to 50%. This indicates that MeshXL can produce diverse and high-quality 3D meshes. + +Table 3: Quantitative Comparisons with Prior Arts on ShapeNet [9]. We scale MMD, JSD, KID by 103. MeshXL can produce diverse and high-quality 3D meshes. + +
CategoryMethodsCOV↑MMD↓1-NNAJSD↓FID↓KID↓
ChairPolyGen [53]7.7916.0099.16228.8063.4943.73
GET3D [23]11.7015.9299.75155.2567.8442.10
MeshGPT [66]42.004.7569.5055.1639.528.97
MeshXL (125M)50.803.1156.559.6928.151.48
MeshXL (350M)50.803.1755.809.6628.291.39
MeshXL (1.3B)51.603.2355.809.489.121.84
TablePolyGen [53]44.003.3667.2025.0654.0814.96
GET3D [23]16.8010.3991.90226.9767.6534.62
MeshGPT [66]34.306.5175.0592.8853.757.75
MeshXL (125M)51.212.9657.9612.8242.550.92
MeshXL (350M)49.703.0756.1013.6443.431.27
MeshXL (1.3B)52.122.9256.8014.9322.292.03
BenchPolyGen [53]31.154.0183.2355.2570.5312.1
MeshGPT [66]34.922.2268.6557.3252.476.49
MeshXL (125M)54.371.6543.7516.4335.310.82
MeshXL (350M)53.371.6542.9615.4136.350.96
MeshXL (1.3B)56.551.6239.7815.5135.501.60
LampPolyGen [53]35.047.8775.4996.5765.1512.78
MeshGPT [66]41.594.9261.5961.8247.195.19
MeshXL (125M)55.865.0648.2443.4134.610.84
MeshXL (350M)53.524.1849.4134.8725.941.92
MeshXL (1.3B)51.954.8947.2741.8931.660.99
+ +User Study. To evaluate how well the generated 3D meshes align with human preference, we perform user studies on the chair category in Tab. 4 with several baseline methods [53, 23]. We recruit and instruct the participants to score each mesh from 0 to 5 based on its 1) quality: the smoothness of object surfaces and completeness of the mesh, 2) artistic: how much do you believe this object is designed and created by artists, and 3) triangulation: how well do the connectivity among vertices aligns with the models created by professional designing software [14]. For the above mentioned metrics, the higher score means better quality. As a baseline evaluation, we also ask the participants to score the ground truth 3D geometries sampled from the ShapeNet data. We have collected a total of 434 valid responses. The results show that the 3D meshes created by MeshXL are consistently preferred by human in all dimensions. + +![](images/d06e184c553ec05435444e2274b7f39c38c8637fb0ffbb95840c2be6c331d410.jpg) + +
+text_image + +Input +Completed Mesh +Ground Truth +
+ +Figure 4: Evaluation of Partial Mesh Completion. Given some partial observation of the 3D mesh (white), MeshXL is able to produce diverse object completion results (blue). + +Table 4: User Study. Compared to baseline methods, the meshes generated by MeshXL are better aligned with human preference in terms of both geometry and designs. + +
MethodsQuality↑Artistic↑Triangulation↑
PolyGen [53]2.532.723.15
GET3D [23]3.152.463.15
MeshXL3.963.453.72
Reals4.083.333.75
+ +## 6.3 Ablation Studies + +Necessity of Mesh VQVAE. Comparing to MeshGPT [66], MeshXL is an end-to-end trainable model that produces 3D meshes with next-coordinate prediction. We show in Tab. 3 that, MeshXL outperforms MeshGPT with similar numbers of parameters. Furthermore, MeshXL can save the effort training a mesh autoencoder [66, 73], which further facilitates scaling up generative pre-training. + +Shape Completion. To analysis whether our method is capable of producing diverse outputs, we ask MeshXL (1.3B) model to predict the whole object given some partial observations of the 3D mesh. In practice, we use 50% of the object mesh as input, and ask the model to predict the rest 50% of the 3D mesh. We illustrate completion examples on chairs and tables in Fig. 4. One can see that Mesh-XL is able to produce diverse outputs given the partial observation of the 3D mesh. + +X -to-Mesh Generation. We showcases several conditional generation results in Fig. 5. We show that MeshXL can generate high-quality 3D meshes given the corresponding image or text as the additional inputs. + +Effectiveness of Model Sizes. To analyze whether large-scale pre-training a larger model benefits 3D mesh generation, we evaluate MeshXL base models with different sizes on the Objaverse [17] dataset in Tab. 5. We observe that as the model size grows, the generated samples exhibits a closer 1-NNA to 50%, a larger COV, and smaller JSD score, which indicates an improving diversity and quality. + +![](images/94cdc9b3c5ee464d5f15cdcfe4da92287cb1c8599f3bf67892456c268bdd3ed2.jpg) + +
+flowchart + +```mermaid +graph LR + subgraph Image + A1["Image"] --> B1["Generated"] + B1 --> C1["Ground Truth"] + end + + subgraph Text + D1["Text: "A basic chair with four leges and an open back.""] + E1["Text: "4 legs, solid seat and backing.""] + F1["Text: "A basic looking square wooden table.""] + end + + subgraph Ground Truth + G1["Ground Truth"] + H1["Ground Truth"] + I1["Ground Truth"] + end + + B1 -.-> C1 + C1 -.-> D1 + C1 -.-> E1 + C1 -.-> F1 + C1 -.-> F1 + C1 -.-> I1 + C1 -.-> I1 +``` +
+ +Figure 5: Evaluation of X -to-mesh generation. We show that MeshXL can generate high-quality 3D meshes given the corresponding image or text as the additional inputs. + +![](images/0d0145de4d358ac6abbe978025ee1410f1a06e356a75c94e17ebed75daf318ad.jpg) + +
+text_image + +Generated Mesh +Textured Mesh +UV Map +Generated Mesh +Textured Mesh +UV Map +
+ +Figure 6: Texture Generation for the Generated 3D Meshes. We adopt Paint3D [93] to generate textures for 3D meshes produced by MeshXL. + +Table 5: Effectiveness of Model Sizes on Objaverse. We observe that as the model size grows, the generated meshes exhibit a closer 1-NNA to 50%, a larger COV and a smaller JSD, indicating better diversity and quality. + +
MethodCOV↑MMD↓1-NNAJSD↓FID↓KID ↓
MeshXL (125M)39.765.2167.3426.0317.324.48
MeshXL (350M)40.795.2065.6823.7115.143.33
MeshXL (1.3B)42.864.1661.5620.9912.492.94
+ +Texturing. We adopt Paint3D [93], a coarse-to-fine texture generation pipeline, to generate textures for the 3D meshes produced by MeshXL in Fig. 6. We show that 3D meshes produced by MeshXL can easily fit the existing texturing methods to produce high-quality 3D assets. + +![](images/25d8b0ad0310574d3a5b0d0102818a9ac33b4b5aee0bf2849ed58541fd041bb1.jpg) + +
+text_image + +PolyGen +GET3D +MeshGPT +MeshXL +
+ +Figure 7: Qualitative comparison on the generated meshes. We present qualitative comparisons on the generated meshes as well as normal vectors. MeshXL is able to produce high-quality 3D meshes with both sharp edges and smooth surfaces. + +## 6.4 Visualizations + +We provide qualitative comparisons on the meshes generated by our method as well as the meshes generated by other baseline models. + +Qualitative Comparison. We provide category specified visualization results as well as their normal vectors on the generated meshes in Fig. 7. With the ability to generate 3D meshes directly, MeshXL is able to produce high-quality 3D meshes with both sharp edges and smooth surfaces. + +Unconditional Results on ShapeNet. We visualize unconditional 3D mesh generation results for chair, table, lamp and bench in Fig. 8. One can see that MeshXL is able to produce diverse and high-quality 3D meshes. + +Unconditional Generation on Objaverse. We visualize 3D meshes randomly sampled from MeshXL base model in Fig. 9. After training on a large-scale collection of 3D mesh data, MeshXL is able to produce diverse and high-quality 3D meshes. + +## 7 Discussions + +Difference with PolyGen [53]. PolyGen explores the auto-regressive generation of 3D polynomial meshes with two transformers [74], i.e. the vertex transformer and theface transformer. PolyGen first generates a set of points representing the vertices of the 3D meshes with a vertex transformer. After that, PolyGen inputs the generated point cloud into the face transformer and predicts the connectivity among the generated with a face transformer. However, our proposed MeshXL is a more straightforward and end-to-end approach that directly generates the polynomial meshes auto-regressively with decoder-only transformers. + +Difference with MeshGPT [66]. MeshGPT consists of a mesh VQVAE [73] and a decoder-only transformer [59]. MeshGPT first learns a mesh VQVAE to quantize the 3D meshes into discrete tokens. After that, MeshGPT trains a decoder-only transformer to generate the discrete tokens for 3D mesh reconstruction. In comparison, our proposed MeshXL is an end-to-end method that learns the neural representation of coordinates and outputs 3D meshes directly. + +Extensibility. Our method, MeshXL, is built upon the concept of auto-regressive methods. Therefore, our method is not restricted to the decoder-only transformers [59, 95, 70, 71], and can also be extended to other causal language models (i.e. Mamba [26], RWKV [55], and xLSTM [6]). + +![](images/9823d03c3275775daf170f63688821882c8a92b19ce8a68090eae5adcd463cf8.jpg) + +
+natural_image + +Collection of 3D wireframe models of various furniture and home items, including chairs, tables, lamps, and benches (no text or labels) +
+ +Figure 8: Gallery results. Additional generation results for chair, table, lamp, and bench. + +![](images/ce83307bf835382378c4d93301fb661bf5692d92a75bb66c2e0b398510477e6e.jpg) + +
+natural_image + +Collection of 3D wireframe models of various architectural and furniture objects, no text or symbols present. +
+ +Figure 9: Gallery results. MeshXL is able to produce diverse 3D meshes with high quality. + +## 8 Limitations, Future Work, and Conclusions + +Limitations and Future Work. The main drawback of MeshXLs is the inference time. During sampling, MeshXL will generate 7,200 tokens for an 800-faced 3D mesh, which takes a relatively long time because of the auto-regressive process. As for future works, recent endeavors on the RNN-related methods [6, 55, 26] and multiple tokens prediction for LLMs [24] might open up great opportunities in saving the inference cost. + +Conclusion. We validate that NeurCF, an explicit coordinate representation with implicit neural embeddings, is a simple-and-effective representation of 3D meshes. By modelling the 3D mesh generation as an auto-regressive problem, we seek help from modern LLM approaches and present a family of generative pre-trained models, MeshXL, for high-fidelity 3D mesh generation. 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Hifa: High-fidelity text-to-3d with advanced diffusion guidance. arXiv preprint arXiv:2305.18766, 2023. +[102] Xiangyang Zhu, Renrui Zhang, Bowei He, Ziyu Guo, Ziyao Zeng, Zipeng Qin, Shanghang Zhang, and Peng Gao. Pointclip v2: Prompting clip and gpt for powerful 3d open-world learning. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2639–2650, 2023. \ No newline at end of file diff --git a/papers/markdown/2405.20853_MeshXL_Neural_Coordinate_Field_for_Generative_3D_Foundation_Models/hybrid_auto/2405.20853_MeshXL_Neural_Coordinate_Field_for_Generative_3D_Foundation_Models_content_list.json b/papers/markdown/2405.20853_MeshXL_Neural_Coordinate_Field_for_Generative_3D_Foundation_Models/hybrid_auto/2405.20853_MeshXL_Neural_Coordinate_Field_for_Generative_3D_Foundation_Models_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..dfdbdcfd51752626bcc29668d36ee6d1be7758cf --- /dev/null +++ b/papers/markdown/2405.20853_MeshXL_Neural_Coordinate_Field_for_Generative_3D_Foundation_Models/hybrid_auto/2405.20853_MeshXL_Neural_Coordinate_Field_for_Generative_3D_Foundation_Models_content_list.json @@ -0,0 +1,1513 @@ +[ + { + "type": "image", + "img_path": "images/1f8d1cd969800e902f0e3d13359bf240ad064db047501854dc33189a0c3f5546.jpg", + "image_caption": [], + "image_footnote": [], + "content": "", + "bbox": [ + 222, + 127, + 284, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "MeshXL: Neural Coordinate Field for Generative 3D Foundation Models", + "text_level": 1, + "bbox": [ + 287, + 127, + 750, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sijin Chen1,2,∗, Xin Chen2,†, Anqi Pang2, Xianfang Zeng2, Wei Cheng2, Yijun Fu2, Fukun Yin1,2", + "bbox": [ + 194, + 229, + 805, + 246 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yanru Wang2, Zhibin Wang2, Chi Zhang2, Jingyi Yu3, Gang Yu2, Bin Fu2, Tao Chen1,‡", + "bbox": [ + 223, + 246, + 772, + 260 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://github.com/OpenMeshLab/MeshXL", + "bbox": [ + 352, + 261, + 642, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Fudan University 2Tencent PCG 3ShanghaiTech University", + "bbox": [ + 284, + 273, + 712, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "† project lead ‡ corresponding author", + "bbox": [ + 380, + 287, + 617, + 303 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bad59a0dbcab584b56c1908c15cc14424b2c80d21846732b59f69d53796ee558.jpg", + "image_caption": [ + "Figure 1: MeshXL can auto-regressively generate high-quality 3D meshes. We validate that Neural Coordinate Field (NeurCF), an explicit coordinate representation with implicit neural embeddings, is a simple-yet-effective sequence representation for large-scale mesh modelling." + ], + "image_footnote": [], + "content": "Collection of 3D wireframe models of various furniture and home items, including sofas, chairs, tables, and chairs (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 169, + 321, + 826, + 609 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 2, + "bbox": [ + 459, + 676, + 537, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The polygon mesh representation of 3D data exhibits great flexibility, fast rendering speed, and storage efficiency, which is widely preferred in various applications. However, given its unstructured graph representation, the direct generation of high-fidelity 3D meshes is challenging. Fortunately, with a pre-defined ordering strategy, 3D meshes can be represented as sequences, and the generation process can be seamlessly treated as an auto-regressive problem. In this paper, we validate the Neural Coordinate Field (NeurCF), an explicit coordinate representation with implicit neural embeddings, is a simple-yet-effective representation for largescale sequential mesh modeling. After that, we present MeshXL, a family of generative pre-trained auto-regressive models, which addresses the process of 3D mesh generation with modern large language model approaches. Extensive experiments show that MeshXL is able to generate high-quality 3D meshes, and can also serve as foundation models for various down-stream applications.", + "bbox": [ + 228, + 705, + 767, + 887 + ], + "page_idx": 0 + }, + { + "type": "aside_text", + "text": "arXiv:2405.20853v2 [cs.CV] 18 Jun 2024", + "bbox": [ + 22, + 265, + 57, + 707 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "∗Research done when Sijin Chen was a Research Intern at Tencent PCG.", + "bbox": [ + 191, + 898, + 624, + 912 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Introduction", + "text_level": 2, + "bbox": [ + 171, + 89, + 313, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The generation of high-quality 3D assets [61, 79, 29] is essential for various applications in video games, virtual reality, and robotics. Among existing 3D representations [51, 38, 57, 61], the 3D mesh represents the 3D data with graphs, which has the flexibility and accuracy for sharp edges as well as both flat and curved surfaces. However, the direct generation of high-quality 3D meshes is challenging, given 1) the unstructured graph representation and 2) the demand for accurate spatial locations and connectivity estimation within vertices.", + "bbox": [ + 169, + 119, + 823, + 203 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To generate 3D meshes, many works adopt an indirect way by first producing data in other 3D representations, including point clouds [99, 49, 54], SDF [90, 96], and multi-view images [46, 84, 30]. After that, re-meshing methods [37] are required for post-processing the generated geometries. There are also attempts towards the direct generation of 3D polynomial meshes. PolyGen [53] adopts two separate decoder-only transformers for vertices generation and connectivity prediction. MeshGPT [66] builds a mesh VQVAE to reconstruct the tokens generated by a GPT model [59] into 3D meshes. Meanwhile, PolyDiff [2] directly adopts discrete denoising diffusion [4] on the discretized mesh coordinates.", + "bbox": [ + 169, + 209, + 826, + 320 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Though these methods have achieved initial success in 3D assets generation, they suffer from certain limitations. To preserve high-frequency information, the point cloud and voxel representations will make dense samplings on the object surfaces, which inevitably lead to great redundancy when representing flat surfaces. The reconstruction-based methods [84, 30, 68], however, rely heavily on the quality of the multi-vew generation pipeline [46]. Additionally, the VQVAE-based 3D generation methods [90, 66] will inevitably result in cumulative errors when reconstructing the generated tokens into 3D structures.", + "bbox": [ + 169, + 327, + 823, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle the above challenges and explore the potential of scaling up 3D generative pre-training, we introduce a simple-yet-effective way of 3D mesh representation, the Neural Coordinate Field (NeurCF). NeurCF represents the explicit 3D coordinates with implicit neural embeddings. We show that with a pre-defined ordering strategy, the generation of 3D meshes can be formulated as an auto-regressive problem. After that, we present MeshXL, a family of generative pre-trained transformers [95, 59], for the direct generation of high-fidelity 3D meshes. Without resorting to intermediate 3D representations, NeurCF facilitates an end-to-end learning pipeline for the direct pre-training on large-scale 3D mesh data.", + "bbox": [ + 169, + 430, + 825, + 541 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "By organizing high-quality 3D assets from ShapeNet [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16], we achieve a collection of over 2.5 million 3D meshes to support large-scale generative pre-training. Extensive experiments demonstrate that the NeurCF representation facilitates MeshXL to generate higher-quality 3D meshes with an increased number of parameters and largescale pre-training data. By training on the collection of large-scale 3D mesh data, MeshXL can achieve better performance with larger numbers of parameters (Fig. 3 and Tab. 5), and surpass prior arts on multiple categories task of the ShapeNet dataset [9] (Tab. 3).", + "bbox": [ + 169, + 547, + 825, + 645 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions can be summarized as follows:", + "bbox": [ + 171, + 650, + 578, + 664 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "• We validate that Neural Coordinate Field is a simple-and-effective representation of 3D mesh, which is also friendly to large-scale auto-regressive pre-training.", + "• We present a family of MeshXLs that can be treated as strong base models for image-conditioned or text-conditioned 3D mesh generation tasks.", + "• We show that MeshXL surpasses state-of-the-art 3D mesh generation methods, and can produce delicate 3D meshes compatible with existing texturing methods." + ], + "bbox": [ + 169, + 676, + 823, + 770 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 Related Work", + "text_level": 2, + "bbox": [ + 171, + 789, + 321, + 804 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "First, we present a concise review of existing 3D representations. Subsequently, we discuss related works on 3D generation and recent efforts in developing 3D foundation models.", + "bbox": [ + 169, + 819, + 823, + 848 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Representations. Researchers have long sought for accurate and efficient methods to represent 3D data. Point Cloud [54, 57, 58, 91] captures the spatial positions of discrete points in the Euclidean space, which is preferred by various 3D sensors [15, 89, 67, 3, 7]. Mesh [53, 2, 66, 12] represents the 3D structure with graphs. By connecting the vertices with edges, mesh can also be interpreted into a set of polygons in the 3D space. Similar to point clouds, 3D Gaussians [38, 69] also record the discrete Euclidean distribution in 3D space. However, each point is represented by a 3D Gaussian distribution function parameterized by its covariance matrix, color, and opacity. Given their fast convergence and rendering speed, 3D gaussians are often utilized for 3D reconstruction. Neural Radiance Field (NeRF) [51, 5] constructs a learnable volumetric function f using neural networks trained on multi-view images. Due to its derivability and flexibility, NeRF is also favored for 3D generative models [46, 101, 78, 56]. Additionally, there are other 3D representations such as multi-view images [76, 92, 102], voxel fields [61, 13, 45], and signed distance fields [96], among others [65, 90, 64]. In this paper, we consider the Neural Coordinate Field (NeurCF), an explicit spatial representation with implicit neural embeddings, and investigate its potential for scalable 3D asset generation.", + "bbox": [ + 169, + 854, + 825, + 912 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2", + "bbox": [ + 493, + 935, + 504, + 946 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 169, + 90, + 826, + 243 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D Generation. With the exploration of various 3D representations and the collection of large-scale 3D datasets [17, 9, 16], researchers have also put much effort exploring the generation of high-fidelity 3D assets [42, 39]. The Generative Adversarial Network (GAN) [25, 82, 1, 33] produces synthetic 3D data with a generator G, and train a discriminator network D to distinguish the generated and real data. Additionally, the potential of diffusion models [54, 28, 62] in the direct generation of 3D data is also widely explored [99, 2, 54, 50, 47]. The key idea behind diffusion is to transform the desired data distribution into a simpler distribution (e.g. gaussian) and learn a desnoising model for the reverse process. Besides, researchers have also explored the potential of diffusion models in generating multi-view images [46, 16, 84, 43], and reconstruct them into 3D structures. In this paper, we mainly explore the auto-regressive methods for 3D generation. AutoSDF [52] and MeshGPT [66] learn to generate discrete tokens and reconstruct them into 3D representations with a VQVAE model [73]. PolyGen [53] adopts two decoder-only transformers that predict the location and connectivity of vertices, sequentially. In this paper, we explore the potential of an explicit sequential modelling method for 3D meshes, and present a family of generative pre-trained transformers, MeshXL, for high-fidelity 3D mesh generation.", + "bbox": [ + 169, + 250, + 826, + 459 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D Foundation Models. The collection of large-scale high-quality 3D data [17, 16, 9, 83, 72, 21, 22] builds up the foundation for various 3D-related tasks [85, 27, 10, 41]. To explore the scaling effects in 3D learning, researchers have made great endeavors in building 3D foundation models for 3D understanding [98, 44, 100, 87, 88, 94, 102], reconstruction [30, 80, 68, 46, 16, 86, 75], and generation [61, 29, 66, 8]. With the introduction of large-scale 3D data in both variety and granularity [34, 41, 16], existing 3D foundation models are capable of generalizing to unseen concepts [102, 88, 44], generating high-fidelity 3D assets [90, 36, 66], responding to complex instructions [31, 10, 32, 41], and generating actions that interacts with the 3D environments [20, 81, 97]. In this paper, we present a fully end-to-end 3D mesh generation pipeline, explore the scaling effect for large-scale pre-training, and test whether our method can serve as a well-trained foundation model for various down-stream tasks.", + "bbox": [ + 169, + 465, + 826, + 617 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 Data", + "text_level": 2, + "bbox": [ + 171, + 641, + 246, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Data Sources. We provide details on the 3D data collections we use to train and evaluate our models. The whole data collection is built upon four widely-acknowledged 3D mesh datasets, i.e. ShapeNet V2 [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16].", + "bbox": [ + 169, + 676, + 826, + 719 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "• ShapeNet V2 [9] collects about 51k 3D CAD models for 55 categories. We split the data in 9:1 for training and validation by each category.", + "• 3D-FUTURE [22] present about 10k high-quality 3D mesh data for indoor furniture. However, because of the delicate design, the objects contain many faces. Therefore, only a small proportion of the data can be used to train our MeshXL models.", + "• Objaverse [17] is a large 3D data collection with more than 800k 3D objects for about 21k categories collected from Sketchfab. We split the data in 99:1 for training and validation, respectively.", + "• Objaverse-XL [16] further expand Objaverse [17] into a dataset with more than 10M 3D objects with additional data collected from GitHub, Polycam, Thingiverse, and Smithsonian. We split the Github and Thingiverse part of the Objaverse-XL dataset into 99:1 for training and validation, respectively." + ], + "bbox": [ + 169, + 732, + 826, + 912 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3", + "bbox": [ + 493, + 935, + 503, + 946 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Data collection and filtering. To organize existing datasets, we build up a filtering and pre-processing pipeline to ensure that the meshes met our demand. We first collect meshes with fewer than 800 faces, and ensure that they have corresponding UV maps for rendering. After that, we render the 3D meshes, and discard those are not center-aligned or occupying less than 10% of the frame. For those 3D meshes with more than 800 but less than 20,000 faces, we use planar decimation whether their meshes can be simplified. Finally, we achieve approximately 2.5 million pieces of data remained.", + "bbox": [ + 169, + 90, + 823, + 175 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Planar Decimation Pipeline. To ensure the quality of the decimated 3D meshes, we make sure either a lower Hausdorff distance $\\delta _ { \\mathrm { h a u s d o r f f } }$ [66] or a similar rendered views [11].", + "bbox": [ + 169, + 181, + 823, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Collecting mesh-text pairs. We first render each 3D mesh with 12 different views, and concatenate them into one single image. Then, we annotate both the front view image and the fused multi-view image using CogVLM [77]. After that, we adopt the Mistral-7B-Instruct model [35] with few-shot in-context examples to extract information on category and geometry from the CogVLM annotations. We tag each 3D mesh with the resulting categories and 3 to 5 geometry descriptors.", + "bbox": [ + 169, + 218, + 826, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Collecting mesh-image pairs. To produce diverse image conditions for 3D mesh generation, we first generate images with multi-view image and depth rendering. After that, we use the sentences produced by CogVLM [77] as the prompt, and use a find-tuned Stable Diffusion model [63] to augment the rendered images for diverse textures and backgrounds. To ensure the quality of the generated images, we also adopt a manually cleansing procedure.", + "bbox": [ + 169, + 295, + 823, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Data Statistics. We present the data statistics of our large-scale 3D mesh collection in Tab. 1. After organizing and combing 3D assets from ShapeNet [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16], we could achieve a total of 2.5 million 3D meshes.", + "bbox": [ + 169, + 372, + 826, + 415 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/a75d2fc68468ed036d2e236d9a876b1cf72496d612e2bbd7f7b7a558740308d0.jpg", + "table_caption": [ + "Table 1: Statistics for the Training Data and Validation Data. After combining four data sources, our proposed MeshXL models are trained on approximately 2.5 million 3D meshes." + ], + "table_footnote": [], + "table_body": "
DatasetPre-trainingText-to-3D
TrainValTrainVal
ShapeNet [9]16,0011,75415,3841,728
3D-Future [22]1,603---
Objaverse [17]85,28285483,501820
Objaverse-XL [16]2,407,33715,2001,347,80213,579
Total2,510,22317,8081,446,67816,127
", + "bbox": [ + 272, + 462, + 725, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4 Neural Coordinate Field", + "text_level": 2, + "bbox": [ + 171, + 594, + 410, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Neural Coordinate Field (NeurCF) is an explicit representation with implicit neural embeddings. To be specific, for a Euclidean 3D coordinate system, we can partition the vertices coordinates into an $N ^ { 3 }$ grid. Then, each discretized coordinate $p = ( x , y , z )$ can be encoded with the coordinate embedding layer E, where $\\mathcal { F } ( \\boldsymbol { p } ) = ( \\mathcal { E } ( \\boldsymbol { x } ) , \\mathcal { E } ( \\boldsymbol { y } ) , \\mathcal { E } ( \\boldsymbol { z } ) )$ . Therefore, a k-sided polynomial face $f ^ { ( i ) }$ can be encoded with $\\mathcal { E } _ { \\mathrm { f a c e } } ( \\boldsymbol { f } ^ { ( i ) } ) = ( \\mathcal { F } ( \\boldsymbol { p } _ { 1 } ^ { ( i ) } ) , \\cdot \\cdot \\cdot , \\mathcal { F } ( \\boldsymbol { p } _ { k } ^ { ( i ) } ) )$ ). For simplicity, the learnable coordinate embeddings E are shared among axes.", + "bbox": [ + 169, + 625, + 823, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Ordering. Due to the graph representation, the order of the mesh vertices and the order of the edges between them are permutation-invariant. A pre-defined ordering strategy is essential to facilitate the sequence modelling in MeshXL. We employ the same ordering strategy as PolyGen [53] and MeshGPT [66]. The mesh coordinates are first normalized into a unit cube based on the mesh’s longest axis, and discretized into unsigned integers. Within each face, the vertices are cyclically permuted based their coordinates (z-y-x order, from lower to higher), which helps to preserve the direction of normal vectors. Then, we order these faces based on the permuted coordinates (lower to high). To this end, an n-faced 3D k-sided polynomial mesh can be represented as $\\mathcal { M } \\in \\mathbb { Z } ^ { n \\times k \\times 3 }$ , and we can encode M with $\\mathcal { E } _ { \\mathrm { m e s h } } = ( \\mathcal { E } _ { \\mathrm { f a c e } } ( f ^ { ( 1 ) } ) , \\cdot \\cdot \\cdot , \\mathcal { E } _ { \\mathrm { f a c e } } ( f ^ { ( n ) } ) )$ ).", + "bbox": [ + 169, + 720, + 823, + 849 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A Sequential Mesh Representation. One direct way to represent the 3D meshes is to directly reshape M into a vector with $( n \\cdot k \\cdot 3 )$ tokens. As a special case, an n-faced triangular mesh can be represented by a vector with 9n tokens. Meanwhile, our representation can also be expanded to hybrid polynomial mesh representations with the proper introduction of separate tokens. For example, we can generate triangles within “ · · · ” and quadrilaterals within “ · · · ”. To identify the start and end of a mesh sequence, we add a (“begin-of-sequence”) token before the mesh sequence and an (“end-of-sequence”) token after.", + "bbox": [ + 169, + 854, + 826, + 912 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4", + "bbox": [ + 493, + 935, + 504, + 946 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a630cfe35c3ec609be24eeec3d723fe2b40be6f1211dbc75599c6cd0359ed5a8.jpg", + "image_caption": [ + "(a) Neural Coordinate Field" + ], + "image_footnote": [], + "content": "```mermaid\ngraph LR\n A[\"Coordinate Embeddings: ε\"] --> B[\"p = (x,y,z)\"]\n B --> C[\"F(p) = (ε(x), ε(y), ε(z))\"]\n D[\"Face Embedding:\\nε_face(f^(i)) = (F(p_1^(i)), ..., F(p_k^(i)))\"]\n E[\"Mesh Embedding:\\nε_mesh(M) = (ε_face(f^(1)), ..., ε_face(f^(n)))\"]\n```", + "sub_type": "flowchart", + "bbox": [ + 192, + 92, + 514, + 210 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/51c707d52655b90586d370683125db668549db2f46c0499de79259dea0e59432.jpg", + "image_caption": [ + "(b) Auto-regressive Mesh Generation", + "Figure 2: Mesh Representation. We present the Neural Coordinate Field (NeurCF) to encode the discretized coordinates in the Euclidean space. Benefiting from NeurCF and a pre-defined ordering strategy, our proposed MeshXL can directly generate the unstructured 3D mesh auto-regressively." + ], + "image_footnote": [], + "content": "Next Coordinate Prediction", + "sub_type": "text_image", + "bbox": [ + 519, + 92, + 821, + 209 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "", + "bbox": [ + 169, + 305, + 825, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comparisons. Compared to other forms of 3D representations, NeurCF is a direct representation for 3D meshes. Since we represent each coordinate with learnable embeddings, NeurCF is an end-toend trainable representation for unstructured 3D meshes. Additionally, NeurCF is storage efficient comparing to voxel fields $( O ( N ^ { 3 } ) )$ ) and point clouds, since it can naturally model the flat surfaces with graph structures.", + "bbox": [ + 169, + 354, + 826, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5 Method", + "text_level": 2, + "bbox": [ + 171, + 443, + 272, + 458 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first present the architecture and training objective for MeshXL models. Then, we show that MeshXL models can take an additional modality as the condition for controllable 3D assets generation. After this, we investigate the effects of scaling.", + "bbox": [ + 169, + 474, + 826, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Architecture. In Sec. 4, we present a simple-yet-effective way to represent a 3D mesh into a sequence. Therefore, the learning of 3D mesh generation can be formulated into an auto-regressive problem, and can be seaminglessly addressed by modern Large Language Model (LLM) approaches. In our paper, we adopt the decoder-only transformers using the OPT [95] codebase as our base models. To adapt the pre-trained OPT models to our next-coordinate prediction setting, we fine-tune the whole model with newly-initialized coordinate and position embeddings.", + "bbox": [ + 169, + 523, + 823, + 608 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Generative Pre-Training. We use the standard next-token prediction loss to train our models. Given the trainable weights θ and an |s|-length sequence s, the generation loss is calculated as:", + "bbox": [ + 169, + 614, + 823, + 643 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {L} _ {\\mathrm{MeshXL}} \\left(\\theta\\right) = - \\sum_ {i = 1} ^ {| s |} \\log P \\left(s _ {[ i ]} | s _ {[ 1, \\dots , i - 1 ]}; \\theta\\right). \\tag {1}\n$$", + "text_format": "latex", + "bbox": [ + 341, + 652, + 825, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each mesh sequence, we add a token before the mesh tokens, and an token after the mesh tokens to identify the ending of a 3D mesh. During inference, we adopt the top-k and top-p sampling strategy to produce diverse outputs.", + "bbox": [ + 169, + 707, + 823, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "X-to-Mesh Generation. Here we mainly consider generating 3D meshes from images and texts. We adopt a pre-trained BERT [18] model for text feature encoding, and a pre-trained ViT [19] model for image feature encoding. To align the additional text/image feature with the mesh coordinate field, we adopt the Q-Former architecture [40] to compress the encoded feature into a fixed-length of 32 learnable tokens as the prefix of the MeshXL model. The overall training objective of the conditional mesh generation is shown in Eq. (2):", + "bbox": [ + 169, + 756, + 826, + 840 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {L} _ {\\mathcal {X} \\text {-to - mesh}} (\\theta) = - \\sum_ {i = 1} ^ {| s |} \\log P \\left(s _ {[ i ]} | s _ {[ 1, \\dots , i - 1 ]}; \\mathcal {X}\\right). \\tag {2}\n$$", + "text_format": "latex", + "bbox": [ + 331, + 848, + 825, + 888 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During inference, the model predicts the mesh tokens after the fixed-length prefix.", + "bbox": [ + 171, + 897, + 710, + 912 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5", + "bbox": [ + 493, + 935, + 503, + 946 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f5a493f49eb91e662a5f269332e0b435babbd67f87842f82cfe63479c24abc2f.jpg", + "image_caption": [ + "Figure 3: Training and Validation Perplexity (PPL) for MeshXL Models. We train all the models from scratch on 150 billion tokens. We observe that the performance grows with model sizes." + ], + "image_footnote": [], + "content": "", + "bbox": [ + 176, + 90, + 821, + 273 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Scaling Up. We present MeshXL in various sizes, including 125M, 350M, and 1.3B. The detailed hyperparameters for training different models can be found in Tab. 2. To better analyze the scaling effects, we train all models from scratch on 150 billion tokens. We provide both training curve and validation perplexity for different models in Fig. 3. One can see that as the number of parameters grows, the model achieves a lower validation perplexity, indicating a higher probability to produce the validation data.", + "bbox": [ + 169, + 342, + 823, + 426 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6 Experiments", + "text_level": 2, + "bbox": [ + 171, + 446, + 313, + 464 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first briefly introduce the data, metrics, and implementation details in Sec. 6.1. Then, we provide evaluations and comparisons on the generated meshes (cf. Sec. 6.2) and ablations (cf. Sec. 6.3). We also provide visualization results in Sec. 6.4.", + "bbox": [ + 169, + 478, + 823, + 520 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1 Data, Metrics, and Implementation Details", + "text_level": 2, + "bbox": [ + 171, + 537, + 511, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Data. We pre-train the base model with 2.5 million 3D meshes collected from the combination of ShapeNet [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16]. We use planar decimation on meshes with more than 800 faces following MeshGPT [66] and RobustLowPoly [11]. More details on the data collection and processing pipeline can be found in the appendix. For generative mesh pre-training, we randomly rotate these meshes with degrees from (0◦, 90◦, 180◦, 270◦), and adopt random scaling along each axis within range [0.9, 1.1] for data augmentation.", + "bbox": [ + 169, + 563, + 823, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We follow the standard evaluation protocols in MeshGPT [66] and PolyDiff [2] with the following metrics. Coverage (COV) is sensitive to mode dropping and is used to quantify the diversity of the generated meshes. However, COV does not assess the quality of the generated results. Minimum Matching Distance (MMD) calculates the average distance between the reference set and their closest neighbors in the generated set. However, MMD is not sensitive to low-quality results. The 1-Nearest Neighbor Accuracy (1-NNA) directly quantifies the quality and diversity between the generation set and the reference set. The optimal value of 1-NNA is 50%. We adopt the Jensen-Shannon Divergence (JSD) score to directly evaluate 3D meshes. We use Chamfer Distance to measure the similarity between two samples. We also adopt the Frechet Inception Distance (FID) and Kernel Inception Distance (KID) on the rendered images for feature-level evaluation. The MMD, JSD, and KID scores are multiplied by 103.", + "bbox": [ + 169, + 654, + 826, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation. All experiments are conducted on a cluster consisting of 128 A100 GPUs. We train our models under bfloat16 and the ZeRO-2 strategy [60] using the AdamW [48] optimizer with a learning rate decaying from $1 0 ^ { - 4 } ~ \\mathrm { t o } ~ 1 0 ^ { - 6 }$ and a weight decay of 0.1. The detailed hyperparameters for different models can be found in Tab. 2. To train our base models, we load the weights from the pre-trained OPT models [95] and initialize the word embeddings and positional embeddings from scratch. Without further specification, we generate 3D meshes with the top-k and top-p sampling strategy with k = 50 and p = 0.95.", + "bbox": [ + 169, + 814, + 823, + 912 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6", + "bbox": [ + 493, + 936, + 503, + 946 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4c5c6e15a6fac6fe7bb087b8c62cf0a5bf0719a0e52ba97300fa72f7d1d9a017.jpg", + "table_caption": [ + "Table 2: Hyperparameters for different MeshXL Base Models. We present three MeshXL models with 125M, 350M, and 1.3B parameters, respectively." + ], + "table_footnote": [], + "table_body": "
HyperparametersMeshXL(125M)MeshXL(350M)MeshXL(1.3B)
# Layers122424
# Heads121632
$d_{model}$ 7681,0242,048
$d_{FFN}$ 3,0724,0968,192
OptimizerAdamW( $\\beta_1$ =0.9, $\\beta_2$ =0.999)
Learning rate $1.0 \\times 10^{-4}$ $1.0 \\times 10^{-4}$ $1.0 \\times 10^{-4}$
LR schedulerCosineCosineCosine
Weight decay0.10.10.1
Gradient Clip1.01.01.0
Number of GPUs81632
# GPU hrs (A100)1,9446,00023,232
", + "bbox": [ + 241, + 125, + 756, + 299 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2 Evaluations and Comparisons", + "text_level": 2, + "bbox": [ + 169, + 323, + 421, + 339 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We provide quantitative as well as qualitative comparisons on both unconditional and conditional 3D mesh generation on public benchmarks", + "bbox": [ + 169, + 349, + 823, + 378 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Unconditional Generation. We evaluate MeshXL as well as other baseline methods using the ShapeNet [9] data in Tab. 3. We split the data by 9:1 for training and validation by each category. For evaluation, we fine-tune our pre-trained base model and sample 1,000 meshes for each category. Among the listed methods, we reproduce the MeshGPT [66] with a GPT2-medium model (355M) [59]. With a similar number of parameters, Mesh-XL (350M) out-performs MeshGPT by a large margin, showing a higher COV score, a lower MMD score, and a closer 1-NNA score to 50%. This indicates that MeshXL can produce diverse and high-quality 3D meshes.", + "bbox": [ + 169, + 383, + 826, + 482 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b6e8725a40f83bd4e3f1bda72c89293fd60376897fa53329d6b4ad7adaabf129.jpg", + "table_caption": [ + "Table 3: Quantitative Comparisons with Prior Arts on ShapeNet [9]. We scale MMD, JSD, KID by 103. MeshXL can produce diverse and high-quality 3D meshes." + ], + "table_footnote": [], + "table_body": "
CategoryMethodsCOV↑MMD↓1-NNAJSD↓FID↓KID↓
ChairPolyGen [53]7.7916.0099.16228.8063.4943.73
GET3D [23]11.7015.9299.75155.2567.8442.10
MeshGPT [66]42.004.7569.5055.1639.528.97
MeshXL (125M)50.803.1156.559.6928.151.48
MeshXL (350M)50.803.1755.809.6628.291.39
MeshXL (1.3B)51.603.2355.809.489.121.84
TablePolyGen [53]44.003.3667.2025.0654.0814.96
GET3D [23]16.8010.3991.90226.9767.6534.62
MeshGPT [66]34.306.5175.0592.8853.757.75
MeshXL (125M)51.212.9657.9612.8242.550.92
MeshXL (350M)49.703.0756.1013.6443.431.27
MeshXL (1.3B)52.122.9256.8014.9322.292.03
BenchPolyGen [53]31.154.0183.2355.2570.5312.1
MeshGPT [66]34.922.2268.6557.3252.476.49
MeshXL (125M)54.371.6543.7516.4335.310.82
MeshXL (350M)53.371.6542.9615.4136.350.96
MeshXL (1.3B)56.551.6239.7815.5135.501.60
LampPolyGen [53]35.047.8775.4996.5765.1512.78
MeshGPT [66]41.594.9261.5961.8247.195.19
MeshXL (125M)55.865.0648.2443.4134.610.84
MeshXL (350M)53.524.1849.4134.8725.941.92
MeshXL (1.3B)51.954.8947.2741.8931.660.99
", + "bbox": [ + 241, + 529, + 756, + 827 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "User Study. To evaluate how well the generated 3D meshes align with human preference, we perform user studies on the chair category in Tab. 4 with several baseline methods [53, 23]. We recruit and instruct the participants to score each mesh from 0 to 5 based on its 1) quality: the smoothness of object surfaces and completeness of the mesh, 2) artistic: how much do you believe this object is designed and created by artists, and 3) triangulation: how well do the connectivity among vertices aligns with the models created by professional designing software [14]. For the above mentioned metrics, the higher score means better quality. As a baseline evaluation, we also ask the participants to score the ground truth 3D geometries sampled from the ShapeNet data. We have collected a total of 434 valid responses. The results show that the 3D meshes created by MeshXL are consistently preferred by human in all dimensions.", + "bbox": [ + 169, + 842, + 825, + 912 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7", + "bbox": [ + 493, + 935, + 504, + 946 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d06e184c553ec05435444e2274b7f39c38c8637fb0ffbb95840c2be6c331d410.jpg", + "image_caption": [ + "Figure 4: Evaluation of Partial Mesh Completion. Given some partial observation of the 3D mesh (white), MeshXL is able to produce diverse object completion results (blue)." + ], + "image_footnote": [], + "content": "Input\nCompleted Mesh\nGround Truth", + "sub_type": "text_image", + "bbox": [ + 181, + 88, + 823, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 169, + 450, + 823, + 522 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7be20ee8332f4b4a39b7aed0272e9dae1f72d2090462df67fa45e41de61a8007.jpg", + "table_caption": [ + "Table 4: User Study. Compared to baseline methods, the meshes generated by MeshXL are better aligned with human preference in terms of both geometry and designs." + ], + "table_footnote": [], + "table_body": "
MethodsQuality↑Artistic↑Triangulation↑
PolyGen [53]2.532.723.15
GET3D [23]3.152.463.15
MeshXL3.963.453.72
Reals4.083.333.75
", + "bbox": [ + 321, + 569, + 674, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.3 Ablation Studies", + "text_level": 2, + "bbox": [ + 171, + 666, + 328, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Necessity of Mesh VQVAE. Comparing to MeshGPT [66], MeshXL is an end-to-end trainable model that produces 3D meshes with next-coordinate prediction. We show in Tab. 3 that, MeshXL outperforms MeshGPT with similar numbers of parameters. Furthermore, MeshXL can save the effort training a mesh autoencoder [66, 73], which further facilitates scaling up generative pre-training.", + "bbox": [ + 169, + 693, + 826, + 751 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Shape Completion. To analysis whether our method is capable of producing diverse outputs, we ask MeshXL (1.3B) model to predict the whole object given some partial observations of the 3D mesh. In practice, we use 50% of the object mesh as input, and ask the model to predict the rest 50% of the 3D mesh. We illustrate completion examples on chairs and tables in Fig. 4. One can see that Mesh-XL is able to produce diverse outputs given the partial observation of the 3D mesh.", + "bbox": [ + 169, + 756, + 826, + 828 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "X -to-Mesh Generation. We showcases several conditional generation results in Fig. 5. We show that MeshXL can generate high-quality 3D meshes given the corresponding image or text as the additional inputs.", + "bbox": [ + 169, + 833, + 823, + 877 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of Model Sizes. To analyze whether large-scale pre-training a larger model benefits 3D mesh generation, we evaluate MeshXL base models with different sizes on the Objaverse [17] dataset in Tab. 5. We observe that as the model size grows, the generated samples exhibits a closer 1-NNA to 50%, a larger COV, and smaller JSD score, which indicates an improving diversity and quality.", + "bbox": [ + 169, + 883, + 823, + 912 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8", + "bbox": [ + 493, + 935, + 503, + 946 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/94cdc9b3c5ee464d5f15cdcfe4da92287cb1c8599f3bf67892456c268bdd3ed2.jpg", + "image_caption": [ + "Figure 5: Evaluation of X -to-mesh generation. We show that MeshXL can generate high-quality 3D meshes given the corresponding image or text as the additional inputs." + ], + "image_footnote": [], + "content": "```mermaid\ngraph LR\n subgraph Image\n A1[\"Image\"] --> B1[\"Generated\"]\n B1 --> C1[\"Ground Truth\"]\n end\n\n subgraph Text\n D1[\"Text: "A basic chair with four leges and an open back."\"]\n E1[\"Text: "4 legs, solid seat and backing."\"]\n F1[\"Text: "A basic looking square wooden table."\"]\n end\n\n subgraph Ground Truth\n G1[\"Ground Truth\"]\n H1[\"Ground Truth\"]\n I1[\"Ground Truth\"]\n end\n\n B1 -.-> C1\n C1 -.-> D1\n C1 -.-> E1\n C1 -.-> F1\n C1 -.-> F1\n C1 -.-> I1\n C1 -.-> I1\n```", + "sub_type": "flowchart", + "bbox": [ + 178, + 99, + 823, + 349 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/0d0145de4d358ac6abbe978025ee1410f1a06e356a75c94e17ebed75daf318ad.jpg", + "image_caption": [ + "Figure 6: Texture Generation for the Generated 3D Meshes. We adopt Paint3D [93] to generate textures for 3D meshes produced by MeshXL." + ], + "image_footnote": [], + "content": "Generated Mesh\nTextured Mesh\nUV Map\nGenerated Mesh\nTextured Mesh\nUV Map", + "sub_type": "text_image", + "bbox": [ + 173, + 395, + 823, + 648 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "", + "bbox": [ + 169, + 705, + 823, + 736 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/6cb4e5ae622dcf2dea00c2743b764c9c6a73ee80191f4942cbd03f97a3629408.jpg", + "table_caption": [ + "Table 5: Effectiveness of Model Sizes on Objaverse. We observe that as the model size grows, the generated meshes exhibit a closer 1-NNA to 50%, a larger COV and a smaller JSD, indicating better diversity and quality." + ], + "table_footnote": [], + "table_body": "
MethodCOV↑MMD↓1-NNAJSD↓FID↓KID ↓
MeshXL (125M)39.765.2167.3426.0317.324.48
MeshXL (350M)40.795.2065.6823.7115.143.33
MeshXL (1.3B)42.864.1661.5620.9912.492.94
", + "bbox": [ + 274, + 796, + 723, + 854 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Texturing. We adopt Paint3D [93], a coarse-to-fine texture generation pipeline, to generate textures for the 3D meshes produced by MeshXL in Fig. 6. We show that 3D meshes produced by MeshXL can easily fit the existing texturing methods to produce high-quality 3D assets.", + "bbox": [ + 169, + 869, + 823, + 912 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "9", + "bbox": [ + 493, + 935, + 504, + 946 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/25d8b0ad0310574d3a5b0d0102818a9ac33b4b5aee0bf2849ed58541fd041bb1.jpg", + "image_caption": [ + "Figure 7: Qualitative comparison on the generated meshes. We present qualitative comparisons on the generated meshes as well as normal vectors. MeshXL is able to produce high-quality 3D meshes with both sharp edges and smooth surfaces." + ], + "image_footnote": [], + "content": "PolyGen\nGET3D\nMeshGPT\nMeshXL", + "sub_type": "text_image", + "bbox": [ + 181, + 90, + 826, + 324 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "6.4 Visualizations", + "text_level": 2, + "bbox": [ + 171, + 414, + 312, + 428 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "We provide qualitative comparisons on the meshes generated by our method as well as the meshes generated by other baseline models.", + "bbox": [ + 169, + 443, + 823, + 470 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Qualitative Comparison. We provide category specified visualization results as well as their normal vectors on the generated meshes in Fig. 7. With the ability to generate 3D meshes directly, MeshXL is able to produce high-quality 3D meshes with both sharp edges and smooth surfaces.", + "bbox": [ + 169, + 479, + 823, + 522 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Unconditional Results on ShapeNet. We visualize unconditional 3D mesh generation results for chair, table, lamp and bench in Fig. 8. One can see that MeshXL is able to produce diverse and high-quality 3D meshes.", + "bbox": [ + 169, + 529, + 823, + 571 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Unconditional Generation on Objaverse. We visualize 3D meshes randomly sampled from MeshXL base model in Fig. 9. After training on a large-scale collection of 3D mesh data, MeshXL is able to produce diverse and high-quality 3D meshes.", + "bbox": [ + 169, + 578, + 823, + 621 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "7 Discussions", + "text_level": 2, + "bbox": [ + 171, + 648, + 302, + 666 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Difference with PolyGen [53]. PolyGen explores the auto-regressive generation of 3D polynomial meshes with two transformers [74], i.e. the vertex transformer and theface transformer. PolyGen first generates a set of points representing the vertices of the 3D meshes with a vertex transformer. After that, PolyGen inputs the generated point cloud into the face transformer and predicts the connectivity among the generated with a face transformer. However, our proposed MeshXL is a more straightforward and end-to-end approach that directly generates the polynomial meshes auto-regressively with decoder-only transformers.", + "bbox": [ + 169, + 686, + 826, + 785 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Difference with MeshGPT [66]. MeshGPT consists of a mesh VQVAE [73] and a decoder-only transformer [59]. MeshGPT first learns a mesh VQVAE to quantize the 3D meshes into discrete tokens. After that, MeshGPT trains a decoder-only transformer to generate the discrete tokens for 3D mesh reconstruction. In comparison, our proposed MeshXL is an end-to-end method that learns the neural representation of coordinates and outputs 3D meshes directly.", + "bbox": [ + 169, + 792, + 823, + 862 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Extensibility. Our method, MeshXL, is built upon the concept of auto-regressive methods. Therefore, our method is not restricted to the decoder-only transformers [59, 95, 70, 71], and can also be extended to other causal language models (i.e. Mamba [26], RWKV [55], and xLSTM [6]).", + "bbox": [ + 169, + 869, + 826, + 912 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10", + "bbox": [ + 490, + 935, + 508, + 946 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/9823d03c3275775daf170f63688821882c8a92b19ce8a68090eae5adcd463cf8.jpg", + "image_caption": [ + "Figure 8: Gallery results. Additional generation results for chair, table, lamp, and bench." + ], + "image_footnote": [], + "content": "Collection of 3D wireframe models of various furniture and home items, including chairs, tables, lamps, and benches (no text or labels)", + "sub_type": "natural_image", + "bbox": [ + 96, + 127, + 906, + 847 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11", + "bbox": [ + 490, + 935, + 506, + 946 + ], + "page_idx": 10 + }, + { + "type": "image", + "img_path": "images/ce83307bf835382378c4d93301fb661bf5692d92a75bb66c2e0b398510477e6e.jpg", + "image_caption": [ + "Figure 9: Gallery results. MeshXL is able to produce diverse 3D meshes with high quality." + ], + "image_footnote": [], + "content": "Collection of 3D wireframe models of various architectural and furniture objects, no text or symbols present.", + "sub_type": "natural_image", + "bbox": [ + 109, + 119, + 903, + 864 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "12", + "bbox": [ + 490, + 935, + 509, + 946 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "8 Limitations, Future Work, and Conclusions", + "text_level": 2, + "bbox": [ + 171, + 89, + 571, + 107 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Limitations and Future Work. The main drawback of MeshXLs is the inference time. During sampling, MeshXL will generate 7,200 tokens for an 800-faced 3D mesh, which takes a relatively long time because of the auto-regressive process. As for future works, recent endeavors on the RNN-related methods [6, 55, 26] and multiple tokens prediction for LLMs [24] might open up great opportunities in saving the inference cost.", + "bbox": [ + 169, + 121, + 823, + 191 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Conclusion. We validate that NeurCF, an explicit coordinate representation with implicit neural embeddings, is a simple-and-effective representation of 3D meshes. By modelling the 3D mesh generation as an auto-regressive problem, we seek help from modern LLM approaches and present a family of generative pre-trained models, MeshXL, for high-fidelity 3D mesh generation. We show that MeshXL performs better given larger-scale training data and increased parameters. Extensive results show our proposed MeshXL can not only generate high-quality 3D meshes, but also exhibits great potential serving as base models for conditional 3D assets generation.", + "bbox": [ + 169, + 198, + 826, + 299 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "13", + "bbox": [ + 490, + 935, + 508, + 946 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "References", + "text_level": 2, + "bbox": [ + 173, + 89, + 267, + 104 + ], + "page_idx": 13 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40–49. PMLR, 2018.", + "[2] Antonio Alliegro, Yawar Siddiqui, Tatiana Tommasi, and Matthias Nießner. 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We validate that Neural Coordinate Field (NeurCF), an explicit coordinate representation with implicit neural embeddings, is a simple-yet-effective sequence representation for large-scale mesh modelling." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 169, + 321, + 826, + 609 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "Abstract" + } + ], + "level": 2 + }, + "bbox": [ + 459, + 676, + 537, + 691 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The polygon mesh representation of 3D data exhibits great flexibility, fast rendering speed, and storage efficiency, which is widely preferred in various applications. However, given its unstructured graph representation, the direct generation of high-fidelity 3D meshes is challenging. Fortunately, with a pre-defined ordering strategy, 3D meshes can be represented as sequences, and the generation process can be seamlessly treated as an auto-regressive problem. In this paper, we validate the Neural Coordinate Field (NeurCF), an explicit coordinate representation with implicit neural embeddings, is a simple-yet-effective representation for largescale sequential mesh modeling. After that, we present MeshXL, a family of generative pre-trained auto-regressive models, which addresses the process of 3D mesh generation with modern large language model approaches. Extensive experiments show that MeshXL is able to generate high-quality 3D meshes, and can also serve as foundation models for various down-stream applications." + } + ] + }, + "bbox": [ + 228, + 705, + 767, + 887 + ] + }, + { + "type": "page_aside_text", + "content": { + "page_aside_text_content": [ + { + "type": "text", + "content": "arXiv:2405.20853v2 [cs.CV] 18 Jun 2024" + } + ] + }, + "bbox": [ + 22, + 265, + 57, + 707 + ] + }, + { + "type": "page_footnote", + "content": { + "page_footnote_content": [ + { + "type": "text", + "content": "∗Research done when Sijin Chen was a Research Intern at Tencent PCG." + } + ] + }, + "bbox": [ + 191, + 898, + 624, + 912 + ] + } + ], + [ + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "1 Introduction" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 89, + 313, + 104 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The generation of high-quality 3D assets [61, 79, 29] is essential for various applications in video games, virtual reality, and robotics. Among existing 3D representations [51, 38, 57, 61], the 3D mesh represents the 3D data with graphs, which has the flexibility and accuracy for sharp edges as well as both flat and curved surfaces. However, the direct generation of high-quality 3D meshes is challenging, given 1) the unstructured graph representation and 2) the demand for accurate spatial locations and connectivity estimation within vertices." + } + ] + }, + "bbox": [ + 169, + 119, + 823, + 203 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "To generate 3D meshes, many works adopt an indirect way by first producing data in other 3D representations, including point clouds [99, 49, 54], SDF [90, 96], and multi-view images [46, 84, 30]. After that, re-meshing methods [37] are required for post-processing the generated geometries. There are also attempts towards the direct generation of 3D polynomial meshes. PolyGen [53] adopts two separate decoder-only transformers for vertices generation and connectivity prediction. MeshGPT [66] builds a mesh VQVAE to reconstruct the tokens generated by a GPT model [59] into 3D meshes. Meanwhile, PolyDiff [2] directly adopts discrete denoising diffusion [4] on the discretized mesh coordinates." + } + ] + }, + "bbox": [ + 169, + 209, + 826, + 320 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Though these methods have achieved initial success in 3D assets generation, they suffer from certain limitations. To preserve high-frequency information, the point cloud and voxel representations will make dense samplings on the object surfaces, which inevitably lead to great redundancy when representing flat surfaces. The reconstruction-based methods [84, 30, 68], however, rely heavily on the quality of the multi-vew generation pipeline [46]. Additionally, the VQVAE-based 3D generation methods [90, 66] will inevitably result in cumulative errors when reconstructing the generated tokens into 3D structures." + } + ] + }, + "bbox": [ + 169, + 327, + 823, + 422 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "To tackle the above challenges and explore the potential of scaling up 3D generative pre-training, we introduce a simple-yet-effective way of 3D mesh representation, the Neural Coordinate Field (NeurCF). NeurCF represents the explicit 3D coordinates with implicit neural embeddings. We show that with a pre-defined ordering strategy, the generation of 3D meshes can be formulated as an auto-regressive problem. After that, we present MeshXL, a family of generative pre-trained transformers [95, 59], for the direct generation of high-fidelity 3D meshes. Without resorting to intermediate 3D representations, NeurCF facilitates an end-to-end learning pipeline for the direct pre-training on large-scale 3D mesh data." + } + ] + }, + "bbox": [ + 169, + 430, + 825, + 541 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "By organizing high-quality 3D assets from ShapeNet [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16], we achieve a collection of over 2.5 million 3D meshes to support large-scale generative pre-training. Extensive experiments demonstrate that the NeurCF representation facilitates MeshXL to generate higher-quality 3D meshes with an increased number of parameters and largescale pre-training data. By training on the collection of large-scale 3D mesh data, MeshXL can achieve better performance with larger numbers of parameters (Fig. 3 and Tab. 5), and surpass prior arts on multiple categories task of the ShapeNet dataset [9] (Tab. 3)." + } + ] + }, + "bbox": [ + 169, + 547, + 825, + 645 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In summary, our contributions can be summarized as follows:" + } + ] + }, + "bbox": [ + 171, + 650, + 578, + 664 + ] + }, + { + "type": "list", + "content": { + "list_type": "text_list", + "list_items": [ + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "• We validate that Neural Coordinate Field is a simple-and-effective representation of 3D mesh, which is also friendly to large-scale auto-regressive pre-training." + } + ] + }, + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "• We present a family of MeshXLs that can be treated as strong base models for image-conditioned or text-conditioned 3D mesh generation tasks." + } + ] + }, + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "• We show that MeshXL surpasses state-of-the-art 3D mesh generation methods, and can produce delicate 3D meshes compatible with existing texturing methods." + } + ] + } + ] + }, + "bbox": [ + 169, + 676, + 823, + 770 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "2 Related Work" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 789, + 321, + 804 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "First, we present a concise review of existing 3D representations. Subsequently, we discuss related works on 3D generation and recent efforts in developing 3D foundation models." + } + ] + }, + "bbox": [ + 169, + 819, + 823, + 848 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "3D Representations. Researchers have long sought for accurate and efficient methods to represent 3D data. Point Cloud [54, 57, 58, 91] captures the spatial positions of discrete points in the Euclidean space, which is preferred by various 3D sensors [15, 89, 67, 3, 7]. Mesh [53, 2, 66, 12] represents the 3D structure with graphs. By connecting the vertices with edges, mesh can also be interpreted into a set of polygons in the 3D space. Similar to point clouds, 3D Gaussians [38, 69] also record the discrete Euclidean distribution in 3D space. However, each point is represented by a 3D Gaussian distribution function parameterized by its covariance matrix, color, and opacity. Given their fast convergence and rendering speed, 3D gaussians are often utilized for 3D reconstruction. Neural Radiance Field (NeRF) [51, 5] constructs a learnable volumetric function f using neural networks trained on multi-view images. Due to its derivability and flexibility, NeRF is also favored for 3D generative models [46, 101, 78, 56]. Additionally, there are other 3D representations such as multi-view images [76, 92, 102], voxel fields [61, 13, 45], and signed distance fields [96], among others [65, 90, 64]. In this paper, we consider the Neural Coordinate Field (NeurCF), an explicit spatial representation with implicit neural embeddings, and investigate its potential for scalable 3D asset generation." + } + ] + }, + "bbox": [ + 169, + 854, + 825, + 912 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "2" + } + ] + }, + "bbox": [ + 493, + 935, + 504, + 946 + ] + } + ], + [ + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 169, + 90, + 826, + 243 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "3D Generation. With the exploration of various 3D representations and the collection of large-scale 3D datasets [17, 9, 16], researchers have also put much effort exploring the generation of high-fidelity 3D assets [42, 39]. The Generative Adversarial Network (GAN) [25, 82, 1, 33] produces synthetic 3D data with a generator G, and train a discriminator network D to distinguish the generated and real data. Additionally, the potential of diffusion models [54, 28, 62] in the direct generation of 3D data is also widely explored [99, 2, 54, 50, 47]. The key idea behind diffusion is to transform the desired data distribution into a simpler distribution (e.g. gaussian) and learn a desnoising model for the reverse process. Besides, researchers have also explored the potential of diffusion models in generating multi-view images [46, 16, 84, 43], and reconstruct them into 3D structures. In this paper, we mainly explore the auto-regressive methods for 3D generation. AutoSDF [52] and MeshGPT [66] learn to generate discrete tokens and reconstruct them into 3D representations with a VQVAE model [73]. PolyGen [53] adopts two decoder-only transformers that predict the location and connectivity of vertices, sequentially. In this paper, we explore the potential of an explicit sequential modelling method for 3D meshes, and present a family of generative pre-trained transformers, MeshXL, for high-fidelity 3D mesh generation." + } + ] + }, + "bbox": [ + 169, + 250, + 826, + 459 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "3D Foundation Models. The collection of large-scale high-quality 3D data [17, 16, 9, 83, 72, 21, 22] builds up the foundation for various 3D-related tasks [85, 27, 10, 41]. To explore the scaling effects in 3D learning, researchers have made great endeavors in building 3D foundation models for 3D understanding [98, 44, 100, 87, 88, 94, 102], reconstruction [30, 80, 68, 46, 16, 86, 75], and generation [61, 29, 66, 8]. With the introduction of large-scale 3D data in both variety and granularity [34, 41, 16], existing 3D foundation models are capable of generalizing to unseen concepts [102, 88, 44], generating high-fidelity 3D assets [90, 36, 66], responding to complex instructions [31, 10, 32, 41], and generating actions that interacts with the 3D environments [20, 81, 97]. In this paper, we present a fully end-to-end 3D mesh generation pipeline, explore the scaling effect for large-scale pre-training, and test whether our method can serve as a well-trained foundation model for various down-stream tasks." + } + ] + }, + "bbox": [ + 169, + 465, + 826, + 617 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "3 Data" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 641, + 246, + 656 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Data Sources. We provide details on the 3D data collections we use to train and evaluate our models. The whole data collection is built upon four widely-acknowledged 3D mesh datasets, i.e. ShapeNet V2 [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16]." + } + ] + }, + "bbox": [ + 169, + 676, + 826, + 719 + ] + }, + { + "type": "list", + "content": { + "list_type": "text_list", + "list_items": [ + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "• ShapeNet V2 [9] collects about 51k 3D CAD models for 55 categories. We split the data in 9:1 for training and validation by each category." + } + ] + }, + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "• 3D-FUTURE [22] present about 10k high-quality 3D mesh data for indoor furniture. However, because of the delicate design, the objects contain many faces. Therefore, only a small proportion of the data can be used to train our MeshXL models." + } + ] + }, + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "• Objaverse [17] is a large 3D data collection with more than 800k 3D objects for about 21k categories collected from Sketchfab. We split the data in 99:1 for training and validation, respectively." + } + ] + }, + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "• Objaverse-XL [16] further expand Objaverse [17] into a dataset with more than 10M 3D objects with additional data collected from GitHub, Polycam, Thingiverse, and Smithsonian. We split the Github and Thingiverse part of the Objaverse-XL dataset into 99:1 for training and validation, respectively." + } + ] + } + ] + }, + "bbox": [ + 169, + 732, + 826, + 912 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "3" + } + ] + }, + "bbox": [ + 493, + 935, + 503, + 946 + ] + } + ], + [ + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Data collection and filtering. To organize existing datasets, we build up a filtering and pre-processing pipeline to ensure that the meshes met our demand. We first collect meshes with fewer than 800 faces, and ensure that they have corresponding UV maps for rendering. After that, we render the 3D meshes, and discard those are not center-aligned or occupying less than 10% of the frame. For those 3D meshes with more than 800 but less than 20,000 faces, we use planar decimation whether their meshes can be simplified. Finally, we achieve approximately 2.5 million pieces of data remained." + } + ] + }, + "bbox": [ + 169, + 90, + 823, + 175 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Planar Decimation Pipeline. To ensure the quality of the decimated 3D meshes, we make sure either a lower Hausdorff distance " + }, + { + "type": "equation_inline", + "content": "\\delta _ { \\mathrm { h a u s d o r f f } }" + }, + { + "type": "text", + "content": "[66] or a similar rendered views [11]." + } + ] + }, + "bbox": [ + 169, + 181, + 823, + 212 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Collecting mesh-text pairs. We first render each 3D mesh with 12 different views, and concatenate them into one single image. Then, we annotate both the front view image and the fused multi-view image using CogVLM [77]. After that, we adopt the Mistral-7B-Instruct model [35] with few-shot in-context examples to extract information on category and geometry from the CogVLM annotations. We tag each 3D mesh with the resulting categories and 3 to 5 geometry descriptors." + } + ] + }, + "bbox": [ + 169, + 218, + 826, + 287 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Collecting mesh-image pairs. To produce diverse image conditions for 3D mesh generation, we first generate images with multi-view image and depth rendering. After that, we use the sentences produced by CogVLM [77] as the prompt, and use a find-tuned Stable Diffusion model [63] to augment the rendered images for diverse textures and backgrounds. To ensure the quality of the generated images, we also adopt a manually cleansing procedure." + } + ] + }, + "bbox": [ + 169, + 295, + 823, + 364 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Data Statistics. We present the data statistics of our large-scale 3D mesh collection in Tab. 1. After organizing and combing 3D assets from ShapeNet [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16], we could achieve a total of 2.5 million 3D meshes." + } + ] + }, + "bbox": [ + 169, + 372, + 826, + 415 + ] + }, + { + "type": "table", + "content": { + "image_source": { + "path": "images/a75d2fc68468ed036d2e236d9a876b1cf72496d612e2bbd7f7b7a558740308d0.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 1: Statistics for the Training Data and Validation Data. After combining four data sources, our proposed MeshXL models are trained on approximately 2.5 million 3D meshes." + } + ], + "table_footnote": [], + "html": "
DatasetPre-trainingText-to-3D
TrainValTrainVal
ShapeNet [9]16,0011,75415,3841,728
3D-Future [22]1,603---
Objaverse [17]85,28285483,501820
Objaverse-XL [16]2,407,33715,2001,347,80213,579
Total2,510,22317,8081,446,67816,127
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Then, each discretized coordinate " + }, + { + "type": "equation_inline", + "content": "p = ( x , y , z )" + }, + { + "type": "text", + "content": "can be encoded with the coordinate embedding layer E, where " + }, + { + "type": "equation_inline", + "content": "\\mathcal { F } ( \\boldsymbol { p } ) = ( \\mathcal { E } ( \\boldsymbol { x } ) , \\mathcal { E } ( \\boldsymbol { y } ) , \\mathcal { E } ( \\boldsymbol { z } ) )" + }, + { + "type": "text", + "content": ". Therefore, a k-sided polynomial face " + }, + { + "type": "equation_inline", + "content": "f ^ { ( i ) }" + }, + { + "type": "text", + "content": "can be encoded with " + }, + { + "type": "equation_inline", + "content": "\\mathcal { E } _ { \\mathrm { f a c e } } ( \\boldsymbol { f } ^ { ( i ) } ) = ( \\mathcal { F } ( \\boldsymbol { p } _ { 1 } ^ { ( i ) } ) , \\cdot \\cdot \\cdot , \\mathcal { F } ( \\boldsymbol { p } _ { k } ^ { ( i ) } ) )" + }, + { + "type": "text", + "content": "). For simplicity, the learnable coordinate embeddings E are shared among axes." + } + ] + }, + "bbox": [ + 169, + 625, + 823, + 715 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Ordering. Due to the graph representation, the order of the mesh vertices and the order of the edges between them are permutation-invariant. A pre-defined ordering strategy is essential to facilitate the sequence modelling in MeshXL. We employ the same ordering strategy as PolyGen [53] and MeshGPT [66]. The mesh coordinates are first normalized into a unit cube based on the mesh’s longest axis, and discretized into unsigned integers. Within each face, the vertices are cyclically permuted based their coordinates (z-y-x order, from lower to higher), which helps to preserve the direction of normal vectors. Then, we order these faces based on the permuted coordinates (lower to high). To this end, an n-faced 3D k-sided polynomial mesh can be represented as " + }, + { + "type": "equation_inline", + "content": "\\mathcal { M } \\in \\mathbb { Z } ^ { n \\times k \\times 3 }" + }, + { + "type": "text", + "content": ", and we can encode M with " + }, + { + "type": "equation_inline", + "content": "\\mathcal { E } _ { \\mathrm { m e s h } } = ( \\mathcal { E } _ { \\mathrm { f a c e } } ( f ^ { ( 1 ) } ) , \\cdot \\cdot \\cdot , \\mathcal { E } _ { \\mathrm { f a c e } } ( f ^ { ( n ) } ) )" + }, + { + "type": "text", + "content": ")." + } + ] + }, + "bbox": [ + 169, + 720, + 823, + 849 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "A Sequential Mesh Representation. One direct way to represent the 3D meshes is to directly reshape M into a vector with " + }, + { + "type": "equation_inline", + "content": "( n \\cdot k \\cdot 3 )" + }, + { + "type": "text", + "content": "tokens. As a special case, an n-faced triangular mesh can be represented by a vector with 9n tokens. Meanwhile, our representation can also be expanded to hybrid polynomial mesh representations with the proper introduction of separate tokens. For example, we can generate triangles within “ · · · ” and quadrilaterals within “ · · · ”. To identify the start and end of a mesh sequence, we add a (“begin-of-sequence”) token before the mesh sequence and an (“end-of-sequence”) token after." + } + ] + }, + "bbox": [ + 169, + 854, + 826, + 912 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "4" + } + ] + }, + "bbox": [ + 493, + 935, + 504, + 946 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/a630cfe35c3ec609be24eeec3d723fe2b40be6f1211dbc75599c6cd0359ed5a8.jpg" + }, + "content": "```mermaid\ngraph LR\n A[\"Coordinate Embeddings: ε\"] --> B[\"p = (x,y,z)\"]\n B --> C[\"F(p) = (ε(x), ε(y), ε(z))\"]\n D[\"Face Embedding:\\nε_face(f^(i)) = (F(p_1^(i)), ..., F(p_k^(i)))\"]\n E[\"Mesh Embedding:\\nε_mesh(M) = (ε_face(f^(1)), ..., ε_face(f^(n)))\"]\n```", + "image_caption": [ + { + "type": "text", + "content": "(a) Neural Coordinate Field" + } + ], + "image_footnote": [] + }, + "sub_type": "flowchart", + "bbox": [ + 192, + 92, + 514, + 210 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/51c707d52655b90586d370683125db668549db2f46c0499de79259dea0e59432.jpg" + }, + "content": "Next Coordinate Prediction", + "image_caption": [ + { + "type": "text", + "content": "(b) Auto-regressive Mesh Generation" + }, + { + "type": "text", + "content": "Figure 2: Mesh Representation. We present the Neural Coordinate Field (NeurCF) to encode the discretized coordinates in the Euclidean space. Benefiting from NeurCF and a pre-defined ordering strategy, our proposed MeshXL can directly generate the unstructured 3D mesh auto-regressively." + } + ], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 519, + 92, + 821, + 209 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 169, + 305, + 825, + 348 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Comparisons. Compared to other forms of 3D representations, NeurCF is a direct representation for 3D meshes. Since we represent each coordinate with learnable embeddings, NeurCF is an end-toend trainable representation for unstructured 3D meshes. Additionally, NeurCF is storage efficient comparing to voxel fields " + }, + { + "type": "equation_inline", + "content": "( O ( N ^ { 3 } ) )" + }, + { + "type": "text", + "content": ") and point clouds, since it can naturally model the flat surfaces with graph structures." + } + ] + }, + "bbox": [ + 169, + 354, + 826, + 425 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "5 Method" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 443, + 272, + 458 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We first present the architecture and training objective for MeshXL models. Then, we show that MeshXL models can take an additional modality as the condition for controllable 3D assets generation. After this, we investigate the effects of scaling." + } + ] + }, + "bbox": [ + 169, + 474, + 826, + 517 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Architecture. In Sec. 4, we present a simple-yet-effective way to represent a 3D mesh into a sequence. Therefore, the learning of 3D mesh generation can be formulated into an auto-regressive problem, and can be seaminglessly addressed by modern Large Language Model (LLM) approaches. In our paper, we adopt the decoder-only transformers using the OPT [95] codebase as our base models. To adapt the pre-trained OPT models to our next-coordinate prediction setting, we fine-tune the whole model with newly-initialized coordinate and position embeddings." + } + ] + }, + "bbox": [ + 169, + 523, + 823, + 608 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Generative Pre-Training. We use the standard next-token prediction loss to train our models. Given the trainable weights θ and an |s|-length sequence s, the generation loss is calculated as:" + } + ] + }, + "bbox": [ + 169, + 614, + 823, + 643 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {L} _ {\\mathrm{MeshXL}} \\left(\\theta\\right) = - \\sum_ {i = 1} ^ {| s |} \\log P \\left(s _ {[ i ]} | s _ {[ 1, \\dots , i - 1 ]}; \\theta\\right). \\tag {1}", + "math_type": "latex", + "image_source": { + "path": "images/65c96116172ab6b1d9061673ef89a187bc94b20443f6afc5971bb03cf0744c40.jpg" + } + }, + "bbox": [ + 341, + 652, + 825, + 694 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "For each mesh sequence, we add a token before the mesh tokens, and an token after the mesh tokens to identify the ending of a 3D mesh. During inference, we adopt the top-k and top-p sampling strategy to produce diverse outputs." + } + ] + }, + "bbox": [ + 169, + 707, + 823, + 750 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "X-to-Mesh Generation. Here we mainly consider generating 3D meshes from images and texts. We adopt a pre-trained BERT [18] model for text feature encoding, and a pre-trained ViT [19] model for image feature encoding. To align the additional text/image feature with the mesh coordinate field, we adopt the Q-Former architecture [40] to compress the encoded feature into a fixed-length of 32 learnable tokens as the prefix of the MeshXL model. The overall training objective of the conditional mesh generation is shown in Eq. (2):" + } + ] + }, + "bbox": [ + 169, + 756, + 826, + 840 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {L} _ {\\mathcal {X} \\text {-to - mesh}} (\\theta) = - \\sum_ {i = 1} ^ {| s |} \\log P \\left(s _ {[ i ]} | s _ {[ 1, \\dots , i - 1 ]}; \\mathcal {X}\\right). \\tag {2}", + "math_type": "latex", + "image_source": { + "path": "images/04938518bf9de86d30af320478a6e132d9a28a19e6a24234c3a8a3eb6e54467e.jpg" + } + }, + "bbox": [ + 331, + 848, + 825, + 888 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "During inference, the model predicts the mesh tokens after the fixed-length prefix." + } + ] + }, + "bbox": [ + 171, + 897, + 710, + 912 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "5" + } + ] + }, + "bbox": [ + 493, + 935, + 503, + 946 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/f5a493f49eb91e662a5f269332e0b435babbd67f87842f82cfe63479c24abc2f.jpg" + }, + "content": "", + "image_caption": [ + { + "type": "text", + "content": "Figure 3: Training and Validation Perplexity (PPL) for MeshXL Models. We train all the models from scratch on 150 billion tokens. We observe that the performance grows with model sizes." + } + ], + "image_footnote": [] + }, + "bbox": [ + 176, + 90, + 821, + 273 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Scaling Up. We present MeshXL in various sizes, including 125M, 350M, and 1.3B. The detailed hyperparameters for training different models can be found in Tab. 2. To better analyze the scaling effects, we train all models from scratch on 150 billion tokens. We provide both training curve and validation perplexity for different models in Fig. 3. One can see that as the number of parameters grows, the model achieves a lower validation perplexity, indicating a higher probability to produce the validation data." + } + ] + }, + "bbox": [ + 169, + 342, + 823, + 426 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "6 Experiments" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 446, + 313, + 464 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We first briefly introduce the data, metrics, and implementation details in Sec. 6.1. Then, we provide evaluations and comparisons on the generated meshes (cf. Sec. 6.2) and ablations (cf. Sec. 6.3). We also provide visualization results in Sec. 6.4." + } + ] + }, + "bbox": [ + 169, + 478, + 823, + 520 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "6.1 Data, Metrics, and Implementation Details" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 537, + 511, + 551 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Data. We pre-train the base model with 2.5 million 3D meshes collected from the combination of ShapeNet [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16]. We use planar decimation on meshes with more than 800 faces following MeshGPT [66] and RobustLowPoly [11]. More details on the data collection and processing pipeline can be found in the appendix. For generative mesh pre-training, we randomly rotate these meshes with degrees from (0◦, 90◦, 180◦, 270◦), and adopt random scaling along each axis within range [0.9, 1.1] for data augmentation." + } + ] + }, + "bbox": [ + 169, + 563, + 823, + 648 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Metrics. We follow the standard evaluation protocols in MeshGPT [66] and PolyDiff [2] with the following metrics. Coverage (COV) is sensitive to mode dropping and is used to quantify the diversity of the generated meshes. However, COV does not assess the quality of the generated results. Minimum Matching Distance (MMD) calculates the average distance between the reference set and their closest neighbors in the generated set. However, MMD is not sensitive to low-quality results. The 1-Nearest Neighbor Accuracy (1-NNA) directly quantifies the quality and diversity between the generation set and the reference set. The optimal value of 1-NNA is 50%. We adopt the Jensen-Shannon Divergence (JSD) score to directly evaluate 3D meshes. We use Chamfer Distance to measure the similarity between two samples. We also adopt the Frechet Inception Distance (FID) and Kernel Inception Distance (KID) on the rendered images for feature-level evaluation. The MMD, JSD, and KID scores are multiplied by 103." + } + ] + }, + "bbox": [ + 169, + 654, + 826, + 808 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Implementation. All experiments are conducted on a cluster consisting of 128 A100 GPUs. We train our models under bfloat16 and the ZeRO-2 strategy [60] using the AdamW [48] optimizer with a learning rate decaying from " + }, + { + "type": "equation_inline", + "content": "1 0 ^ { - 4 } ~ \\mathrm { t o } ~ 1 0 ^ { - 6 }" + }, + { + "type": "text", + "content": "and a weight decay of 0.1. The detailed hyperparameters for different models can be found in Tab. 2. To train our base models, we load the weights from the pre-trained OPT models [95] and initialize the word embeddings and positional embeddings from scratch. Without further specification, we generate 3D meshes with the top-k and top-p sampling strategy with k = 50 and p = 0.95." + } + ] + }, + "bbox": [ + 169, + 814, + 823, + 912 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "6" + } + ] + }, + "bbox": [ + 493, + 936, + 503, + 946 + ] + } + ], + [ + { + "type": "table", + "content": { + "image_source": { + "path": "images/4c5c6e15a6fac6fe7bb087b8c62cf0a5bf0719a0e52ba97300fa72f7d1d9a017.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 2: Hyperparameters for different MeshXL Base Models. We present three MeshXL models with 125M, 350M, and 1.3B parameters, respectively." + } + ], + "table_footnote": [], + "html": "
HyperparametersMeshXL(125M)MeshXL(350M)MeshXL(1.3B)
# Layers122424
# Heads121632
$d_{model}$ 7681,0242,048
$d_{FFN}$ 3,0724,0968,192
OptimizerAdamW( $\\beta_1$ =0.9, $\\beta_2$ =0.999)
Learning rate $1.0 \\times 10^{-4}$ $1.0 \\times 10^{-4}$ $1.0 \\times 10^{-4}$
LR schedulerCosineCosineCosine
Weight decay0.10.10.1
Gradient Clip1.01.01.0
Number of GPUs81632
# GPU hrs (A100)1,9446,00023,232
", + "table_type": "complex_table", + "table_nest_level": 1 + }, + "bbox": [ + 241, + 125, + 756, + 299 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "6.2 Evaluations and Comparisons" + } + ], + "level": 2 + }, + "bbox": [ + 169, + 323, + 421, + 339 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We provide quantitative as well as qualitative comparisons on both unconditional and conditional 3D mesh generation on public benchmarks" + } + ] + }, + "bbox": [ + 169, + 349, + 823, + 378 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Unconditional Generation. We evaluate MeshXL as well as other baseline methods using the ShapeNet [9] data in Tab. 3. We split the data by 9:1 for training and validation by each category. For evaluation, we fine-tune our pre-trained base model and sample 1,000 meshes for each category. Among the listed methods, we reproduce the MeshGPT [66] with a GPT2-medium model (355M) [59]. With a similar number of parameters, Mesh-XL (350M) out-performs MeshGPT by a large margin, showing a higher COV score, a lower MMD score, and a closer 1-NNA score to 50%. This indicates that MeshXL can produce diverse and high-quality 3D meshes." + } + ] + }, + "bbox": [ + 169, + 383, + 826, + 482 + ] + }, + { + "type": "table", + "content": { + "image_source": { + "path": "images/b6e8725a40f83bd4e3f1bda72c89293fd60376897fa53329d6b4ad7adaabf129.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 3: Quantitative Comparisons with Prior Arts on ShapeNet [9]. We scale MMD, JSD, KID by 103. MeshXL can produce diverse and high-quality 3D meshes." + } + ], + "table_footnote": [], + "html": "
CategoryMethodsCOV↑MMD↓1-NNAJSD↓FID↓KID↓
ChairPolyGen [53]7.7916.0099.16228.8063.4943.73
GET3D [23]11.7015.9299.75155.2567.8442.10
MeshGPT [66]42.004.7569.5055.1639.528.97
MeshXL (125M)50.803.1156.559.6928.151.48
MeshXL (350M)50.803.1755.809.6628.291.39
MeshXL (1.3B)51.603.2355.809.489.121.84
TablePolyGen [53]44.003.3667.2025.0654.0814.96
GET3D [23]16.8010.3991.90226.9767.6534.62
MeshGPT [66]34.306.5175.0592.8853.757.75
MeshXL (125M)51.212.9657.9612.8242.550.92
MeshXL (350M)49.703.0756.1013.6443.431.27
MeshXL (1.3B)52.122.9256.8014.9322.292.03
BenchPolyGen [53]31.154.0183.2355.2570.5312.1
MeshGPT [66]34.922.2268.6557.3252.476.49
MeshXL (125M)54.371.6543.7516.4335.310.82
MeshXL (350M)53.371.6542.9615.4136.350.96
MeshXL (1.3B)56.551.6239.7815.5135.501.60
LampPolyGen [53]35.047.8775.4996.5765.1512.78
MeshGPT [66]41.594.9261.5961.8247.195.19
MeshXL (125M)55.865.0648.2443.4134.610.84
MeshXL (350M)53.524.1849.4134.8725.941.92
MeshXL (1.3B)51.954.8947.2741.8931.660.99
", + "table_type": "complex_table", + "table_nest_level": 1 + }, + "bbox": [ + 241, + 529, + 756, + 827 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "User Study. To evaluate how well the generated 3D meshes align with human preference, we perform user studies on the chair category in Tab. 4 with several baseline methods [53, 23]. We recruit and instruct the participants to score each mesh from 0 to 5 based on its 1) quality: the smoothness of object surfaces and completeness of the mesh, 2) artistic: how much do you believe this object is designed and created by artists, and 3) triangulation: how well do the connectivity among vertices aligns with the models created by professional designing software [14]. For the above mentioned metrics, the higher score means better quality. As a baseline evaluation, we also ask the participants to score the ground truth 3D geometries sampled from the ShapeNet data. We have collected a total of 434 valid responses. The results show that the 3D meshes created by MeshXL are consistently preferred by human in all dimensions." + } + ] + }, + "bbox": [ + 169, + 842, + 825, + 912 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "7" + } + ] + }, + "bbox": [ + 493, + 935, + 504, + 946 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/d06e184c553ec05435444e2274b7f39c38c8637fb0ffbb95840c2be6c331d410.jpg" + }, + "content": "Input\nCompleted Mesh\nGround Truth", + "image_caption": [ + { + "type": "text", + "content": "Figure 4: Evaluation of Partial Mesh Completion. Given some partial observation of the 3D mesh (white), MeshXL is able to produce diverse object completion results (blue)." + } + ], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 181, + 88, + 823, + 388 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 169, + 450, + 823, + 522 + ] + }, + { + "type": "table", + "content": { + "image_source": { + "path": "images/7be20ee8332f4b4a39b7aed0272e9dae1f72d2090462df67fa45e41de61a8007.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 4: User Study. Compared to baseline methods, the meshes generated by MeshXL are better aligned with human preference in terms of both geometry and designs." + } + ], + "table_footnote": [], + "html": "
MethodsQuality↑Artistic↑Triangulation↑
PolyGen [53]2.532.723.15
GET3D [23]3.152.463.15
MeshXL3.963.453.72
Reals4.083.333.75
", + "table_type": "simple_table", + "table_nest_level": 1 + }, + "bbox": [ + 321, + 569, + 674, + 643 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "6.3 Ablation Studies" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 666, + 328, + 681 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Necessity of Mesh VQVAE. Comparing to MeshGPT [66], MeshXL is an end-to-end trainable model that produces 3D meshes with next-coordinate prediction. We show in Tab. 3 that, MeshXL outperforms MeshGPT with similar numbers of parameters. Furthermore, MeshXL can save the effort training a mesh autoencoder [66, 73], which further facilitates scaling up generative pre-training." + } + ] + }, + "bbox": [ + 169, + 693, + 826, + 751 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Shape Completion. To analysis whether our method is capable of producing diverse outputs, we ask MeshXL (1.3B) model to predict the whole object given some partial observations of the 3D mesh. In practice, we use 50% of the object mesh as input, and ask the model to predict the rest 50% of the 3D mesh. We illustrate completion examples on chairs and tables in Fig. 4. One can see that Mesh-XL is able to produce diverse outputs given the partial observation of the 3D mesh." + } + ] + }, + "bbox": [ + 169, + 756, + 826, + 828 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "X -to-Mesh Generation. We showcases several conditional generation results in Fig. 5. We show that MeshXL can generate high-quality 3D meshes given the corresponding image or text as the additional inputs." + } + ] + }, + "bbox": [ + 169, + 833, + 823, + 877 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Effectiveness of Model Sizes. To analyze whether large-scale pre-training a larger model benefits 3D mesh generation, we evaluate MeshXL base models with different sizes on the Objaverse [17] dataset in Tab. 5. We observe that as the model size grows, the generated samples exhibits a closer 1-NNA to 50%, a larger COV, and smaller JSD score, which indicates an improving diversity and quality." + } + ] + }, + "bbox": [ + 169, + 883, + 823, + 912 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "8" + } + ] + }, + "bbox": [ + 493, + 935, + 503, + 946 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/94cdc9b3c5ee464d5f15cdcfe4da92287cb1c8599f3bf67892456c268bdd3ed2.jpg" + }, + "content": "```mermaid\ngraph LR\n subgraph Image\n A1[\"Image\"] --> B1[\"Generated\"]\n B1 --> C1[\"Ground Truth\"]\n end\n\n subgraph Text\n D1[\"Text: "A basic chair with four leges and an open back."\"]\n E1[\"Text: "4 legs, solid seat and backing."\"]\n F1[\"Text: "A basic looking square wooden table."\"]\n end\n\n subgraph Ground Truth\n G1[\"Ground Truth\"]\n H1[\"Ground Truth\"]\n I1[\"Ground Truth\"]\n end\n\n B1 -.-> C1\n C1 -.-> D1\n C1 -.-> E1\n C1 -.-> F1\n C1 -.-> F1\n C1 -.-> I1\n C1 -.-> I1\n```", + "image_caption": [ + { + "type": "text", + "content": "Figure 5: Evaluation of X -to-mesh generation. We show that MeshXL can generate high-quality 3D meshes given the corresponding image or text as the additional inputs." + } + ], + "image_footnote": [] + }, + "sub_type": "flowchart", + "bbox": [ + 178, + 99, + 823, + 349 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/0d0145de4d358ac6abbe978025ee1410f1a06e356a75c94e17ebed75daf318ad.jpg" + }, + "content": "Generated Mesh\nTextured Mesh\nUV Map\nGenerated Mesh\nTextured Mesh\nUV Map", + "image_caption": [ + { + "type": "text", + "content": "Figure 6: Texture Generation for the Generated 3D Meshes. We adopt Paint3D [93] to generate textures for 3D meshes produced by MeshXL." + } + ], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 173, + 395, + 823, + 648 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 169, + 705, + 823, + 736 + ] + }, + { + "type": "table", + "content": { + "image_source": { + "path": "images/6cb4e5ae622dcf2dea00c2743b764c9c6a73ee80191f4942cbd03f97a3629408.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 5: Effectiveness of Model Sizes on Objaverse. We observe that as the model size grows, the generated meshes exhibit a closer 1-NNA to 50%, a larger COV and a smaller JSD, indicating better diversity and quality." + } + ], + "table_footnote": [], + "html": "
MethodCOV↑MMD↓1-NNAJSD↓FID↓KID ↓
MeshXL (125M)39.765.2167.3426.0317.324.48
MeshXL (350M)40.795.2065.6823.7115.143.33
MeshXL (1.3B)42.864.1661.5620.9912.492.94
", + "table_type": "simple_table", + "table_nest_level": 1 + }, + "bbox": [ + 274, + 796, + 723, + 854 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Texturing. We adopt Paint3D [93], a coarse-to-fine texture generation pipeline, to generate textures for the 3D meshes produced by MeshXL in Fig. 6. We show that 3D meshes produced by MeshXL can easily fit the existing texturing methods to produce high-quality 3D assets." + } + ] + }, + "bbox": [ + 169, + 869, + 823, + 912 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "9" + } + ] + }, + "bbox": [ + 493, + 935, + 504, + 946 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/25d8b0ad0310574d3a5b0d0102818a9ac33b4b5aee0bf2849ed58541fd041bb1.jpg" + }, + "content": "PolyGen\nGET3D\nMeshGPT\nMeshXL", + "image_caption": [ + { + "type": "text", + "content": "Figure 7: Qualitative comparison on the generated meshes. We present qualitative comparisons on the generated meshes as well as normal vectors. MeshXL is able to produce high-quality 3D meshes with both sharp edges and smooth surfaces." + } + ], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 181, + 90, + 826, + 324 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "6.4 Visualizations" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 414, + 312, + 428 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We provide qualitative comparisons on the meshes generated by our method as well as the meshes generated by other baseline models." + } + ] + }, + "bbox": [ + 169, + 443, + 823, + 470 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Qualitative Comparison. We provide category specified visualization results as well as their normal vectors on the generated meshes in Fig. 7. With the ability to generate 3D meshes directly, MeshXL is able to produce high-quality 3D meshes with both sharp edges and smooth surfaces." + } + ] + }, + "bbox": [ + 169, + 479, + 823, + 522 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Unconditional Results on ShapeNet. We visualize unconditional 3D mesh generation results for chair, table, lamp and bench in Fig. 8. One can see that MeshXL is able to produce diverse and high-quality 3D meshes." + } + ] + }, + "bbox": [ + 169, + 529, + 823, + 571 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Unconditional Generation on Objaverse. We visualize 3D meshes randomly sampled from MeshXL base model in Fig. 9. After training on a large-scale collection of 3D mesh data, MeshXL is able to produce diverse and high-quality 3D meshes." + } + ] + }, + "bbox": [ + 169, + 578, + 823, + 621 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "7 Discussions" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 648, + 302, + 666 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Difference with PolyGen [53]. PolyGen explores the auto-regressive generation of 3D polynomial meshes with two transformers [74], i.e. the vertex transformer and theface transformer. PolyGen first generates a set of points representing the vertices of the 3D meshes with a vertex transformer. After that, PolyGen inputs the generated point cloud into the face transformer and predicts the connectivity among the generated with a face transformer. However, our proposed MeshXL is a more straightforward and end-to-end approach that directly generates the polynomial meshes auto-regressively with decoder-only transformers." + } + ] + }, + "bbox": [ + 169, + 686, + 826, + 785 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Difference with MeshGPT [66]. MeshGPT consists of a mesh VQVAE [73] and a decoder-only transformer [59]. MeshGPT first learns a mesh VQVAE to quantize the 3D meshes into discrete tokens. After that, MeshGPT trains a decoder-only transformer to generate the discrete tokens for 3D mesh reconstruction. In comparison, our proposed MeshXL is an end-to-end method that learns the neural representation of coordinates and outputs 3D meshes directly." + } + ] + }, + "bbox": [ + 169, + 792, + 823, + 862 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Extensibility. Our method, MeshXL, is built upon the concept of auto-regressive methods. Therefore, our method is not restricted to the decoder-only transformers [59, 95, 70, 71], and can also be extended to other causal language models (i.e. Mamba [26], RWKV [55], and xLSTM [6])." + } + ] + }, + "bbox": [ + 169, + 869, + 826, + 912 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "10" + } + ] + }, + "bbox": [ + 490, + 935, + 508, + 946 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/9823d03c3275775daf170f63688821882c8a92b19ce8a68090eae5adcd463cf8.jpg" + }, + "content": "Collection of 3D wireframe models of various furniture and home items, including chairs, tables, lamps, and benches (no text or labels)", + "image_caption": [ + { + "type": "text", + "content": "Figure 8: Gallery results. Additional generation results for chair, table, lamp, and bench." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 96, + 127, + 906, + 847 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "11" + } + ] + }, + "bbox": [ + 490, + 935, + 506, + 946 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/ce83307bf835382378c4d93301fb661bf5692d92a75bb66c2e0b398510477e6e.jpg" + }, + "content": "Collection of 3D wireframe models of various architectural and furniture objects, no text or symbols present.", + "image_caption": [ + { + "type": "text", + "content": "Figure 9: Gallery results. MeshXL is able to produce diverse 3D meshes with high quality." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 109, + 119, + 903, + 864 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "12" + } + ] + }, + "bbox": [ + 490, + 935, + 509, + 946 + ] + } + ], + [ + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "8 Limitations, Future Work, and Conclusions" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 89, + 571, + 107 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Limitations and Future Work. The main drawback of MeshXLs is the inference time. During sampling, MeshXL will generate 7,200 tokens for an 800-faced 3D mesh, which takes a relatively long time because of the auto-regressive process. As for future works, recent endeavors on the RNN-related methods [6, 55, 26] and multiple tokens prediction for LLMs [24] might open up great opportunities in saving the inference cost." + } + ] + }, + "bbox": [ + 169, + 121, + 823, + 191 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Conclusion. We validate that NeurCF, an explicit coordinate representation with implicit neural embeddings, is a simple-and-effective representation of 3D meshes. By modelling the 3D mesh generation as an auto-regressive problem, we seek help from modern LLM approaches and present a family of generative pre-trained models, MeshXL, for high-fidelity 3D mesh generation. We show that MeshXL performs better given larger-scale training data and increased parameters. Extensive results show our proposed MeshXL can not only generate high-quality 3D meshes, but also exhibits great potential serving as base models for conditional 3D assets generation." + } + ] + }, + "bbox": [ + 169, + 198, + 826, + 299 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "13" + } + ] + }, + "bbox": [ + 490, + 935, + 508, + 946 + ] + } + ], + [ + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "References" + } + ], + "level": 2 + }, + "bbox": [ + 173, + 89, + 267, + 104 + ] + }, + { + "type": "list", + "content": { + "list_type": "reference_list", + "list_items": [ + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40–49. 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Extensive", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 681, + 468, + 691 + ], + "spans": [ + { + "bbox": [ + 143, + 681, + 468, + 691 + ], + "type": "text", + "content": "experiments show that MeshXL is able to generate high-quality 3D meshes, and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 693, + 440, + 701 + ], + "spans": [ + { + "bbox": [ + 143, + 693, + 440, + 701 + ], + "type": "text", + "content": "can also serve as foundation models for various down-stream applications.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "bbox": [ + 105, + 71, + 192, + 83 + ], + "type": "title", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 106, + 72, + 190, + 83 + ], + "spans": [ + { + "bbox": [ + 106, + 72, + 190, + 83 + ], + "type": "text", + "content": "1 Introduction", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 95, + 504, + 161 + ], + "type": "text", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 97, + 504, + 106 + ], + "spans": [ + { + "bbox": [ + 107, + 97, + 504, + 106 + ], + "type": "text", + "content": "The generation of high-quality 3D assets [61, 79, 29] is essential for various applications in video", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 107, + 504, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 107, + 504, + 118 + ], + "type": "text", + "content": "games, virtual reality, and robotics. Among existing 3D representations [51, 38, 57, 61], the 3D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 119, + 504, + 128 + ], + "spans": [ + { + "bbox": [ + 107, + 119, + 504, + 128 + ], + "type": "text", + "content": "mesh represents the 3D data with graphs, which has the flexibility and accuracy for sharp edges as", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 130, + 504, + 139 + ], + "spans": [ + { + "bbox": [ + 107, + 130, + 504, + 139 + ], + "type": "text", + "content": "well as both flat and curved surfaces. However, the direct generation of high-quality 3D meshes is", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 140, + 503, + 150 + ], + "spans": [ + { + "bbox": [ + 107, + 140, + 503, + 150 + ], + "type": "text", + "content": "challenging, given 1) the unstructured graph representation and 2) the demand for accurate spatial", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 152, + 320, + 161 + ], + "spans": [ + { + "bbox": [ + 107, + 152, + 320, + 161 + ], + "type": "text", + "content": "locations and connectivity estimation within vertices.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 166, + 506, + 254 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 167, + 503, + 177 + ], + "spans": [ + { + "bbox": [ + 107, + 167, + 503, + 177 + ], + "type": "text", + "content": "To generate 3D meshes, many works adopt an indirect way by first producing data in other 3D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 178, + 504, + 188 + ], + "spans": [ + { + "bbox": [ + 107, + 178, + 504, + 188 + ], + "type": "text", + "content": "representations, including point clouds [99, 49, 54], SDF [90, 96], and multi-view images [46, 84, 30].", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 189, + 504, + 199 + ], + "spans": [ + { + "bbox": [ + 106, + 189, + 504, + 199 + ], + "type": "text", + "content": "After that, re-meshing methods [37] are required for post-processing the generated geometries.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 200, + 504, + 209 + ], + "spans": [ + { + "bbox": [ + 107, + 200, + 504, + 209 + ], + "type": "text", + "content": "There are also attempts towards the direct generation of 3D polynomial meshes. PolyGen [53]", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 213, + 504, + 220 + ], + "spans": [ + { + "bbox": [ + 107, + 213, + 504, + 220 + ], + "type": "text", + "content": "adopts two separate decoder-only transformers for vertices generation and connectivity prediction.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 222, + 503, + 232 + ], + "spans": [ + { + "bbox": [ + 107, + 222, + 503, + 232 + ], + "type": "text", + "content": "MeshGPT [66] builds a mesh VQVAE to reconstruct the tokens generated by a GPT model [59]", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 233, + 504, + 243 + ], + "spans": [ + { + "bbox": [ + 107, + 233, + 504, + 243 + ], + "type": "text", + "content": "into 3D meshes. 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To preserve high-frequency information, the point cloud and voxel representations", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 282, + 504, + 293 + ], + "spans": [ + { + "bbox": [ + 106, + 282, + 504, + 293 + ], + "type": "text", + "content": "will make dense samplings on the object surfaces, which inevitably lead to great redundancy when", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 293, + 504, + 303 + ], + "spans": [ + { + "bbox": [ + 106, + 293, + 504, + 303 + ], + "type": "text", + "content": "representing flat surfaces. The reconstruction-based methods [84, 30, 68], however, rely heavily on", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 304, + 504, + 313 + ], + "spans": [ + { + "bbox": [ + 107, + 304, + 504, + 313 + ], + "type": "text", + "content": "the quality of the multi-vew generation pipeline [46]. 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Subsequently, we discuss related", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 662, + 425, + 671 + ], + "spans": [ + { + "bbox": [ + 107, + 662, + 425, + 671 + ], + "type": "text", + "content": "works on 3D generation and recent efforts in developing 3D foundation models.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 677, + 505, + 723 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 107, + 679, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 107, + 679, + 504, + 689 + ], + "type": "text", + "content": "3D Representations. Researchers have long sought for accurate and efficient methods to represent", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 689, + 504, + 700 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 504, + 700 + ], + "type": "text", + "content": "3D data. Point Cloud [54, 57, 58, 91] captures the spatial positions of discrete points in the Euclidean", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 701, + 504, + 711 + ], + "spans": [ + { + "bbox": [ + 107, + 701, + 504, + 711 + ], + "type": "text", + "content": "space, which is preferred by various 3D sensors [15, 89, 67, 3, 7]. Mesh [53, 2, 66, 12] represents", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 712, + 504, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 712, + 504, + 721 + ], + "type": "text", + "content": "the 3D structure with graphs. 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However, the direct generation of high-quality 3D meshes is", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 140, + 503, + 150 + ], + "spans": [ + { + "bbox": [ + 107, + 140, + 503, + 150 + ], + "type": "text", + "content": "challenging, given 1) the unstructured graph representation and 2) the demand for accurate spatial", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 152, + 320, + 161 + ], + "spans": [ + { + "bbox": [ + 107, + 152, + 320, + 161 + ], + "type": "text", + "content": "locations and connectivity estimation within vertices.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 166, + 506, + 254 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 167, + 503, + 177 + ], + "spans": [ + { + "bbox": [ + 107, + 167, + 503, + 177 + ], + "type": "text", + "content": "To generate 3D meshes, many works adopt an indirect way by first producing data in other 3D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 178, + 504, + 188 + ], + "spans": [ + { + "bbox": [ + 107, + 178, + 504, + 188 + ], + "type": "text", + "content": "representations, including point clouds [99, 49, 54], SDF [90, 96], and multi-view images [46, 84, 30].", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 189, + 504, + 199 + ], + "spans": [ + { + "bbox": [ + 106, + 189, + 504, + 199 + ], + "type": "text", + "content": "After that, re-meshing methods [37] are required for post-processing the generated geometries.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 200, + 504, + 209 + ], + "spans": [ + { + "bbox": [ + 107, + 200, + 504, + 209 + ], + "type": "text", + "content": "There are also attempts towards the direct generation of 3D polynomial meshes. PolyGen [53]", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 213, + 504, + 220 + ], + "spans": [ + { + "bbox": [ + 107, + 213, + 504, + 220 + ], + "type": "text", + "content": "adopts two separate decoder-only transformers for vertices generation and connectivity prediction.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 222, + 503, + 232 + ], + "spans": [ + { + "bbox": [ + 107, + 222, + 503, + 232 + ], + "type": "text", + "content": "MeshGPT [66] builds a mesh VQVAE to reconstruct the tokens generated by a GPT model [59]", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 233, + 504, + 243 + ], + "spans": [ + { + "bbox": [ + 107, + 233, + 504, + 243 + ], + "type": "text", + "content": "into 3D meshes. Meanwhile, PolyDiff [2] directly adopts discrete denoising diffusion [4] on the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 243, + 225, + 253 + ], + "spans": [ + { + "bbox": [ + 107, + 243, + 225, + 253 + ], + "type": "text", + "content": "discretized mesh coordinates.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 259, + 504, + 335 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 261, + 504, + 270 + ], + "spans": [ + { + "bbox": [ + 107, + 261, + 504, + 270 + ], + "type": "text", + "content": "Though these methods have achieved initial success in 3D assets generation, they suffer from certain", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 272, + 504, + 281 + ], + "spans": [ + { + "bbox": [ + 107, + 272, + 504, + 281 + ], + "type": "text", + "content": "limitations. To preserve high-frequency information, the point cloud and voxel representations", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 282, + 504, + 293 + ], + "spans": [ + { + "bbox": [ + 106, + 282, + 504, + 293 + ], + "type": "text", + "content": "will make dense samplings on the object surfaces, which inevitably lead to great redundancy when", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 293, + 504, + 303 + ], + "spans": [ + { + "bbox": [ + 106, + 293, + 504, + 303 + ], + "type": "text", + "content": "representing flat surfaces. The reconstruction-based methods [84, 30, 68], however, rely heavily on", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 304, + 504, + 313 + ], + "spans": [ + { + "bbox": [ + 107, + 304, + 504, + 313 + ], + "type": "text", + "content": "the quality of the multi-vew generation pipeline [46]. Additionally, the VQVAE-based 3D generation", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 316, + 503, + 324 + ], + "spans": [ + { + "bbox": [ + 107, + 316, + 503, + 324 + ], + "type": "text", + "content": "methods [90, 66] will inevitably result in cumulative errors when reconstructing the generated tokens", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 327, + 181, + 335 + ], + "spans": [ + { + "bbox": [ + 107, + 327, + 181, + 335 + ], + "type": "text", + "content": "into 3D structures.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 341, + 505, + 429 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 341, + 504, + 352 + ], + "spans": [ + { + "bbox": [ + 107, + 341, + 504, + 352 + ], + "type": "text", + "content": "To tackle the above challenges and explore the potential of scaling up 3D generative pre-training,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 354, + 504, + 363 + ], + "spans": [ + { + "bbox": [ + 107, + 354, + 504, + 363 + ], + "type": "text", + "content": "we introduce a simple-yet-effective way of 3D mesh representation, the Neural Coordinate Field", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 364, + 504, + 373 + ], + "spans": [ + { + "bbox": [ + 107, + 364, + 504, + 373 + ], + "type": "text", + "content": "(NeurCF). NeurCF represents the explicit 3D coordinates with implicit neural embeddings. We", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 375, + 504, + 384 + ], + "spans": [ + { + "bbox": [ + 107, + 375, + 504, + 384 + ], + "type": "text", + "content": "show that with a pre-defined ordering strategy, the generation of 3D meshes can be formulated", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 386, + 504, + 396 + ], + "spans": [ + { + "bbox": [ + 107, + 386, + 504, + 396 + ], + "type": "text", + "content": "as an auto-regressive problem. After that, we present MeshXL, a family of generative pre-trained", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 397, + 504, + 407 + ], + "spans": [ + { + "bbox": [ + 107, + 397, + 504, + 407 + ], + "type": "text", + "content": "transformers [95, 59], for the direct generation of high-fidelity 3D meshes. Without resorting to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 407, + 504, + 417 + ], + "spans": [ + { + "bbox": [ + 107, + 407, + 504, + 417 + ], + "type": "text", + "content": "intermediate 3D representations, NeurCF facilitates an end-to-end learning pipeline for the direct", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 418, + 272, + 428 + ], + "spans": [ + { + "bbox": [ + 107, + 418, + 272, + 428 + ], + "type": "text", + "content": "pre-training on large-scale 3D mesh data.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 434, + 505, + 511 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 434, + 504, + 445 + ], + "spans": [ + { + "bbox": [ + 107, + 434, + 504, + 445 + ], + "type": "text", + "content": "By organizing high-quality 3D assets from ShapeNet [9], 3D-FUTURE [22], Objaverse [17], and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 445, + 504, + 456 + ], + "spans": [ + { + "bbox": [ + 106, + 445, + 504, + 456 + ], + "type": "text", + "content": "Objaverse-XL [16], we achieve a collection of over 2.5 million 3D meshes to support large-scale", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 457, + 504, + 466 + ], + "spans": [ + { + "bbox": [ + 107, + 457, + 504, + 466 + ], + "type": "text", + "content": "generative pre-training. Extensive experiments demonstrate that the NeurCF representation facilitates", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 467, + 504, + 478 + ], + "spans": [ + { + "bbox": [ + 106, + 467, + 504, + 478 + ], + "type": "text", + "content": "MeshXL to generate higher-quality 3D meshes with an increased number of parameters and large-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 479, + 504, + 488 + ], + "spans": [ + { + "bbox": [ + 106, + 479, + 504, + 488 + ], + "type": "text", + "content": "scale pre-training data. By training on the collection of large-scale 3D mesh data, MeshXL can", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 490, + 504, + 500 + ], + "spans": [ + { + "bbox": [ + 107, + 490, + 504, + 500 + ], + "type": "text", + "content": "achieve better performance with larger numbers of parameters (Fig. 3 and Tab. 5), and surpass prior", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 500, + 378, + 510 + ], + "spans": [ + { + "bbox": [ + 107, + 500, + 378, + 510 + ], + "type": "text", + "content": "arts on multiple categories task of the ShapeNet dataset [9] (Tab. 3).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 515, + 354, + 526 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 517, + 353, + 526 + ], + "spans": [ + { + "bbox": [ + 107, + 517, + 353, + 526 + ], + "type": "text", + "content": "In summary, our contributions can be summarized as follows:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 536, + 504, + 610 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 105, + 536, + 504, + 559 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 106, + 537, + 504, + 547 + ], + "spans": [ + { + "bbox": [ + 106, + 537, + 504, + 547 + ], + "type": "text", + "content": "• We validate that Neural Coordinate Field is a simple-and-effective representation of 3D mesh,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 115, + 548, + 372, + 558 + ], + "spans": [ + { + "bbox": [ + 115, + 548, + 372, + 558 + ], + "type": "text", + "content": "which is also friendly to large-scale auto-regressive pre-training.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 562, + 504, + 584 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 563, + 503, + 572 + ], + "spans": [ + { + "bbox": [ + 107, + 563, + 503, + 572 + ], + "type": "text", + "content": "• We present a family of MeshXLs that can be treated as strong base models for image-conditioned", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 115, + 574, + 299, + 583 + ], + "spans": [ + { + "bbox": [ + 115, + 574, + 299, + 583 + ], + "type": "text", + "content": "or text-conditioned 3D mesh generation tasks.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 587, + 504, + 610 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 106, + 587, + 504, + 599 + ], + "spans": [ + { + "bbox": [ + 106, + 587, + 504, + 599 + ], + "type": "text", + "content": "• We show that MeshXL surpasses state-of-the-art 3D mesh generation methods, and can produce", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 115, + 600, + 370, + 609 + ], + "spans": [ + { + "bbox": [ + 115, + 600, + 370, + 609 + ], + "type": "text", + "content": "delicate 3D meshes compatible with existing texturing methods.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 105, + 625, + 197, + 637 + ], + "type": "title", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 106, + 626, + 197, + 637 + ], + "spans": [ + { + "bbox": [ + 106, + 626, + 197, + 637 + ], + "type": "text", + "content": "2 Related Work", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 649, + 504, + 672 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 106, + 650, + 504, + 661 + ], + "spans": [ + { + "bbox": [ + 106, + 650, + 504, + 661 + ], + "type": "text", + "content": "First, we present a concise review of existing 3D representations. Subsequently, we discuss related", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 662, + 425, + 671 + ], + "spans": [ + { + "bbox": [ + 107, + 662, + 425, + 671 + ], + "type": "text", + "content": "works on 3D generation and recent efforts in developing 3D foundation models.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 677, + 505, + 723 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 107, + 679, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 107, + 679, + 504, + 689 + ], + "type": "text", + "content": "3D Representations. Researchers have long sought for accurate and efficient methods to represent", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 689, + 504, + 700 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 504, + 700 + ], + "type": "text", + "content": "3D data. Point Cloud [54, 57, 58, 91] captures the spatial positions of discrete points in the Euclidean", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 701, + 504, + 711 + ], + "spans": [ + { + "bbox": [ + 107, + 701, + 504, + 711 + ], + "type": "text", + "content": "space, which is preferred by various 3D sensors [15, 89, 67, 3, 7]. Mesh [53, 2, 66, 12] represents", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 712, + 504, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 712, + 504, + 721 + ], + "type": "text", + "content": "the 3D structure with graphs. By connecting the vertices with edges, mesh can also be interpreted", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 73, + 504, + 83 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 504, + 83 + ], + "type": "text", + "content": "into a set of polygons in the 3D space. Similar to point clouds, 3D Gaussians [38, 69] also record", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 85, + 504, + 94 + ], + "spans": [ + { + "bbox": [ + 107, + 85, + 504, + 94 + ], + "type": "text", + "content": "the discrete Euclidean distribution in 3D space. However, each point is represented by a 3D Gaussian", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 106, + 95, + 504, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 95, + 504, + 106 + ], + "type": "text", + "content": "distribution function parameterized by its covariance matrix, color, and opacity. Given their fast", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 107, + 504, + 116 + ], + "spans": [ + { + "bbox": [ + 107, + 107, + 504, + 116 + ], + "type": "text", + "content": "convergence and rendering speed, 3D gaussians are often utilized for 3D reconstruction. Neural", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 106, + 117, + 504, + 127 + ], + "spans": [ + { + "bbox": [ + 106, + 117, + 504, + 127 + ], + "type": "text", + "content": "Radiance Field (NeRF) [51, 5] constructs a learnable volumetric function f using neural networks", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 129, + 504, + 137 + ], + "spans": [ + { + "bbox": [ + 107, + 129, + 504, + 137 + ], + "type": "text", + "content": "trained on multi-view images. Due to its derivability and flexibility, NeRF is also favored for", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 140, + 504, + 148 + ], + "spans": [ + { + "bbox": [ + 107, + 140, + 504, + 148 + ], + "type": "text", + "content": "3D generative models [46, 101, 78, 56]. Additionally, there are other 3D representations such as", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 151, + 504, + 159 + ], + "spans": [ + { + "bbox": [ + 107, + 151, + 504, + 159 + ], + "type": "text", + "content": "multi-view images [76, 92, 102], voxel fields [61, 13, 45], and signed distance fields [96], among", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 161, + 504, + 171 + ], + "spans": [ + { + "bbox": [ + 107, + 161, + 504, + 171 + ], + "type": "text", + "content": "others [65, 90, 64]. In this paper, we consider the Neural Coordinate Field (NeurCF), an explicit", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 172, + 503, + 181 + ], + "spans": [ + { + "bbox": [ + 107, + 172, + 503, + 181 + ], + "type": "text", + "content": "spatial representation with implicit neural embeddings, and investigate its potential for scalable 3D", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 184, + 174, + 193 + ], + "spans": [ + { + "bbox": [ + 107, + 184, + 174, + 193 + ], + "type": "text", + "content": "asset generation.", + "score": 1.0, + "cross_page": true + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "bbox": [ + 104, + 72, + 506, + 193 + ], + "type": "text", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 106, + 73, + 504, + 83 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 504, + 83 + ], + "type": "text", + "content": "into a set of polygons in the 3D space. Similar to point clouds, 3D Gaussians [38, 69] also record", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 85, + 504, + 94 + ], + "spans": [ + { + "bbox": [ + 107, + 85, + 504, + 94 + ], + "type": "text", + "content": "the discrete Euclidean distribution in 3D space. However, each point is represented by a 3D Gaussian", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 95, + 504, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 95, + 504, + 106 + ], + "type": "text", + "content": "distribution function parameterized by its covariance matrix, color, and opacity. Given their fast", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 107, + 504, + 116 + ], + "spans": [ + { + "bbox": [ + 107, + 107, + 504, + 116 + ], + "type": "text", + "content": "convergence and rendering speed, 3D gaussians are often utilized for 3D reconstruction. Neural", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 117, + 504, + 127 + ], + "spans": [ + { + "bbox": [ + 106, + 117, + 504, + 127 + ], + "type": "text", + "content": "Radiance Field (NeRF) [51, 5] constructs a learnable volumetric function f using neural networks", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 129, + 504, + 137 + ], + "spans": [ + { + "bbox": [ + 107, + 129, + 504, + 137 + ], + "type": "text", + "content": "trained on multi-view images. Due to its derivability and flexibility, NeRF is also favored for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 140, + 504, + 148 + ], + "spans": [ + { + "bbox": [ + 107, + 140, + 504, + 148 + ], + "type": "text", + "content": "3D generative models [46, 101, 78, 56]. Additionally, there are other 3D representations such as", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 151, + 504, + 159 + ], + "spans": [ + { + "bbox": [ + 107, + 151, + 504, + 159 + ], + "type": "text", + "content": "multi-view images [76, 92, 102], voxel fields [61, 13, 45], and signed distance fields [96], among", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 161, + 504, + 171 + ], + "spans": [ + { + "bbox": [ + 107, + 161, + 504, + 171 + ], + "type": "text", + "content": "others [65, 90, 64]. In this paper, we consider the Neural Coordinate Field (NeurCF), an explicit", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 172, + 503, + 181 + ], + "spans": [ + { + "bbox": [ + 107, + 172, + 503, + 181 + ], + "type": "text", + "content": "spatial representation with implicit neural embeddings, and investigate its potential for scalable 3D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 184, + 174, + 193 + ], + "spans": [ + { + "bbox": [ + 107, + 184, + 174, + 193 + ], + "type": "text", + "content": "asset generation.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 198, + 506, + 364 + ], + "type": "text", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 200, + 504, + 209 + ], + "spans": [ + { + "bbox": [ + 107, + 200, + 504, + 209 + ], + "type": "text", + "content": "3D Generation. With the exploration of various 3D representations and the collection of large-scale", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 209, + 504, + 221 + ], + "spans": [ + { + "bbox": [ + 106, + 209, + 504, + 221 + ], + "type": "text", + "content": "3D datasets [17, 9, 16], researchers have also put much effort exploring the generation of high-fidelity", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 221, + 504, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 504, + 232 + ], + "type": "text", + "content": "3D assets [42, 39]. The Generative Adversarial Network (GAN) [25, 82, 1, 33] produces synthetic", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 233, + 503, + 242 + ], + "spans": [ + { + "bbox": [ + 107, + 233, + 503, + 242 + ], + "type": "text", + "content": "3D data with a generator G, and train a discriminator network D to distinguish the generated and real", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 243, + 503, + 253 + ], + "spans": [ + { + "bbox": [ + 107, + 243, + 503, + 253 + ], + "type": "text", + "content": "data. Additionally, the potential of diffusion models [54, 28, 62] in the direct generation of 3D data is", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 255, + 504, + 265 + ], + "spans": [ + { + "bbox": [ + 107, + 255, + 504, + 265 + ], + "type": "text", + "content": "also widely explored [99, 2, 54, 50, 47]. 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In this paper, we mainly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 299, + 504, + 308 + ], + "spans": [ + { + "bbox": [ + 107, + 299, + 504, + 308 + ], + "type": "text", + "content": "explore the auto-regressive methods for 3D generation. 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In this paper, we explore the potential of an explicit sequential modelling", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 342, + 503, + 351 + ], + "spans": [ + { + "bbox": [ + 107, + 342, + 503, + 351 + ], + "type": "text", + "content": "method for 3D meshes, and present a family of generative pre-trained transformers, MeshXL, for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 354, + 241, + 362 + ], + "spans": [ + { + "bbox": [ + 107, + 354, + 241, + 362 + ], + "type": "text", + "content": "high-fidelity 3D mesh generation.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 369, + 506, + 489 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 370, + 504, + 380 + ], + "spans": [ + { + "bbox": [ + 107, + 370, + 504, + 380 + ], + "type": "text", + "content": "3D Foundation Models. The collection of large-scale high-quality 3D data [17, 16, 9, 83, 72, 21, 22]", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 381, + 503, + 390 + ], + "spans": [ + { + "bbox": [ + 107, + 381, + 503, + 390 + ], + "type": "text", + "content": "builds up the foundation for various 3D-related tasks [85, 27, 10, 41]. 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With the introduction of large-scale 3D data in both variety and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 425, + 504, + 435 + ], + "spans": [ + { + "bbox": [ + 107, + 425, + 504, + 435 + ], + "type": "text", + "content": "granularity [34, 41, 16], existing 3D foundation models are capable of generalizing to unseen", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 435, + 504, + 445 + ], + "spans": [ + { + "bbox": [ + 106, + 435, + 504, + 445 + ], + "type": "text", + "content": "concepts [102, 88, 44], generating high-fidelity 3D assets [90, 36, 66], responding to complex", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 447, + 504, + 456 + ], + "spans": [ + { + "bbox": [ + 107, + 447, + 504, + 456 + ], + "type": "text", + "content": "instructions [31, 10, 32, 41], and generating actions that interacts with the 3D environments [20, 81,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 457, + 504, + 468 + ], + "spans": [ + { + "bbox": [ + 107, + 457, + 504, + 468 + ], + "type": "text", + "content": "97]. In this paper, we present a fully end-to-end 3D mesh generation pipeline, explore the scaling", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 468, + 503, + 477 + ], + "spans": [ + { + "bbox": [ + 107, + 468, + 503, + 477 + ], + "type": "text", + "content": "effect for large-scale pre-training, and test whether our method can serve as a well-trained foundation", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 480, + 257, + 488 + ], + "spans": [ + { + "bbox": [ + 107, + 480, + 257, + 488 + ], + "type": "text", + "content": "model for various down-stream tasks.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 508, + 151, + 520 + ], + "type": "title", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 105, + 507, + 151, + 522 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 151, + 522 + ], + "type": "text", + "content": "3 Data", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 536, + 506, + 570 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 106, + 536, + 504, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 536, + 504, + 546 + ], + "type": "text", + "content": "Data Sources. We provide details on the 3D data collections we use to train and evaluate our models.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 548, + 504, + 557 + ], + "spans": [ + { + "bbox": [ + 107, + 548, + 504, + 557 + ], + "type": "text", + "content": "The whole data collection is built upon four widely-acknowledged 3D mesh datasets, i.e. ShapeNet", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 559, + 375, + 568 + ], + "spans": [ + { + "bbox": [ + 107, + 559, + 375, + 568 + ], + "type": "text", + "content": "V2 [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16].", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 580, + 506, + 723 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 105, + 580, + 504, + 604 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 582, + 504, + 592 + ], + "spans": [ + { + "bbox": [ + 107, + 582, + 504, + 592 + ], + "type": "text", + "content": "• ShapeNet V2 [9] collects about 51k 3D CAD models for 55 categories. We split the data in 9:1 for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 115, + 594, + 277, + 603 + ], + "spans": [ + { + "bbox": [ + 115, + 594, + 277, + 603 + ], + "type": "text", + "content": "training and validation by each category.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 609, + 504, + 642 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 106, + 610, + 505, + 621 + ], + "spans": [ + { + "bbox": [ + 106, + 610, + 505, + 621 + ], + "type": "text", + "content": "• 3D-FUTURE [22] present about 10k high-quality 3D mesh data for indoor furniture. However,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 114, + 621, + 504, + 632 + ], + "spans": [ + { + "bbox": [ + 114, + 621, + 504, + 632 + ], + "type": "text", + "content": "because of the delicate design, the objects contain many faces. 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We split the data in 99:1 for training and validation, respectively.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 677, + 506, + 723 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 679, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 107, + 679, + 504, + 689 + ], + "type": "text", + "content": "• Objaverse-XL [16] further expand Objaverse [17] into a dataset with more than 10M 3D objects", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 115, + 689, + 503, + 699 + ], + "spans": [ + { + "bbox": [ + 115, + 689, + 503, + 699 + ], + "type": "text", + "content": "with additional data collected from GitHub, Polycam, Thingiverse, and Smithsonian. We split", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 115, + 700, + 504, + 711 + ], + "spans": [ + { + "bbox": [ + 115, + 700, + 504, + 711 + ], + "type": "text", + "content": "the Github and Thingiverse part of the Objaverse-XL dataset into 99:1 for training and validation,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 115, + 712, + 165, + 723 + ], + "spans": [ + { + "bbox": [ + 115, + 712, + 165, + 723 + ], + "type": "text", + "content": "respectively.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "page_number", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 302, + 742, + 309, + 752 + ], + "spans": [ + { + "bbox": [ + 302, + 742, + 309, + 752 + ], + "type": "text", + "content": "3", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2, + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 506, + 193 + ], + "type": "text", + "angle": 0, + "index": 0, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 104, + 198, + 506, + 364 + ], + "type": "text", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 200, + 504, + 209 + ], + "spans": [ + { + "bbox": [ + 107, + 200, + 504, + 209 + ], + "type": "text", + "content": "3D Generation. With the exploration of various 3D representations and the collection of large-scale", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 209, + 504, + 221 + ], + "spans": [ + { + "bbox": [ + 106, + 209, + 504, + 221 + ], + "type": "text", + "content": "3D datasets [17, 9, 16], researchers have also put much effort exploring the generation of high-fidelity", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 221, + 504, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 504, + 232 + ], + "type": "text", + "content": "3D assets [42, 39]. The Generative Adversarial Network (GAN) [25, 82, 1, 33] produces synthetic", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 233, + 503, + 242 + ], + "spans": [ + { + "bbox": [ + 107, + 233, + 503, + 242 + ], + "type": "text", + "content": "3D data with a generator G, and train a discriminator network D to distinguish the generated and real", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 243, + 503, + 253 + ], + "spans": [ + { + "bbox": [ + 107, + 243, + 503, + 253 + ], + "type": "text", + "content": "data. Additionally, the potential of diffusion models [54, 28, 62] in the direct generation of 3D data is", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 255, + 504, + 265 + ], + "spans": [ + { + "bbox": [ + 107, + 255, + 504, + 265 + ], + "type": "text", + "content": "also widely explored [99, 2, 54, 50, 47]. 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The collection of large-scale high-quality 3D data [17, 16, 9, 83, 72, 21, 22]", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 381, + 503, + 390 + ], + "spans": [ + { + "bbox": [ + 107, + 381, + 503, + 390 + ], + "type": "text", + "content": "builds up the foundation for various 3D-related tasks [85, 27, 10, 41]. 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With the introduction of large-scale 3D data in both variety and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 425, + 504, + 435 + ], + "spans": [ + { + "bbox": [ + 107, + 425, + 504, + 435 + ], + "type": "text", + "content": "granularity [34, 41, 16], existing 3D foundation models are capable of generalizing to unseen", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 435, + 504, + 445 + ], + "spans": [ + { + "bbox": [ + 106, + 435, + 504, + 445 + ], + "type": "text", + "content": "concepts [102, 88, 44], generating high-fidelity 3D assets [90, 36, 66], responding to complex", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 447, + 504, + 456 + ], + "spans": [ + { + "bbox": [ + 107, + 447, + 504, + 456 + ], + "type": "text", + "content": "instructions [31, 10, 32, 41], and generating actions that interacts with the 3D environments [20, 81,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 457, + 504, + 468 + ], + "spans": [ + { + "bbox": [ + 107, + 457, + 504, + 468 + ], + "type": "text", + "content": "97]. In this paper, we present a fully end-to-end 3D mesh generation pipeline, explore the scaling", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 468, + 503, + 477 + ], + "spans": [ + { + "bbox": [ + 107, + 468, + 503, + 477 + ], + "type": "text", + "content": "effect for large-scale pre-training, and test whether our method can serve as a well-trained foundation", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 480, + 257, + 488 + ], + "spans": [ + { + "bbox": [ + 107, + 480, + 257, + 488 + ], + "type": "text", + "content": "model for various down-stream tasks.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 508, + 151, + 520 + ], + "type": "title", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 105, + 507, + 151, + 522 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 151, + 522 + ], + "type": "text", + "content": "3 Data", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 536, + 506, + 570 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 106, + 536, + 504, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 536, + 504, + 546 + ], + "type": "text", + "content": "Data Sources. We provide details on the 3D data collections we use to train and evaluate our models.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 548, + 504, + 557 + ], + "spans": [ + { + "bbox": [ + 107, + 548, + 504, + 557 + ], + "type": "text", + "content": "The whole data collection is built upon four widely-acknowledged 3D mesh datasets, i.e. ShapeNet", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 559, + 375, + 568 + ], + "spans": [ + { + "bbox": [ + 107, + 559, + 375, + 568 + ], + "type": "text", + "content": "V2 [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16].", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 580, + 506, + 723 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 105, + 580, + 504, + 604 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 582, + 504, + 592 + ], + "spans": [ + { + "bbox": [ + 107, + 582, + 504, + 592 + ], + "type": "text", + "content": "• ShapeNet V2 [9] collects about 51k 3D CAD models for 55 categories. We split the data in 9:1 for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 115, + 594, + 277, + 603 + ], + "spans": [ + { + "bbox": [ + 115, + 594, + 277, + 603 + ], + "type": "text", + "content": "training and validation by each category.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 609, + 504, + 642 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 106, + 610, + 505, + 621 + ], + "spans": [ + { + "bbox": [ + 106, + 610, + 505, + 621 + ], + "type": "text", + "content": "• 3D-FUTURE [22] present about 10k high-quality 3D mesh data for indoor furniture. However,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 114, + 621, + 504, + 632 + ], + "spans": [ + { + "bbox": [ + 114, + 621, + 504, + 632 + ], + "type": "text", + "content": "because of the delicate design, the objects contain many faces. Therefore, only a small proportion", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 115, + 633, + 325, + 642 + ], + "spans": [ + { + "bbox": [ + 115, + 633, + 325, + 642 + ], + "type": "text", + "content": "of the data can be used to train our MeshXL models.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 649, + 506, + 672 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 651, + 505, + 660 + ], + "spans": [ + { + "bbox": [ + 107, + 651, + 505, + 660 + ], + "type": "text", + "content": "• Objaverse [17] is a large 3D data collection with more than 800k 3D objects for about 21k cate-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 115, + 661, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 115, + 661, + 505, + 672 + ], + "type": "text", + "content": "gories collected from Sketchfab. We split the data in 99:1 for training and validation, respectively.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 677, + 506, + 723 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 679, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 107, + 679, + 504, + 689 + ], + "type": "text", + "content": "• Objaverse-XL [16] further expand Objaverse [17] into a dataset with more than 10M 3D objects", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 115, + 689, + 503, + 699 + ], + "spans": [ + { + "bbox": [ + 115, + 689, + 503, + 699 + ], + "type": "text", + "content": "with additional data collected from GitHub, Polycam, Thingiverse, and Smithsonian. We split", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 115, + 700, + 504, + 711 + ], + "spans": [ + { + "bbox": [ + 115, + 700, + 504, + 711 + ], + "type": "text", + "content": "the Github and Thingiverse part of the Objaverse-XL dataset into 99:1 for training and validation,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 115, + 712, + 165, + 723 + ], + "spans": [ + { + "bbox": [ + 115, + 712, + 165, + 723 + ], + "type": "text", + "content": "respectively.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "sub_type": "text" + } + ] + }, + { + "preproc_blocks": [ + { + "bbox": [ + 104, + 72, + 504, + 139 + ], + "type": "text", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 107, + 73, + 504, + 83 + ], + "spans": [ + { + "bbox": [ + 107, + 73, + 504, + 83 + ], + "type": "text", + "content": "Data collection and filtering. To organize existing datasets, we build up a filtering and pre-processing", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 84, + 504, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 84, + 504, + 95 + ], + "type": "text", + "content": "pipeline to ensure that the meshes met our demand. We first collect meshes with fewer than 800", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 96, + 503, + 105 + ], + "spans": [ + { + "bbox": [ + 107, + 96, + 503, + 105 + ], + "type": "text", + "content": "faces, and ensure that they have corresponding UV maps for rendering. After that, we render the 3D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 106, + 504, + 116 + ], + "spans": [ + { + "bbox": [ + 107, + 106, + 504, + 116 + ], + "type": "text", + "content": "meshes, and discard those are not center-aligned or occupying less than 10% of the frame. For those", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 118, + 504, + 126 + ], + "spans": [ + { + "bbox": [ + 107, + 118, + 504, + 126 + ], + "type": "text", + "content": "3D meshes with more than 800 but less than 20,000 faces, we use planar decimation whether their", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 128, + 494, + 137 + ], + "spans": [ + { + "bbox": [ + 107, + 128, + 494, + 137 + ], + "type": "text", + "content": "meshes can be simplified. Finally, we achieve approximately 2.5 million pieces of data remained.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 144, + 504, + 168 + ], + "type": "text", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 145, + 504, + 155 + ], + "spans": [ + { + "bbox": [ + 107, + 145, + 504, + 155 + ], + "type": "text", + "content": "Planar Decimation Pipeline. To ensure the quality of the decimated 3D meshes, we make sure either", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 156, + 400, + 167 + ], + "spans": [ + { + "bbox": [ + 107, + 157, + 214, + 165 + ], + "type": "text", + "content": "a lower Hausdorff distance", + "score": 1.0 + }, + { + "bbox": [ + 216, + 156, + 249, + 167 + ], + "type": "inline_equation", + "content": "\\delta _ { \\mathrm { h a u s d o r f f } }", + "score": 0.7149 + }, + { + "bbox": [ + 250, + 157, + 400, + 166 + ], + "type": "text", + "content": "[66] or a similar rendered views [11].", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 173, + 506, + 228 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 174, + 504, + 183 + ], + "spans": [ + { + "bbox": [ + 107, + 174, + 504, + 183 + ], + "type": "text", + "content": "Collecting mesh-text pairs. We first render each 3D mesh with 12 different views, and concatenate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 186, + 503, + 194 + ], + "spans": [ + { + "bbox": [ + 107, + 186, + 503, + 194 + ], + "type": "text", + "content": "them into one single image. Then, we annotate both the front view image and the fused multi-view", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 196, + 504, + 205 + ], + "spans": [ + { + "bbox": [ + 107, + 196, + 504, + 205 + ], + "type": "text", + "content": "image using CogVLM [77]. After that, we adopt the Mistral-7B-Instruct model [35] with few-shot", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 208, + 504, + 216 + ], + "spans": [ + { + "bbox": [ + 107, + 208, + 504, + 216 + ], + "type": "text", + "content": "in-context examples to extract information on category and geometry from the CogVLM annotations.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 217, + 439, + 228 + ], + "spans": [ + { + "bbox": [ + 107, + 217, + 439, + 228 + ], + "type": "text", + "content": "We tag each 3D mesh with the resulting categories and 3 to 5 geometry descriptors.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 234, + 504, + 289 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 235, + 504, + 244 + ], + "spans": [ + { + "bbox": [ + 107, + 235, + 504, + 244 + ], + "type": "text", + "content": "Collecting mesh-image pairs. To produce diverse image conditions for 3D mesh generation, we", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 247, + 503, + 255 + ], + "spans": [ + { + "bbox": [ + 107, + 247, + 503, + 255 + ], + "type": "text", + "content": "first generate images with multi-view image and depth rendering. After that, we use the sentences", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 257, + 504, + 266 + ], + "spans": [ + { + "bbox": [ + 107, + 257, + 504, + 266 + ], + "type": "text", + "content": "produced by CogVLM [77] as the prompt, and use a find-tuned Stable Diffusion model [63] to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 268, + 503, + 277 + ], + "spans": [ + { + "bbox": [ + 107, + 268, + 503, + 277 + ], + "type": "text", + "content": "augment the rendered images for diverse textures and backgrounds. To ensure the quality of the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 279, + 368, + 289 + ], + "spans": [ + { + "bbox": [ + 107, + 279, + 368, + 289 + ], + "type": "text", + "content": "generated images, we also adopt a manually cleansing procedure.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 295, + 506, + 329 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 297, + 505, + 305 + ], + "spans": [ + { + "bbox": [ + 107, + 297, + 505, + 305 + ], + "type": "text", + "content": "Data Statistics. We present the data statistics of our large-scale 3D mesh collection in Tab. 1.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 307, + 504, + 316 + ], + "spans": [ + { + "bbox": [ + 107, + 307, + 504, + 316 + ], + "type": "text", + "content": "After organizing and combing 3D assets from ShapeNet [9], 3D-FUTURE [22], Objaverse [17], and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 319, + 390, + 327 + ], + "spans": [ + { + "bbox": [ + 107, + 319, + 390, + 327 + ], + "type": "text", + "content": "Objaverse-XL [16], we could achieve a total of 2.5 million 3D meshes.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "table", + "bbox": [ + 167, + 366, + 444, + 449 + ], + "blocks": [ + { + "bbox": [ + 104, + 338, + 505, + 361 + ], + "type": "table_caption", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 339, + 504, + 349 + ], + "spans": [ + { + "bbox": [ + 107, + 339, + 504, + 349 + ], + "type": "text", + "content": "Table 1: Statistics for the Training Data and Validation Data. After combining four data sources,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 350, + 441, + 361 + ], + "spans": [ + { + "bbox": [ + 107, + 350, + 441, + 361 + ], + "type": "text", + "content": "our proposed MeshXL models are trained on approximately 2.5 million 3D meshes.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 167, + 366, + 444, + 449 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 167, + 366, + 444, + 449 + ], + "spans": [ + { + "bbox": [ + 167, + 366, + 444, + 449 + ], + "type": "table", + "html": "
DatasetPre-trainingText-to-3D
TrainValTrainVal
ShapeNet [9]16,0011,75415,3841,728
3D-Future [22]1,603---
Objaverse [17]85,28285483,501820
Objaverse-XL [16]2,407,33715,2001,347,80213,579
Total2,510,22317,8081,446,67816,127
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Then, each discretized coordinate", + "score": 1.0 + }, + { + "bbox": [ + 300, + 518, + 354, + 529 + ], + "type": "inline_equation", + "content": "p = ( x , y , z )", + "score": 0.8628 + }, + { + "bbox": [ + 357, + 519, + 503, + 528 + ], + "type": "text", + "content": "can be encoded with the coordinate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 529, + 504, + 541 + ], + "spans": [ + { + "bbox": [ + 107, + 531, + 216, + 541 + ], + "type": "text", + "content": "embedding layer E, where", + "score": 1.0 + }, + { + "bbox": [ + 217, + 529, + 326, + 541 + ], + "type": "inline_equation", + "content": "\\mathcal { F } ( \\boldsymbol { p } ) = ( \\mathcal { E } ( \\boldsymbol { x } ) , \\mathcal { E } ( \\boldsymbol { y } ) , \\mathcal { E } ( \\boldsymbol { z } ) )", + "score": 0.9381 + }, + { + "bbox": [ + 327, + 530, + 486, + 541 + ], + "type": "text", + "content": ". Therefore, a k-sided polynomial face", + "score": 1.0 + }, + { + "bbox": [ + 488, + 529, + 504, + 541 + ], + "type": "inline_equation", + "content": "f ^ { ( i ) }", + "score": 0.6778 + } + ] + }, + { + "bbox": [ + 107, + 542, + 503, + 556 + ], + "spans": [ + { + "bbox": [ + 107, + 546, + 190, + 554 + ], + "type": "text", + "content": "can be encoded with", + "score": 1.0 + }, + { + "bbox": [ + 192, + 542, + 337, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal { E } _ { \\mathrm { f a c e } } ( \\boldsymbol { f } ^ { ( i ) } ) = ( \\mathcal { F } ( \\boldsymbol { p } _ { 1 } ^ { ( i ) } ) , \\cdot \\cdot \\cdot , \\mathcal { F } ( \\boldsymbol { p } _ { k } ^ { ( i ) } ) )", + "score": 0.9496 + }, + { + "bbox": [ + 337, + 545, + 503, + 555 + ], + "type": "text", + "content": "). For simplicity, the learnable coordinate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 556, + 259, + 566 + ], + "spans": [ + { + "bbox": [ + 107, + 556, + 259, + 566 + ], + "type": "text", + "content": "embeddings E are shared among axes.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 571, + 504, + 673 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 573, + 504, + 583 + ], + "spans": [ + { + "bbox": [ + 107, + 573, + 504, + 583 + ], + "type": "text", + "content": "Ordering. Due to the graph representation, the order of the mesh vertices and the order of the edges", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 584, + 504, + 594 + ], + "spans": [ + { + "bbox": [ + 107, + 584, + 504, + 594 + ], + "type": "text", + "content": "between them are permutation-invariant. A pre-defined ordering strategy is essential to facilitate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 595, + 504, + 605 + ], + "spans": [ + { + "bbox": [ + 107, + 595, + 504, + 605 + ], + "type": "text", + "content": "the sequence modelling in MeshXL. We employ the same ordering strategy as PolyGen [53] and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 606, + 504, + 615 + ], + "spans": [ + { + "bbox": [ + 107, + 606, + 504, + 615 + ], + "type": "text", + "content": "MeshGPT [66]. The mesh coordinates are first normalized into a unit cube based on the mesh’s", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "spans": [ + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "type": "text", + "content": "longest axis, and discretized into unsigned integers. Within each face, the vertices are cyclically", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 628, + 504, + 638 + ], + "spans": [ + { + "bbox": [ + 107, + 628, + 504, + 638 + ], + "type": "text", + "content": "permuted based their coordinates (z-y-x order, from lower to higher), which helps to preserve the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 639, + 503, + 648 + ], + "spans": [ + { + "bbox": [ + 107, + 639, + 503, + 648 + ], + "type": "text", + "content": "direction of normal vectors. Then, we order these faces based on the permuted coordinates (lower to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 648, + 505, + 659 + ], + "spans": [ + { + "bbox": [ + 107, + 650, + 425, + 659 + ], + "type": "text", + "content": "high). To this end, an n-faced 3D k-sided polynomial mesh can be represented as", + "score": 1.0 + }, + { + "bbox": [ + 427, + 648, + 484, + 659 + ], + "type": "inline_equation", + "content": "\\mathcal { M } \\in \\mathbb { Z } ^ { n \\times k \\times 3 }", + "score": 0.9177 + }, + { + "bbox": [ + 484, + 650, + 505, + 659 + ], + "type": "text", + "content": ", and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 659, + 356, + 672 + ], + "spans": [ + { + "bbox": [ + 107, + 662, + 200, + 670 + ], + "type": "text", + "content": "we can encode M with", + "score": 1.0 + }, + { + "bbox": [ + 202, + 659, + 351, + 672 + ], + "type": "inline_equation", + "content": "\\mathcal { E } _ { \\mathrm { m e s h } } = ( \\mathcal { E } _ { \\mathrm { f a c e } } ( f ^ { ( 1 ) } ) , \\cdot \\cdot \\cdot , \\mathcal { E } _ { \\mathrm { f a c e } } ( f ^ { ( n ) } ) )", + "score": 0.9459 + }, + { + "bbox": [ + 351, + 662, + 356, + 670 + ], + "type": "text", + "content": ").", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 677, + 506, + 723 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 679, + 503, + 689 + ], + "spans": [ + { + "bbox": [ + 107, + 679, + 503, + 689 + ], + "type": "text", + "content": "A Sequential Mesh Representation. One direct way to represent the 3D meshes is to directly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 689, + 504, + 700 + ], + "spans": [ + { + "bbox": [ + 107, + 690, + 227, + 699 + ], + "type": "text", + "content": "reshape M into a vector with", + "score": 1.0 + }, + { + "bbox": [ + 230, + 689, + 268, + 700 + ], + "type": "inline_equation", + "content": "( n \\cdot k \\cdot 3 )", + "score": 0.4677 + }, + { + "bbox": [ + 269, + 690, + 504, + 700 + ], + "type": "text", + "content": "tokens. As a special case, an n-faced triangular mesh can", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 701, + 503, + 711 + ], + "spans": [ + { + "bbox": [ + 107, + 701, + 503, + 711 + ], + "type": "text", + "content": "be represented by a vector with 9n tokens. Meanwhile, our representation can also be expanded to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 712, + 504, + 721 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 504, + 721 + ], + "type": "text", + "content": "hybrid polynomial mesh representations with the proper introduction of separate tokens. For example,", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "page_number", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 302, + 742, + 309, + 751 + ], + "spans": [ + { + "bbox": [ + 302, + 742, + 309, + 751 + ], + "type": "text", + "content": "4", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3, + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 504, + 139 + ], + "type": "text", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 107, + 73, + 504, + 83 + ], + "spans": [ + { + "bbox": [ + 107, + 73, + 504, + 83 + ], + "type": "text", + "content": "Data collection and filtering. To organize existing datasets, we build up a filtering and pre-processing", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 84, + 504, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 84, + 504, + 95 + ], + "type": "text", + "content": "pipeline to ensure that the meshes met our demand. We first collect meshes with fewer than 800", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 96, + 503, + 105 + ], + "spans": [ + { + "bbox": [ + 107, + 96, + 503, + 105 + ], + "type": "text", + "content": "faces, and ensure that they have corresponding UV maps for rendering. After that, we render the 3D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 106, + 504, + 116 + ], + "spans": [ + { + "bbox": [ + 107, + 106, + 504, + 116 + ], + "type": "text", + "content": "meshes, and discard those are not center-aligned or occupying less than 10% of the frame. For those", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 118, + 504, + 126 + ], + "spans": [ + { + "bbox": [ + 107, + 118, + 504, + 126 + ], + "type": "text", + "content": "3D meshes with more than 800 but less than 20,000 faces, we use planar decimation whether their", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 128, + 494, + 137 + ], + "spans": [ + { + "bbox": [ + 107, + 128, + 494, + 137 + ], + "type": "text", + "content": "meshes can be simplified. Finally, we achieve approximately 2.5 million pieces of data remained.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 144, + 504, + 168 + ], + "type": "text", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 145, + 504, + 155 + ], + "spans": [ + { + "bbox": [ + 107, + 145, + 504, + 155 + ], + "type": "text", + "content": "Planar Decimation Pipeline. To ensure the quality of the decimated 3D meshes, we make sure either", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 156, + 400, + 167 + ], + "spans": [ + { + "bbox": [ + 107, + 157, + 214, + 165 + ], + "type": "text", + "content": "a lower Hausdorff distance", + "score": 1.0 + }, + { + "bbox": [ + 216, + 156, + 249, + 167 + ], + "type": "inline_equation", + "content": "\\delta _ { \\mathrm { h a u s d o r f f } }", + "score": 0.7149 + }, + { + "bbox": [ + 250, + 157, + 400, + 166 + ], + "type": "text", + "content": "[66] or a similar rendered views [11].", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 173, + 506, + 228 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 174, + 504, + 183 + ], + "spans": [ + { + "bbox": [ + 107, + 174, + 504, + 183 + ], + "type": "text", + "content": "Collecting mesh-text pairs. We first render each 3D mesh with 12 different views, and concatenate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 186, + 503, + 194 + ], + "spans": [ + { + "bbox": [ + 107, + 186, + 503, + 194 + ], + "type": "text", + "content": "them into one single image. Then, we annotate both the front view image and the fused multi-view", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 196, + 504, + 205 + ], + "spans": [ + { + "bbox": [ + 107, + 196, + 504, + 205 + ], + "type": "text", + "content": "image using CogVLM [77]. After that, we adopt the Mistral-7B-Instruct model [35] with few-shot", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 208, + 504, + 216 + ], + "spans": [ + { + "bbox": [ + 107, + 208, + 504, + 216 + ], + "type": "text", + "content": "in-context examples to extract information on category and geometry from the CogVLM annotations.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 217, + 439, + 228 + ], + "spans": [ + { + "bbox": [ + 107, + 217, + 439, + 228 + ], + "type": "text", + "content": "We tag each 3D mesh with the resulting categories and 3 to 5 geometry descriptors.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 234, + 504, + 289 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 235, + 504, + 244 + ], + "spans": [ + { + "bbox": [ + 107, + 235, + 504, + 244 + ], + "type": "text", + "content": "Collecting mesh-image pairs. To produce diverse image conditions for 3D mesh generation, we", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 247, + 503, + 255 + ], + "spans": [ + { + "bbox": [ + 107, + 247, + 503, + 255 + ], + "type": "text", + "content": "first generate images with multi-view image and depth rendering. After that, we use the sentences", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 257, + 504, + 266 + ], + "spans": [ + { + "bbox": [ + 107, + 257, + 504, + 266 + ], + "type": "text", + "content": "produced by CogVLM [77] as the prompt, and use a find-tuned Stable Diffusion model [63] to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 268, + 503, + 277 + ], + "spans": [ + { + "bbox": [ + 107, + 268, + 503, + 277 + ], + "type": "text", + "content": "augment the rendered images for diverse textures and backgrounds. To ensure the quality of the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 279, + 368, + 289 + ], + "spans": [ + { + "bbox": [ + 107, + 279, + 368, + 289 + ], + "type": "text", + "content": "generated images, we also adopt a manually cleansing procedure.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 295, + 506, + 329 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 297, + 505, + 305 + ], + "spans": [ + { + "bbox": [ + 107, + 297, + 505, + 305 + ], + "type": "text", + "content": "Data Statistics. We present the data statistics of our large-scale 3D mesh collection in Tab. 1.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 307, + 504, + 316 + ], + "spans": [ + { + "bbox": [ + 107, + 307, + 504, + 316 + ], + "type": "text", + "content": "After organizing and combing 3D assets from ShapeNet [9], 3D-FUTURE [22], Objaverse [17], and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 319, + 390, + 327 + ], + "spans": [ + { + "bbox": [ + 107, + 319, + 390, + 327 + ], + "type": "text", + "content": "Objaverse-XL [16], we could achieve a total of 2.5 million 3D meshes.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "table", + "bbox": [ + 167, + 366, + 444, + 449 + ], + "blocks": [ + { + "bbox": [ + 104, + 338, + 505, + 361 + ], + "type": "table_caption", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 339, + 504, + 349 + ], + "spans": [ + { + "bbox": [ + 107, + 339, + 504, + 349 + ], + "type": "text", + "content": "Table 1: Statistics for the Training Data and Validation Data. After combining four data sources,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 350, + 441, + 361 + ], + "spans": [ + { + "bbox": [ + 107, + 350, + 441, + 361 + ], + "type": "text", + "content": "our proposed MeshXL models are trained on approximately 2.5 million 3D meshes.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 167, + 366, + 444, + 449 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 167, + 366, + 444, + 449 + ], + "spans": [ + { + "bbox": [ + 167, + 366, + 444, + 449 + ], + "type": "table", + "html": "
DatasetPre-trainingText-to-3D
TrainValTrainVal
ShapeNet [9]16,0011,75415,3841,728
3D-Future [22]1,603---
Objaverse [17]85,28285483,501820
Objaverse-XL [16]2,407,33715,2001,347,80213,579
Total2,510,22317,8081,446,67816,127
", + "image_path": "a75d2fc68468ed036d2e236d9a876b1cf72496d612e2bbd7f7b7a558740308d0.jpg" + } + ] + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 471, + 251, + 483 + ], + "type": "title", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 106, + 472, + 251, + 483 + ], + "spans": [ + { + "bbox": [ + 106, + 472, + 251, + 483 + ], + "type": "text", + "content": "4 Neural Coordinate Field", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 495, + 504, + 567 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 497, + 504, + 506 + ], + "spans": [ + { + "bbox": [ + 107, + 497, + 504, + 506 + ], + "type": "text", + "content": "Neural Coordinate Field (NeurCF) is an explicit representation with implicit neural embeddings.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 508, + 503, + 517 + ], + "spans": [ + { + "bbox": [ + 107, + 508, + 503, + 517 + ], + "type": "text", + "content": "To be specific, for a Euclidean 3D coordinate system, we can partition the vertices coordinates into", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 517, + 503, + 529 + ], + "spans": [ + { + "bbox": [ + 107, + 519, + 119, + 528 + ], + "type": "text", + "content": "an", + "score": 1.0 + }, + { + "bbox": [ + 119, + 517, + 134, + 529 + ], + "type": "inline_equation", + "content": "N ^ { 3 }", + "score": 0.7741 + }, + { + "bbox": [ + 135, + 519, + 299, + 529 + ], + "type": "text", + "content": "grid. Then, each discretized coordinate", + "score": 1.0 + }, + { + "bbox": [ + 300, + 518, + 354, + 529 + ], + "type": "inline_equation", + "content": "p = ( x , y , z )", + "score": 0.8628 + }, + { + "bbox": [ + 357, + 519, + 503, + 528 + ], + "type": "text", + "content": "can be encoded with the coordinate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 529, + 504, + 541 + ], + "spans": [ + { + "bbox": [ + 107, + 531, + 216, + 541 + ], + "type": "text", + "content": "embedding layer E, where", + "score": 1.0 + }, + { + "bbox": [ + 217, + 529, + 326, + 541 + ], + "type": "inline_equation", + "content": "\\mathcal { F } ( \\boldsymbol { p } ) = ( \\mathcal { E } ( \\boldsymbol { x } ) , \\mathcal { E } ( \\boldsymbol { y } ) , \\mathcal { E } ( \\boldsymbol { z } ) )", + "score": 0.9381 + }, + { + "bbox": [ + 327, + 530, + 486, + 541 + ], + "type": "text", + "content": ". Therefore, a k-sided polynomial face", + "score": 1.0 + }, + { + "bbox": [ + 488, + 529, + 504, + 541 + ], + "type": "inline_equation", + "content": "f ^ { ( i ) }", + "score": 0.6778 + } + ] + }, + { + "bbox": [ + 107, + 542, + 503, + 556 + ], + "spans": [ + { + "bbox": [ + 107, + 546, + 190, + 554 + ], + "type": "text", + "content": "can be encoded with", + "score": 1.0 + }, + { + "bbox": [ + 192, + 542, + 337, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal { E } _ { \\mathrm { f a c e } } ( \\boldsymbol { f } ^ { ( i ) } ) = ( \\mathcal { F } ( \\boldsymbol { p } _ { 1 } ^ { ( i ) } ) , \\cdot \\cdot \\cdot , \\mathcal { F } ( \\boldsymbol { p } _ { k } ^ { ( i ) } ) )", + "score": 0.9496 + }, + { + "bbox": [ + 337, + 545, + 503, + 555 + ], + "type": "text", + "content": "). For simplicity, the learnable coordinate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 556, + 259, + 566 + ], + "spans": [ + { + "bbox": [ + 107, + 556, + 259, + 566 + ], + "type": "text", + "content": "embeddings E are shared among axes.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 571, + 504, + 673 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 573, + 504, + 583 + ], + "spans": [ + { + "bbox": [ + 107, + 573, + 504, + 583 + ], + "type": "text", + "content": "Ordering. Due to the graph representation, the order of the mesh vertices and the order of the edges", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 584, + 504, + 594 + ], + "spans": [ + { + "bbox": [ + 107, + 584, + 504, + 594 + ], + "type": "text", + "content": "between them are permutation-invariant. A pre-defined ordering strategy is essential to facilitate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 595, + 504, + 605 + ], + "spans": [ + { + "bbox": [ + 107, + 595, + 504, + 605 + ], + "type": "text", + "content": "the sequence modelling in MeshXL. We employ the same ordering strategy as PolyGen [53] and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 606, + 504, + 615 + ], + "spans": [ + { + "bbox": [ + 107, + 606, + 504, + 615 + ], + "type": "text", + "content": "MeshGPT [66]. The mesh coordinates are first normalized into a unit cube based on the mesh’s", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "spans": [ + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "type": "text", + "content": "longest axis, and discretized into unsigned integers. Within each face, the vertices are cyclically", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 628, + 504, + 638 + ], + "spans": [ + { + "bbox": [ + 107, + 628, + 504, + 638 + ], + "type": "text", + "content": "permuted based their coordinates (z-y-x order, from lower to higher), which helps to preserve the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 639, + 503, + 648 + ], + "spans": [ + { + "bbox": [ + 107, + 639, + 503, + 648 + ], + "type": "text", + "content": "direction of normal vectors. Then, we order these faces based on the permuted coordinates (lower to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 648, + 505, + 659 + ], + "spans": [ + { + "bbox": [ + 107, + 650, + 425, + 659 + ], + "type": "text", + "content": "high). To this end, an n-faced 3D k-sided polynomial mesh can be represented as", + "score": 1.0 + }, + { + "bbox": [ + 427, + 648, + 484, + 659 + ], + "type": "inline_equation", + "content": "\\mathcal { M } \\in \\mathbb { Z } ^ { n \\times k \\times 3 }", + "score": 0.9177 + }, + { + "bbox": [ + 484, + 650, + 505, + 659 + ], + "type": "text", + "content": ", and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 659, + 356, + 672 + ], + "spans": [ + { + "bbox": [ + 107, + 662, + 200, + 670 + ], + "type": "text", + "content": "we can encode M with", + "score": 1.0 + }, + { + "bbox": [ + 202, + 659, + 351, + 672 + ], + "type": "inline_equation", + "content": "\\mathcal { E } _ { \\mathrm { m e s h } } = ( \\mathcal { E } _ { \\mathrm { f a c e } } ( f ^ { ( 1 ) } ) , \\cdot \\cdot \\cdot , \\mathcal { E } _ { \\mathrm { f a c e } } ( f ^ { ( n ) } ) )", + "score": 0.9459 + }, + { + "bbox": [ + 351, + 662, + 356, + 670 + ], + "type": "text", + "content": ").", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 677, + 506, + 723 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 679, + 503, + 689 + ], + "spans": [ + { + "bbox": [ + 107, + 679, + 503, + 689 + ], + "type": "text", + "content": "A Sequential Mesh Representation. One direct way to represent the 3D meshes is to directly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 689, + 504, + 700 + ], + "spans": [ + { + "bbox": [ + 107, + 690, + 227, + 699 + ], + "type": "text", + "content": "reshape M into a vector with", + "score": 1.0 + }, + { + "bbox": [ + 230, + 689, + 268, + 700 + ], + "type": "inline_equation", + "content": "( n \\cdot k \\cdot 3 )", + "score": 0.4677 + }, + { + "bbox": [ + 269, + 690, + 504, + 700 + ], + "type": "text", + "content": "tokens. As a special case, an n-faced triangular mesh can", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 701, + 503, + 711 + ], + "spans": [ + { + "bbox": [ + 107, + 701, + 503, + 711 + ], + "type": "text", + "content": "be represented by a vector with 9n tokens. Meanwhile, our representation can also be expanded to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 712, + 504, + 721 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 504, + 721 + ], + "type": "text", + "content": "hybrid polynomial mesh representations with the proper introduction of separate tokens. For example,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 243, + 505, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 243, + 505, + 253 + ], + "type": "text", + "content": "we can generate triangles within “ · · · ” and quadrilaterals within “ · · · ”.", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 106, + 253, + 504, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 253, + 504, + 264 + ], + "type": "text", + "content": "To identify the start and end of a mesh sequence, we add a (“begin-of-sequence”) token before", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 265, + 369, + 275 + ], + "spans": [ + { + "bbox": [ + 107, + 265, + 369, + 275 + ], + "type": "text", + "content": "the mesh sequence and an (“end-of-sequence”) token after.", + "score": 1.0, + "cross_page": true + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 118, + 73, + 315, + 167 + ], + "blocks": [ + { + "bbox": [ + 118, + 73, + 315, + 167 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 73, + 315, + 167 + ], + "spans": [ + { + "bbox": [ + 118, + 73, + 315, + 167 + ], + "type": "image", + "content": "```mermaid\ngraph LR\n A[\"Coordinate Embeddings: ε\"] --> B[\"p = (x,y,z)\"]\n B --> C[\"F(p) = (ε(x), ε(y), ε(z))\"]\n D[\"Face Embedding:\\nε_face(f^(i)) = (F(p_1^(i)), ..., F(p_k^(i)))\"]\n E[\"Mesh Embedding:\\nε_mesh(M) = (ε_face(f^(1)), ..., ε_face(f^(n)))\"]\n```", + "image_path": "a630cfe35c3ec609be24eeec3d723fe2b40be6f1211dbc75599c6cd0359ed5a8.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 167, + 168, + 253, + 177 + ], + "type": "image_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 167, + 168, + 253, + 177 + ], + "spans": [ + { + "bbox": [ + 167, + 168, + 253, + 177 + ], + "type": "text", + "content": "(a) Neural Coordinate Field", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_type": "flowchart" + }, + { + "type": "image", + "bbox": [ + 318, + 73, + 503, + 166 + ], + "blocks": [ + { + "bbox": [ + 318, + 73, + 503, + 166 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 73, + 503, + 166 + ], + "spans": [ + { + "bbox": [ + 318, + 73, + 503, + 166 + ], + "type": "image", + "content": "Next Coordinate Prediction", + "image_path": "51c707d52655b90586d370683125db668549db2f46c0499de79259dea0e59432.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 348, + 167, + 463, + 177 + ], + "type": "image_caption", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 348, + 168, + 462, + 177 + ], + "spans": [ + { + "bbox": [ + 348, + 168, + 462, + 177 + ], + "type": "text", + "content": "(b) Auto-regressive Mesh Generation", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 104, + 188, + 504, + 222 + ], + "type": "image_caption", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 190, + 504, + 200 + ], + "spans": [ + { + "bbox": [ + 107, + 190, + 504, + 200 + ], + "type": "text", + "content": "Figure 2: Mesh Representation. We present the Neural Coordinate Field (NeurCF) to encode the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 200, + 504, + 210 + ], + "spans": [ + { + "bbox": [ + 106, + 200, + 504, + 210 + ], + "type": "text", + "content": "discretized coordinates in the Euclidean space. Benefiting from NeurCF and a pre-defined ordering", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 212, + 496, + 221 + ], + "spans": [ + { + "bbox": [ + 107, + 212, + 496, + 221 + ], + "type": "text", + "content": "strategy, our proposed MeshXL can directly generate the unstructured 3D mesh auto-regressively.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 2, + "sub_type": "text_image" + }, + { + "bbox": [ + 104, + 242, + 505, + 276 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 106, + 243, + 505, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 243, + 505, + 253 + ], + "type": "text", + "content": "we can generate triangles within “ · · · ” and quadrilaterals within “ · · · ”.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 253, + 504, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 253, + 504, + 264 + ], + "type": "text", + "content": "To identify the start and end of a mesh sequence, we add a (“begin-of-sequence”) token before", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 265, + 369, + 275 + ], + "spans": [ + { + "bbox": [ + 107, + 265, + 369, + 275 + ], + "type": "text", + "content": "the mesh sequence and an (“end-of-sequence”) token after.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 281, + 506, + 337 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 282, + 504, + 292 + ], + "spans": [ + { + "bbox": [ + 107, + 282, + 504, + 292 + ], + "type": "text", + "content": "Comparisons. Compared to other forms of 3D representations, NeurCF is a direct representation for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 293, + 505, + 303 + ], + "spans": [ + { + "bbox": [ + 107, + 293, + 505, + 303 + ], + "type": "text", + "content": "3D meshes. Since we represent each coordinate with learnable embeddings, NeurCF is an end-to-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 304, + 504, + 314 + ], + "spans": [ + { + "bbox": [ + 107, + 304, + 504, + 314 + ], + "type": "text", + "content": "end trainable representation for unstructured 3D meshes. Additionally, NeurCF is storage efficient", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 313, + 503, + 326 + ], + "spans": [ + { + "bbox": [ + 107, + 316, + 211, + 325 + ], + "type": "text", + "content": "comparing to voxel fields", + "score": 1.0 + }, + { + "bbox": [ + 213, + 313, + 247, + 326 + ], + "type": "inline_equation", + "content": "( O ( N ^ { 3 } ) )", + "score": 0.6782 + }, + { + "bbox": [ + 247, + 316, + 503, + 324 + ], + "type": "text", + "content": ") and point clouds, since it can naturally model the flat surfaces", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 327, + 194, + 336 + ], + "spans": [ + { + "bbox": [ + 107, + 327, + 194, + 336 + ], + "type": "text", + "content": "with graph structures.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 351, + 167, + 363 + ], + "type": "title", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 105, + 351, + 167, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 167, + 365 + ], + "type": "text", + "content": "5 Method", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 376, + 506, + 410 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 378, + 504, + 387 + ], + "spans": [ + { + "bbox": [ + 107, + 378, + 504, + 387 + ], + "type": "text", + "content": "We first present the architecture and training objective for MeshXL models. Then, we show that", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 105, + 388, + 505, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 505, + 399 + ], + "type": "text", + "content": "MeshXL models can take an additional modality as the condition for controllable 3D assets generation.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 399, + 294, + 409 + ], + "spans": [ + { + "bbox": [ + 106, + 399, + 294, + 409 + ], + "type": "text", + "content": "After this, we investigate the effects of scaling.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 415, + 504, + 482 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 416, + 504, + 426 + ], + "spans": [ + { + "bbox": [ + 107, + 416, + 504, + 426 + ], + "type": "text", + "content": "Architecture. In Sec. 4, we present a simple-yet-effective way to represent a 3D mesh into a sequence.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 426, + 505, + 437 + ], + "spans": [ + { + "bbox": [ + 106, + 426, + 505, + 437 + ], + "type": "text", + "content": "Therefore, the learning of 3D mesh generation can be formulated into an auto-regressive problem,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 439, + 504, + 448 + ], + "spans": [ + { + "bbox": [ + 107, + 439, + 504, + 448 + ], + "type": "text", + "content": "and can be seaminglessly addressed by modern Large Language Model (LLM) approaches. In our", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 450, + 504, + 459 + ], + "spans": [ + { + "bbox": [ + 106, + 450, + 504, + 459 + ], + "type": "text", + "content": "paper, we adopt the decoder-only transformers using the OPT [95] codebase as our base models. To", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 460, + 503, + 469 + ], + "spans": [ + { + "bbox": [ + 107, + 460, + 503, + 469 + ], + "type": "text", + "content": "adapt the pre-trained OPT models to our next-coordinate prediction setting, we fine-tune the whole", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 472, + 371, + 481 + ], + "spans": [ + { + "bbox": [ + 107, + 472, + 371, + 481 + ], + "type": "text", + "content": "model with newly-initialized coordinate and position embeddings.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 487, + 504, + 510 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 489, + 503, + 498 + ], + "spans": [ + { + "bbox": [ + 107, + 489, + 503, + 498 + ], + "type": "text", + "content": "Generative Pre-Training. We use the standard next-token prediction loss to train our models. Given", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 499, + 458, + 508 + ], + "spans": [ + { + "bbox": [ + 107, + 499, + 458, + 508 + ], + "type": "text", + "content": "the trainable weights θ and an |s|-length sequence s, the generation loss is calculated as:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 209, + 517, + 505, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 209, + 517, + 505, + 550 + ], + "spans": [ + { + "bbox": [ + 209, + 517, + 505, + 550 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm{MeshXL}} \\left(\\theta\\right) = - \\sum_ {i = 1} ^ {| s |} \\log P \\left(s _ {[ i ]} | s _ {[ 1, \\dots , i - 1 ]}; \\theta\\right). \\tag {1}", + "image_path": "65c96116172ab6b1d9061673ef89a187bc94b20443f6afc5971bb03cf0744c40.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 560, + 504, + 594 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 107, + 562, + 504, + 571 + ], + "spans": [ + { + "bbox": [ + 107, + 562, + 504, + 571 + ], + "type": "text", + "content": "For each mesh sequence, we add a token before the mesh tokens, and an token after the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 572, + 504, + 582 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 504, + 582 + ], + "type": "text", + "content": "mesh tokens to identify the ending of a 3D mesh. During inference, we adopt the top-k and top-p", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 585, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 107, + 585, + 287, + 594 + ], + "type": "text", + "content": "sampling strategy to produce diverse outputs.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 599, + 506, + 666 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 107, + 600, + 504, + 610 + ], + "spans": [ + { + "bbox": [ + 107, + 600, + 504, + 610 + ], + "type": "text", + "content": "X-to-Mesh Generation. Here we mainly consider generating 3D meshes from images and texts.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 611, + 504, + 621 + ], + "spans": [ + { + "bbox": [ + 107, + 611, + 504, + 621 + ], + "type": "text", + "content": "We adopt a pre-trained BERT [18] model for text feature encoding, and a pre-trained ViT [19] model", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 623, + 504, + 632 + ], + "spans": [ + { + "bbox": [ + 107, + 623, + 504, + 632 + ], + "type": "text", + "content": "for image feature encoding. To align the additional text/image feature with the mesh coordinate field,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 633, + 503, + 643 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 503, + 643 + ], + "type": "text", + "content": "we adopt the Q-Former architecture [40] to compress the encoded feature into a fixed-length of 32", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 645, + 503, + 654 + ], + "spans": [ + { + "bbox": [ + 107, + 645, + 503, + 654 + ], + "type": "text", + "content": "learnable tokens as the prefix of the MeshXL model. The overall training objective of the conditional", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 655, + 253, + 665 + ], + "spans": [ + { + "bbox": [ + 107, + 655, + 253, + 665 + ], + "type": "text", + "content": "mesh generation is shown in Eq. (2):", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 203, + 672, + 505, + 704 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 203, + 672, + 505, + 704 + ], + "spans": [ + { + "bbox": [ + 203, + 672, + 505, + 704 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {X} \\text {-to - mesh}} (\\theta) = - \\sum_ {i = 1} ^ {| s |} \\log P \\left(s _ {[ i ]} | s _ {[ 1, \\dots , i - 1 ]}; \\mathcal {X}\\right). \\tag {2}", + "image_path": "04938518bf9de86d30af320478a6e132d9a28a19e6a24234c3a8a3eb6e54467e.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 711, + 435, + 723 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 107, + 712, + 433, + 721 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 433, + 721 + ], + "type": "text", + "content": "During inference, the model predicts the mesh tokens after the fixed-length prefix.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "page_number", + "angle": 0, + "index": 16, + "lines": [ + { + "bbox": [ + 302, + 742, + 309, + 752 + ], + "spans": [ + { + "bbox": [ + 302, + 742, + 309, + 752 + ], + "type": "text", + "content": "5", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4, + "para_blocks": [ + { + "type": "image", + "bbox": [ + 118, + 73, + 315, + 167 + ], + "blocks": [ + { + "bbox": [ + 118, + 73, + 315, + 167 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 73, + 315, + 167 + ], + "spans": [ + { + "bbox": [ + 118, + 73, + 315, + 167 + ], + "type": "image", + "content": "```mermaid\ngraph LR\n A[\"Coordinate Embeddings: ε\"] --> B[\"p = (x,y,z)\"]\n B --> C[\"F(p) = (ε(x), ε(y), ε(z))\"]\n D[\"Face Embedding:\\nε_face(f^(i)) = (F(p_1^(i)), ..., F(p_k^(i)))\"]\n E[\"Mesh Embedding:\\nε_mesh(M) = (ε_face(f^(1)), ..., ε_face(f^(n)))\"]\n```", + "image_path": "a630cfe35c3ec609be24eeec3d723fe2b40be6f1211dbc75599c6cd0359ed5a8.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 167, + 168, + 253, + 177 + ], + "type": "image_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 167, + 168, + 253, + 177 + ], + "spans": [ + { + "bbox": [ + 167, + 168, + 253, + 177 + ], + "type": "text", + "content": "(a) Neural Coordinate Field", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_type": "flowchart" + }, + { + "type": "image", + "bbox": [ + 318, + 73, + 503, + 166 + ], + "blocks": [ + { + "bbox": [ + 318, + 73, + 503, + 166 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 73, + 503, + 166 + ], + "spans": [ + { + "bbox": [ + 318, + 73, + 503, + 166 + ], + "type": "image", + "content": "Next Coordinate Prediction", + "image_path": "51c707d52655b90586d370683125db668549db2f46c0499de79259dea0e59432.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 348, + 167, + 463, + 177 + ], + "type": "image_caption", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 348, + 168, + 462, + 177 + ], + "spans": [ + { + "bbox": [ + 348, + 168, + 462, + 177 + ], + "type": "text", + "content": "(b) Auto-regressive Mesh Generation", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 104, + 188, + 504, + 222 + ], + "type": "image_caption", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 190, + 504, + 200 + ], + "spans": [ + { + "bbox": [ + 107, + 190, + 504, + 200 + ], + "type": "text", + "content": "Figure 2: Mesh Representation. We present the Neural Coordinate Field (NeurCF) to encode the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 200, + 504, + 210 + ], + "spans": [ + { + "bbox": [ + 106, + 200, + 504, + 210 + ], + "type": "text", + "content": "discretized coordinates in the Euclidean space. Benefiting from NeurCF and a pre-defined ordering", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 212, + 496, + 221 + ], + "spans": [ + { + "bbox": [ + 107, + 212, + 496, + 221 + ], + "type": "text", + "content": "strategy, our proposed MeshXL can directly generate the unstructured 3D mesh auto-regressively.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 2, + "sub_type": "text_image" + }, + { + "bbox": [ + 104, + 242, + 505, + 276 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 104, + 281, + 506, + 337 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 282, + 504, + 292 + ], + "spans": [ + { + "bbox": [ + 107, + 282, + 504, + 292 + ], + "type": "text", + "content": "Comparisons. Compared to other forms of 3D representations, NeurCF is a direct representation for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 293, + 505, + 303 + ], + "spans": [ + { + "bbox": [ + 107, + 293, + 505, + 303 + ], + "type": "text", + "content": "3D meshes. Since we represent each coordinate with learnable embeddings, NeurCF is an end-to-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 304, + 504, + 314 + ], + "spans": [ + { + "bbox": [ + 107, + 304, + 504, + 314 + ], + "type": "text", + "content": "end trainable representation for unstructured 3D meshes. Additionally, NeurCF is storage efficient", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 313, + 503, + 326 + ], + "spans": [ + { + "bbox": [ + 107, + 316, + 211, + 325 + ], + "type": "text", + "content": "comparing to voxel fields", + "score": 1.0 + }, + { + "bbox": [ + 213, + 313, + 247, + 326 + ], + "type": "inline_equation", + "content": "( O ( N ^ { 3 } ) )", + "score": 0.6782 + }, + { + "bbox": [ + 247, + 316, + 503, + 324 + ], + "type": "text", + "content": ") and point clouds, since it can naturally model the flat surfaces", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 327, + 194, + 336 + ], + "spans": [ + { + "bbox": [ + 107, + 327, + 194, + 336 + ], + "type": "text", + "content": "with graph structures.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 351, + 167, + 363 + ], + "type": "title", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 105, + 351, + 167, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 167, + 365 + ], + "type": "text", + "content": "5 Method", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 376, + 506, + 410 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 378, + 504, + 387 + ], + "spans": [ + { + "bbox": [ + 107, + 378, + 504, + 387 + ], + "type": "text", + "content": "We first present the architecture and training objective for MeshXL models. Then, we show that", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 105, + 388, + 505, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 505, + 399 + ], + "type": "text", + "content": "MeshXL models can take an additional modality as the condition for controllable 3D assets generation.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 399, + 294, + 409 + ], + "spans": [ + { + "bbox": [ + 106, + 399, + 294, + 409 + ], + "type": "text", + "content": "After this, we investigate the effects of scaling.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 415, + 504, + 482 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 416, + 504, + 426 + ], + "spans": [ + { + "bbox": [ + 107, + 416, + 504, + 426 + ], + "type": "text", + "content": "Architecture. In Sec. 4, we present a simple-yet-effective way to represent a 3D mesh into a sequence.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 426, + 505, + 437 + ], + "spans": [ + { + "bbox": [ + 106, + 426, + 505, + 437 + ], + "type": "text", + "content": "Therefore, the learning of 3D mesh generation can be formulated into an auto-regressive problem,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 439, + 504, + 448 + ], + "spans": [ + { + "bbox": [ + 107, + 439, + 504, + 448 + ], + "type": "text", + "content": "and can be seaminglessly addressed by modern Large Language Model (LLM) approaches. In our", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 450, + 504, + 459 + ], + "spans": [ + { + "bbox": [ + 106, + 450, + 504, + 459 + ], + "type": "text", + "content": "paper, we adopt the decoder-only transformers using the OPT [95] codebase as our base models. To", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 460, + 503, + 469 + ], + "spans": [ + { + "bbox": [ + 107, + 460, + 503, + 469 + ], + "type": "text", + "content": "adapt the pre-trained OPT models to our next-coordinate prediction setting, we fine-tune the whole", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 472, + 371, + 481 + ], + "spans": [ + { + "bbox": [ + 107, + 472, + 371, + 481 + ], + "type": "text", + "content": "model with newly-initialized coordinate and position embeddings.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 487, + 504, + 510 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 489, + 503, + 498 + ], + "spans": [ + { + "bbox": [ + 107, + 489, + 503, + 498 + ], + "type": "text", + "content": "Generative Pre-Training. We use the standard next-token prediction loss to train our models. Given", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 499, + 458, + 508 + ], + "spans": [ + { + "bbox": [ + 107, + 499, + 458, + 508 + ], + "type": "text", + "content": "the trainable weights θ and an |s|-length sequence s, the generation loss is calculated as:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 209, + 517, + 505, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 209, + 517, + 505, + 550 + ], + "spans": [ + { + "bbox": [ + 209, + 517, + 505, + 550 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm{MeshXL}} \\left(\\theta\\right) = - \\sum_ {i = 1} ^ {| s |} \\log P \\left(s _ {[ i ]} | s _ {[ 1, \\dots , i - 1 ]}; \\theta\\right). \\tag {1}", + "image_path": "65c96116172ab6b1d9061673ef89a187bc94b20443f6afc5971bb03cf0744c40.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 560, + 504, + 594 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 107, + 562, + 504, + 571 + ], + "spans": [ + { + "bbox": [ + 107, + 562, + 504, + 571 + ], + "type": "text", + "content": "For each mesh sequence, we add a token before the mesh tokens, and an token after the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 572, + 504, + 582 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 504, + 582 + ], + "type": "text", + "content": "mesh tokens to identify the ending of a 3D mesh. During inference, we adopt the top-k and top-p", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 585, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 107, + 585, + 287, + 594 + ], + "type": "text", + "content": "sampling strategy to produce diverse outputs.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 599, + 506, + 666 + ], + "type": "text", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 107, + 600, + 504, + 610 + ], + "spans": [ + { + "bbox": [ + 107, + 600, + 504, + 610 + ], + "type": "text", + "content": "X-to-Mesh Generation. Here we mainly consider generating 3D meshes from images and texts.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 611, + 504, + 621 + ], + "spans": [ + { + "bbox": [ + 107, + 611, + 504, + 621 + ], + "type": "text", + "content": "We adopt a pre-trained BERT [18] model for text feature encoding, and a pre-trained ViT [19] model", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 623, + 504, + 632 + ], + "spans": [ + { + "bbox": [ + 107, + 623, + 504, + 632 + ], + "type": "text", + "content": "for image feature encoding. To align the additional text/image feature with the mesh coordinate field,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 633, + 503, + 643 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 503, + 643 + ], + "type": "text", + "content": "we adopt the Q-Former architecture [40] to compress the encoded feature into a fixed-length of 32", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 645, + 503, + 654 + ], + "spans": [ + { + "bbox": [ + 107, + 645, + 503, + 654 + ], + "type": "text", + "content": "learnable tokens as the prefix of the MeshXL model. The overall training objective of the conditional", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 655, + 253, + 665 + ], + "spans": [ + { + "bbox": [ + 107, + 655, + 253, + 665 + ], + "type": "text", + "content": "mesh generation is shown in Eq. (2):", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 203, + 672, + 505, + 704 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 203, + 672, + 505, + 704 + ], + "spans": [ + { + "bbox": [ + 203, + 672, + 505, + 704 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {X} \\text {-to - mesh}} (\\theta) = - \\sum_ {i = 1} ^ {| s |} \\log P \\left(s _ {[ i ]} | s _ {[ 1, \\dots , i - 1 ]}; \\mathcal {X}\\right). \\tag {2}", + "image_path": "04938518bf9de86d30af320478a6e132d9a28a19e6a24234c3a8a3eb6e54467e.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 711, + 435, + 723 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 107, + 712, + 433, + 721 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 433, + 721 + ], + "type": "text", + "content": "During inference, the model predicts the mesh tokens after the fixed-length prefix.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 108, + 72, + 503, + 217 + ], + "blocks": [ + { + "bbox": [ + 108, + 72, + 503, + 217 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 72, + 503, + 217 + ], + "spans": [ + { + "bbox": [ + 108, + 72, + 503, + 217 + ], + "type": "image", + "image_path": "f5a493f49eb91e662a5f269332e0b435babbd67f87842f82cfe63479c24abc2f.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 228, + 504, + 251 + ], + "type": "image_caption", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 230, + 504, + 239 + ], + "spans": [ + { + "bbox": [ + 107, + 230, + 504, + 239 + ], + "type": "text", + "content": "Figure 3: Training and Validation Perplexity (PPL) for MeshXL Models. We train all the models", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 241, + 479, + 250 + ], + "spans": [ + { + "bbox": [ + 107, + 241, + 479, + 250 + ], + "type": "text", + "content": "from scratch on 150 billion tokens. We observe that the performance grows with model sizes.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_images": [ + { + "type": "image", + "bbox": [ + 0.0, + 0.0, + 0.39, + 1.0 + ] + }, + { + "type": "image", + "bbox": [ + 0.392, + 0.0, + 0.595, + 1.0 + ] + }, + { + "type": "image", + "bbox": [ + 0.595, + 0.0, + 0.797, + 1.0 + ] + }, + { + "type": "image", + "bbox": [ + 0.797, + 0.0, + 1.0, + 1.0 + ] + } + ] + }, + { + "bbox": [ + 104, + 271, + 504, + 338 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 106, + 273, + 504, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 273, + 504, + 282 + ], + "type": "text", + "content": "Scaling Up. We present MeshXL in various sizes, including 125M, 350M, and 1.3B. The detailed", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 284, + 504, + 294 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 504, + 294 + ], + "type": "text", + "content": "hyperparameters for training different models can be found in Tab. 2. To better analyze the scaling", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 296, + 504, + 304 + ], + "spans": [ + { + "bbox": [ + 107, + 296, + 504, + 304 + ], + "type": "text", + "content": "effects, we train all models from scratch on 150 billion tokens. We provide both training curve and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 307, + 504, + 316 + ], + "spans": [ + { + "bbox": [ + 107, + 307, + 504, + 316 + ], + "type": "text", + "content": "validation perplexity for different models in Fig. 3. One can see that as the number of parameters", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 317, + 504, + 327 + ], + "spans": [ + { + "bbox": [ + 107, + 317, + 504, + 327 + ], + "type": "text", + "content": "grows, the model achieves a lower validation perplexity, indicating a higher probability to produce", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 328, + 182, + 337 + ], + "spans": [ + { + "bbox": [ + 107, + 328, + 182, + 337 + ], + "type": "text", + "content": "the validation data.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 354, + 192, + 368 + ], + "type": "title", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 106, + 354, + 190, + 368 + ], + "spans": [ + { + "bbox": [ + 106, + 354, + 190, + 368 + ], + "type": "text", + "content": "6 Experiments", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 379, + 504, + 412 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 380, + 503, + 389 + ], + "spans": [ + { + "bbox": [ + 107, + 380, + 503, + 389 + ], + "type": "text", + "content": "We first briefly introduce the data, metrics, and implementation details in Sec. 6.1. Then, we provide", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 392, + 503, + 400 + ], + "spans": [ + { + "bbox": [ + 107, + 392, + 503, + 400 + ], + "type": "text", + "content": "evaluations and comparisons on the generated meshes (cf. Sec. 6.2) and ablations (cf. Sec. 6.3). We", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 403, + 285, + 411 + ], + "spans": [ + { + "bbox": [ + 107, + 403, + 285, + 411 + ], + "type": "text", + "content": "also provide visualization results in Sec. 6.4.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 426, + 313, + 437 + ], + "type": "title", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 426, + 312, + 437 + ], + "spans": [ + { + "bbox": [ + 107, + 426, + 312, + 437 + ], + "type": "text", + "content": "6.1 Data, Metrics, and Implementation Details", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 446, + 504, + 514 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 448, + 504, + 457 + ], + "spans": [ + { + "bbox": [ + 107, + 448, + 504, + 457 + ], + "type": "text", + "content": "Data. We pre-train the base model with 2.5 million 3D meshes collected from the combination of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 459, + 504, + 468 + ], + "spans": [ + { + "bbox": [ + 107, + 459, + 504, + 468 + ], + "type": "text", + "content": "ShapeNet [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16]. We use planar decimation", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 470, + 503, + 479 + ], + "spans": [ + { + "bbox": [ + 107, + 470, + 503, + 479 + ], + "type": "text", + "content": "on meshes with more than 800 faces following MeshGPT [66] and RobustLowPoly [11]. More details", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 481, + 504, + 491 + ], + "spans": [ + { + "bbox": [ + 107, + 481, + 504, + 491 + ], + "type": "text", + "content": "on the data collection and processing pipeline can be found in the appendix. For generative mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 491, + 504, + 501 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 504, + 501 + ], + "type": "text", + "content": "pre-training, we randomly rotate these meshes with degrees from (0◦, 90◦, 180◦, 270◦), and adopt", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 503, + 415, + 512 + ], + "spans": [ + { + "bbox": [ + 107, + 503, + 415, + 512 + ], + "type": "text", + "content": "random scaling along each axis within range [0.9, 1.1] for data augmentation.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 518, + 506, + 640 + ], + "type": "text", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 107, + 520, + 503, + 529 + ], + "spans": [ + { + "bbox": [ + 107, + 520, + 503, + 529 + ], + "type": "text", + "content": "Metrics. We follow the standard evaluation protocols in MeshGPT [66] and PolyDiff [2] with", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 530, + 504, + 540 + ], + "spans": [ + { + "bbox": [ + 107, + 530, + 504, + 540 + ], + "type": "text", + "content": "the following metrics. Coverage (COV) is sensitive to mode dropping and is used to quantify the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 541, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 107, + 541, + 505, + 552 + ], + "type": "text", + "content": "diversity of the generated meshes. However, COV does not assess the quality of the generated results.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 552, + 504, + 563 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 504, + 563 + ], + "type": "text", + "content": "Minimum Matching Distance (MMD) calculates the average distance between the reference set", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 563, + 504, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 563, + 504, + 574 + ], + "type": "text", + "content": "and their closest neighbors in the generated set. However, MMD is not sensitive to low-quality", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 105, + 574, + 503, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 503, + 585 + ], + "type": "text", + "content": "results. The 1-Nearest Neighbor Accuracy (1-NNA) directly quantifies the quality and diversity", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 586, + 503, + 595 + ], + "spans": [ + { + "bbox": [ + 107, + 586, + 503, + 595 + ], + "type": "text", + "content": "between the generation set and the reference set. The optimal value of 1-NNA is 50%. We adopt the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 597, + 504, + 605 + ], + "spans": [ + { + "bbox": [ + 107, + 597, + 504, + 605 + ], + "type": "text", + "content": "Jensen-Shannon Divergence (JSD) score to directly evaluate 3D meshes. We use Chamfer Distance", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 607, + 504, + 616 + ], + "spans": [ + { + "bbox": [ + 107, + 607, + 504, + 616 + ], + "type": "text", + "content": "to measure the similarity between two samples. We also adopt the Frechet Inception Distance (FID)", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 618, + 504, + 628 + ], + "spans": [ + { + "bbox": [ + 107, + 618, + 504, + 628 + ], + "type": "text", + "content": "and Kernel Inception Distance (KID) on the rendered images for feature-level evaluation. The MMD,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 628, + 281, + 639 + ], + "spans": [ + { + "bbox": [ + 106, + 628, + 281, + 639 + ], + "type": "text", + "content": "JSD, and KID scores are multiplied by 103.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 645, + 504, + 723 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 106, + 646, + 504, + 655 + ], + "spans": [ + { + "bbox": [ + 106, + 646, + 504, + 655 + ], + "type": "text", + "content": "Implementation. All experiments are conducted on a cluster consisting of 128 A100 GPUs. We", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 657, + 504, + 667 + ], + "spans": [ + { + "bbox": [ + 107, + 657, + 504, + 667 + ], + "type": "text", + "content": "train our models under bfloat16 and the ZeRO-2 strategy [60] using the AdamW [48] optimizer with", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 666, + 504, + 678 + ], + "spans": [ + { + "bbox": [ + 107, + 668, + 223, + 678 + ], + "type": "text", + "content": "a learning rate decaying from", + "score": 1.0 + }, + { + "bbox": [ + 225, + 666, + 279, + 677 + ], + "type": "inline_equation", + "content": "1 0 ^ { - 4 } ~ \\mathrm { t o } ~ 1 0 ^ { - 6 }", + "score": 0.6761 + }, + { + "bbox": [ + 280, + 668, + 504, + 678 + ], + "type": "text", + "content": "and a weight decay of 0.1. The detailed hyperparameters", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 678, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 504, + 689 + ], + "type": "text", + "content": "for different models can be found in Tab. 2. To train our base models, we load the weights from the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 105, + 689, + 504, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 689, + 504, + 700 + ], + "type": "text", + "content": "pre-trained OPT models [95] and initialize the word embeddings and positional embeddings from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 503, + 712 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 503, + 712 + ], + "type": "text", + "content": "scratch. Without further specification, we generate 3D meshes with the top-k and top-p sampling", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 712, + 248, + 721 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 248, + 721 + ], + "type": "text", + "content": "strategy with k = 50 and p = 0.95.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 742, + 308, + 750 + ], + "type": "page_number", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 302, + 742, + 309, + 752 + ], + "spans": [ + { + "bbox": [ + 302, + 742, + 309, + 752 + ], + "type": "text", + "content": "6", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5, + "para_blocks": [ + { + "type": "image", + "bbox": [ + 108, + 72, + 503, + 217 + ], + "blocks": [ + { + "bbox": [ + 108, + 72, + 503, + 217 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 72, + 503, + 217 + ], + "spans": [ + { + "bbox": [ + 108, + 72, + 503, + 217 + ], + "type": "image", + "image_path": "f5a493f49eb91e662a5f269332e0b435babbd67f87842f82cfe63479c24abc2f.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 228, + 504, + 251 + ], + "type": "image_caption", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 230, + 504, + 239 + ], + "spans": [ + { + "bbox": [ + 107, + 230, + 504, + 239 + ], + "type": "text", + "content": "Figure 3: Training and Validation Perplexity (PPL) for MeshXL Models. We train all the models", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 241, + 479, + 250 + ], + "spans": [ + { + "bbox": [ + 107, + 241, + 479, + 250 + ], + "type": "text", + "content": "from scratch on 150 billion tokens. We observe that the performance grows with model sizes.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_images": [ + { + "type": "image", + "bbox": [ + 0.0, + 0.0, + 0.39, + 1.0 + ] + }, + { + "type": "image", + "bbox": [ + 0.392, + 0.0, + 0.595, + 1.0 + ] + }, + { + "type": "image", + "bbox": [ + 0.595, + 0.0, + 0.797, + 1.0 + ] + }, + { + "type": "image", + "bbox": [ + 0.797, + 0.0, + 1.0, + 1.0 + ] + } + ] + }, + { + "bbox": [ + 104, + 271, + 504, + 338 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 106, + 273, + 504, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 273, + 504, + 282 + ], + "type": "text", + "content": "Scaling Up. We present MeshXL in various sizes, including 125M, 350M, and 1.3B. The detailed", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 284, + 504, + 294 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 504, + 294 + ], + "type": "text", + "content": "hyperparameters for training different models can be found in Tab. 2. To better analyze the scaling", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 296, + 504, + 304 + ], + "spans": [ + { + "bbox": [ + 107, + 296, + 504, + 304 + ], + "type": "text", + "content": "effects, we train all models from scratch on 150 billion tokens. We provide both training curve and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 307, + 504, + 316 + ], + "spans": [ + { + "bbox": [ + 107, + 307, + 504, + 316 + ], + "type": "text", + "content": "validation perplexity for different models in Fig. 3. One can see that as the number of parameters", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 317, + 504, + 327 + ], + "spans": [ + { + "bbox": [ + 107, + 317, + 504, + 327 + ], + "type": "text", + "content": "grows, the model achieves a lower validation perplexity, indicating a higher probability to produce", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 328, + 182, + 337 + ], + "spans": [ + { + "bbox": [ + 107, + 328, + 182, + 337 + ], + "type": "text", + "content": "the validation data.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 354, + 192, + 368 + ], + "type": "title", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 106, + 354, + 190, + 368 + ], + "spans": [ + { + "bbox": [ + 106, + 354, + 190, + 368 + ], + "type": "text", + "content": "6 Experiments", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 379, + 504, + 412 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 380, + 503, + 389 + ], + "spans": [ + { + "bbox": [ + 107, + 380, + 503, + 389 + ], + "type": "text", + "content": "We first briefly introduce the data, metrics, and implementation details in Sec. 6.1. Then, we provide", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 392, + 503, + 400 + ], + "spans": [ + { + "bbox": [ + 107, + 392, + 503, + 400 + ], + "type": "text", + "content": "evaluations and comparisons on the generated meshes (cf. Sec. 6.2) and ablations (cf. Sec. 6.3). We", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 403, + 285, + 411 + ], + "spans": [ + { + "bbox": [ + 107, + 403, + 285, + 411 + ], + "type": "text", + "content": "also provide visualization results in Sec. 6.4.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 426, + 313, + 437 + ], + "type": "title", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 426, + 312, + 437 + ], + "spans": [ + { + "bbox": [ + 107, + 426, + 312, + 437 + ], + "type": "text", + "content": "6.1 Data, Metrics, and Implementation Details", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 446, + 504, + 514 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 448, + 504, + 457 + ], + "spans": [ + { + "bbox": [ + 107, + 448, + 504, + 457 + ], + "type": "text", + "content": "Data. We pre-train the base model with 2.5 million 3D meshes collected from the combination of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 459, + 504, + 468 + ], + "spans": [ + { + "bbox": [ + 107, + 459, + 504, + 468 + ], + "type": "text", + "content": "ShapeNet [9], 3D-FUTURE [22], Objaverse [17], and Objaverse-XL [16]. We use planar decimation", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 470, + 503, + 479 + ], + "spans": [ + { + "bbox": [ + 107, + 470, + 503, + 479 + ], + "type": "text", + "content": "on meshes with more than 800 faces following MeshGPT [66] and RobustLowPoly [11]. More details", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 481, + 504, + 491 + ], + "spans": [ + { + "bbox": [ + 107, + 481, + 504, + 491 + ], + "type": "text", + "content": "on the data collection and processing pipeline can be found in the appendix. For generative mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 491, + 504, + 501 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 504, + 501 + ], + "type": "text", + "content": "pre-training, we randomly rotate these meshes with degrees from (0◦, 90◦, 180◦, 270◦), and adopt", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 503, + 415, + 512 + ], + "spans": [ + { + "bbox": [ + 107, + 503, + 415, + 512 + ], + "type": "text", + "content": "random scaling along each axis within range [0.9, 1.1] for data augmentation.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 518, + 506, + 640 + ], + "type": "text", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 107, + 520, + 503, + 529 + ], + "spans": [ + { + "bbox": [ + 107, + 520, + 503, + 529 + ], + "type": "text", + "content": "Metrics. We follow the standard evaluation protocols in MeshGPT [66] and PolyDiff [2] with", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 530, + 504, + 540 + ], + "spans": [ + { + "bbox": [ + 107, + 530, + 504, + 540 + ], + "type": "text", + "content": "the following metrics. Coverage (COV) is sensitive to mode dropping and is used to quantify the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 541, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 107, + 541, + 505, + 552 + ], + "type": "text", + "content": "diversity of the generated meshes. However, COV does not assess the quality of the generated results.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 552, + 504, + 563 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 504, + 563 + ], + "type": "text", + "content": "Minimum Matching Distance (MMD) calculates the average distance between the reference set", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 563, + 504, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 563, + 504, + 574 + ], + "type": "text", + "content": "and their closest neighbors in the generated set. However, MMD is not sensitive to low-quality", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 105, + 574, + 503, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 503, + 585 + ], + "type": "text", + "content": "results. The 1-Nearest Neighbor Accuracy (1-NNA) directly quantifies the quality and diversity", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 586, + 503, + 595 + ], + "spans": [ + { + "bbox": [ + 107, + 586, + 503, + 595 + ], + "type": "text", + "content": "between the generation set and the reference set. The optimal value of 1-NNA is 50%. We adopt the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 597, + 504, + 605 + ], + "spans": [ + { + "bbox": [ + 107, + 597, + 504, + 605 + ], + "type": "text", + "content": "Jensen-Shannon Divergence (JSD) score to directly evaluate 3D meshes. We use Chamfer Distance", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 607, + 504, + 616 + ], + "spans": [ + { + "bbox": [ + 107, + 607, + 504, + 616 + ], + "type": "text", + "content": "to measure the similarity between two samples. We also adopt the Frechet Inception Distance (FID)", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 618, + 504, + 628 + ], + "spans": [ + { + "bbox": [ + 107, + 618, + 504, + 628 + ], + "type": "text", + "content": "and Kernel Inception Distance (KID) on the rendered images for feature-level evaluation. The MMD,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 628, + 281, + 639 + ], + "spans": [ + { + "bbox": [ + 106, + 628, + 281, + 639 + ], + "type": "text", + "content": "JSD, and KID scores are multiplied by 103.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 645, + 504, + 723 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 106, + 646, + 504, + 655 + ], + "spans": [ + { + "bbox": [ + 106, + 646, + 504, + 655 + ], + "type": "text", + "content": "Implementation. All experiments are conducted on a cluster consisting of 128 A100 GPUs. We", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 657, + 504, + 667 + ], + "spans": [ + { + "bbox": [ + 107, + 657, + 504, + 667 + ], + "type": "text", + "content": "train our models under bfloat16 and the ZeRO-2 strategy [60] using the AdamW [48] optimizer with", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 666, + 504, + 678 + ], + "spans": [ + { + "bbox": [ + 107, + 668, + 223, + 678 + ], + "type": "text", + "content": "a learning rate decaying from", + "score": 1.0 + }, + { + "bbox": [ + 225, + 666, + 279, + 677 + ], + "type": "inline_equation", + "content": "1 0 ^ { - 4 } ~ \\mathrm { t o } ~ 1 0 ^ { - 6 }", + "score": 0.6761 + }, + { + "bbox": [ + 280, + 668, + 504, + 678 + ], + "type": "text", + "content": "and a weight decay of 0.1. The detailed hyperparameters", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 678, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 504, + 689 + ], + "type": "text", + "content": "for different models can be found in Tab. 2. To train our base models, we load the weights from the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 105, + 689, + 504, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 689, + 504, + 700 + ], + "type": "text", + "content": "pre-trained OPT models [95] and initialize the word embeddings and positional embeddings from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 503, + 712 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 503, + 712 + ], + "type": "text", + "content": "scratch. Without further specification, we generate 3D meshes with the top-k and top-p sampling", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 712, + 248, + 721 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 248, + 721 + ], + "type": "text", + "content": "strategy with k = 50 and p = 0.95.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 148, + 99, + 463, + 237 + ], + "blocks": [ + { + "bbox": [ + 104, + 69, + 504, + 92 + ], + "type": "table_caption", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 106, + 71, + 504, + 81 + ], + "spans": [ + { + "bbox": [ + 106, + 71, + 504, + 81 + ], + "type": "text", + "content": "Table 2: Hyperparameters for different MeshXL Base Models. We present three MeshXL models", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 81, + 321, + 91 + ], + "spans": [ + { + "bbox": [ + 107, + 81, + 321, + 91 + ], + "type": "text", + "content": "with 125M, 350M, and 1.3B parameters, respectively.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 148, + 99, + 463, + 237 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 148, + 99, + 463, + 237 + ], + "spans": [ + { + "bbox": [ + 148, + 99, + 463, + 237 + ], + "type": "table", + "html": "
HyperparametersMeshXL(125M)MeshXL(350M)MeshXL(1.3B)
# Layers122424
# Heads121632
d_{model}7681,0242,048
d_{FFN}3,0724,0968,192
OptimizerAdamW(\\beta_1=0.9, \\beta_2=0.999)
Learning rate1.0 \\times 10^{-4}1.0 \\times 10^{-4}1.0 \\times 10^{-4}
LR schedulerCosineCosineCosine
Weight decay0.10.10.1
Gradient Clip1.01.01.0
Number of GPUs81632
# GPU hrs (A100)1,9446,00023,232
", + "image_path": "4c5c6e15a6fac6fe7bb087b8c62cf0a5bf0719a0e52ba97300fa72f7d1d9a017.jpg" + } + ] + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 256, + 258, + 269 + ], + "type": "title", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 257, + 258, + 268 + ], + "spans": [ + { + "bbox": [ + 107, + 257, + 258, + 268 + ], + "type": "text", + "content": "6.2 Evaluations and Comparisons", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 277, + 504, + 300 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 278, + 503, + 288 + ], + "spans": [ + { + "bbox": [ + 107, + 278, + 503, + 288 + ], + "type": "text", + "content": "We provide quantitative as well as qualitative comparisons on both unconditional and conditional 3D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 290, + 264, + 297 + ], + "spans": [ + { + "bbox": [ + 107, + 290, + 264, + 297 + ], + "type": "text", + "content": "mesh generation on public benchmarks", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 304, + 506, + 382 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 305, + 504, + 316 + ], + "spans": [ + { + "bbox": [ + 107, + 305, + 504, + 316 + ], + "type": "text", + "content": "Unconditional Generation. We evaluate MeshXL as well as other baseline methods using the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 316, + 505, + 327 + ], + "spans": [ + { + "bbox": [ + 106, + 316, + 505, + 327 + ], + "type": "text", + "content": "ShapeNet [9] data in Tab. 3. We split the data by 9:1 for training and validation by each category.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 105, + 327, + 505, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 505, + 338 + ], + "type": "text", + "content": "For evaluation, we fine-tune our pre-trained base model and sample 1,000 meshes for each category.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 339, + 504, + 348 + ], + "spans": [ + { + "bbox": [ + 107, + 339, + 504, + 348 + ], + "type": "text", + "content": "Among the listed methods, we reproduce the MeshGPT [66] with a GPT2-medium model (355M) [59].", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 349, + 504, + 360 + ], + "spans": [ + { + "bbox": [ + 106, + 349, + 504, + 360 + ], + "type": "text", + "content": "With a similar number of parameters, Mesh-XL (350M) out-performs MeshGPT by a large margin,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 361, + 504, + 369 + ], + "spans": [ + { + "bbox": [ + 107, + 361, + 504, + 369 + ], + "type": "text", + "content": "showing a higher COV score, a lower MMD score, and a closer 1-NNA score to 50%. This indicates", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 372, + 359, + 382 + ], + "spans": [ + { + "bbox": [ + 107, + 372, + 359, + 382 + ], + "type": "text", + "content": "that MeshXL can produce diverse and high-quality 3D meshes.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "table", + "bbox": [ + 148, + 419, + 463, + 655 + ], + "blocks": [ + { + "bbox": [ + 104, + 391, + 504, + 415 + ], + "type": "table_caption", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 392, + 503, + 401 + ], + "spans": [ + { + "bbox": [ + 107, + 392, + 503, + 401 + ], + "type": "text", + "content": "Table 3: Quantitative Comparisons with Prior Arts on ShapeNet [9]. We scale MMD, JSD, KID", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 403, + 373, + 413 + ], + "spans": [ + { + "bbox": [ + 107, + 403, + 373, + 413 + ], + "type": "text", + "content": "by 103. MeshXL can produce diverse and high-quality 3D meshes.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 148, + 419, + 463, + 655 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 148, + 419, + 463, + 655 + ], + "spans": [ + { + "bbox": [ + 148, + 419, + 463, + 655 + ], + "type": "table", + "html": "
CategoryMethodsCOV↑MMD↓1-NNAJSD↓FID↓KID↓
ChairPolyGen [53]7.7916.0099.16228.8063.4943.73
GET3D [23]11.7015.9299.75155.2567.8442.10
MeshGPT [66]42.004.7569.5055.1639.528.97
MeshXL (125M)50.803.1156.559.6928.151.48
MeshXL (350M)50.803.1755.809.6628.291.39
MeshXL (1.3B)51.603.2355.809.489.121.84
TablePolyGen [53]44.003.3667.2025.0654.0814.96
GET3D [23]16.8010.3991.90226.9767.6534.62
MeshGPT [66]34.306.5175.0592.8853.757.75
MeshXL (125M)51.212.9657.9612.8242.550.92
MeshXL (350M)49.703.0756.1013.6443.431.27
MeshXL (1.3B)52.122.9256.8014.9322.292.03
BenchPolyGen [53]31.154.0183.2355.2570.5312.1
MeshGPT [66]34.922.2268.6557.3252.476.49
MeshXL (125M)54.371.6543.7516.4335.310.82
MeshXL (350M)53.371.6542.9615.4136.350.96
MeshXL (1.3B)56.551.6239.7815.5135.501.60
LampPolyGen [53]35.047.8775.4996.5765.1512.78
MeshGPT [66]41.594.9261.5961.8247.195.19
MeshXL (125M)55.865.0648.2443.4134.610.84
MeshXL (350M)53.524.1849.4134.8725.941.92
MeshXL (1.3B)51.954.8947.2741.8931.660.99
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HyperparametersMeshXL(125M)MeshXL(350M)MeshXL(1.3B)
# Layers122424
# Heads121632
d_{model}7681,0242,048
d_{FFN}3,0724,0968,192
OptimizerAdamW(\\beta_1=0.9, \\beta_2=0.999)
Learning rate1.0 \\times 10^{-4}1.0 \\times 10^{-4}1.0 \\times 10^{-4}
LR schedulerCosineCosineCosine
Weight decay0.10.10.1
Gradient Clip1.01.01.0
Number of GPUs81632
# GPU hrs (A100)1,9446,00023,232
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CategoryMethodsCOV↑MMD↓1-NNAJSD↓FID↓KID↓
ChairPolyGen [53]7.7916.0099.16228.8063.4943.73
GET3D [23]11.7015.9299.75155.2567.8442.10
MeshGPT [66]42.004.7569.5055.1639.528.97
MeshXL (125M)50.803.1156.559.6928.151.48
MeshXL (350M)50.803.1755.809.6628.291.39
MeshXL (1.3B)51.603.2355.809.489.121.84
TablePolyGen [53]44.003.3667.2025.0654.0814.96
GET3D [23]16.8010.3991.90226.9767.6534.62
MeshGPT [66]34.306.5175.0592.8853.757.75
MeshXL (125M)51.212.9657.9612.8242.550.92
MeshXL (350M)49.703.0756.1013.6443.431.27
MeshXL (1.3B)52.122.9256.8014.9322.292.03
BenchPolyGen [53]31.154.0183.2355.2570.5312.1
MeshGPT [66]34.922.2268.6557.3252.476.49
MeshXL (125M)54.371.6543.7516.4335.310.82
MeshXL (350M)53.371.6542.9615.4136.350.96
MeshXL (1.3B)56.551.6239.7815.5135.501.60
LampPolyGen [53]35.047.8775.4996.5765.1512.78
MeshGPT [66]41.594.9261.5961.8247.195.19
MeshXL (125M)55.865.0648.2443.4134.610.84
MeshXL (350M)53.524.1849.4134.8725.941.92
MeshXL (1.3B)51.954.8947.2741.8931.660.99
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We recruit and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 689, + 504, + 700 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 504, + 700 + ], + "type": "text", + "content": "instruct the participants to score each mesh from 0 to 5 based on its 1) quality: the smoothness of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 702, + 504, + 710 + ], + "spans": [ + { + "bbox": [ + 107, + 702, + 504, + 710 + ], + "type": "text", + "content": "object surfaces and completeness of the mesh, 2) artistic: how much do you believe this object is", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 712, + 504, + 721 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 504, + 721 + ], + "type": "text", + "content": "designed and created by artists, and 3) triangulation: how well do the connectivity among vertices", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 359, + 504, + 369 + ], + "spans": [ + { + "bbox": [ + 107, + 359, + 504, + 369 + ], + "type": "text", + "content": "aligns with the models created by professional designing software [14]. For the above mentioned", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 370, + 504, + 380 + ], + "spans": [ + { + "bbox": [ + 107, + 370, + 504, + 380 + ], + "type": "text", + "content": "metrics, the higher score means better quality. As a baseline evaluation, we also ask the participants", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 381, + 504, + 391 + ], + "spans": [ + { + "bbox": [ + 107, + 381, + 504, + 391 + ], + "type": "text", + "content": "to score the ground truth 3D geometries sampled from the ShapeNet data. We have collected a total", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 392, + 503, + 402 + ], + "spans": [ + { + "bbox": [ + 107, + 392, + 503, + 402 + ], + "type": "text", + "content": "of 434 valid responses. The results show that the 3D meshes created by MeshXL are consistently", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 403, + 258, + 411 + ], + "spans": [ + { + "bbox": [ + 107, + 403, + 258, + 411 + ], + "type": "text", + "content": "preferred by human in all dimensions.", + "score": 1.0, + "cross_page": true + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 70, + 504, + 308 + ], + "blocks": [ + { + "bbox": [ + 111, + 70, + 504, + 308 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 70, + 504, + 308 + ], + "spans": [ + { + "bbox": [ + 111, + 70, + 504, + 308 + ], + "type": "image", + "content": "Input\nCompleted Mesh\nGround Truth", + "image_path": "d06e184c553ec05435444e2274b7f39c38c8637fb0ffbb95840c2be6c331d410.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 315, + 504, + 339 + ], + "type": "image_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 318, + 503, + 326 + ], + "spans": [ + { + "bbox": [ + 107, + 318, + 503, + 326 + ], + "type": "text", + "content": "Figure 4: Evaluation of Partial Mesh Completion. Given some partial observation of the 3D mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 328, + 411, + 337 + ], + "spans": [ + { + "bbox": [ + 107, + 328, + 411, + 337 + ], + "type": "text", + "content": "(white), MeshXL is able to produce diverse object completion results (blue).", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_type": "text_image" + }, + { + "bbox": [ + 104, + 357, + 504, + 414 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 359, + 504, + 369 + ], + "spans": [ + { + "bbox": [ + 107, + 359, + 504, + 369 + ], + "type": "text", + "content": "aligns with the models created by professional designing software [14]. For the above mentioned", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 370, + 504, + 380 + ], + "spans": [ + { + "bbox": [ + 107, + 370, + 504, + 380 + ], + "type": "text", + "content": "metrics, the higher score means better quality. As a baseline evaluation, we also ask the participants", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 381, + 504, + 391 + ], + "spans": [ + { + "bbox": [ + 107, + 381, + 504, + 391 + ], + "type": "text", + "content": "to score the ground truth 3D geometries sampled from the ShapeNet data. We have collected a total", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 392, + 503, + 402 + ], + "spans": [ + { + "bbox": [ + 107, + 392, + 503, + 402 + ], + "type": "text", + "content": "of 434 valid responses. The results show that the 3D meshes created by MeshXL are consistently", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 403, + 258, + 411 + ], + "spans": [ + { + "bbox": [ + 107, + 403, + 258, + 411 + ], + "type": "text", + "content": "preferred by human in all dimensions.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "table", + "bbox": [ + 197, + 451, + 413, + 510 + ], + "blocks": [ + { + "bbox": [ + 104, + 422, + 504, + 446 + ], + "type": "table_caption", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 423, + 504, + 433 + ], + "spans": [ + { + "bbox": [ + 107, + 423, + 504, + 433 + ], + "type": "text", + "content": "Table 4: User Study. Compared to baseline methods, the meshes generated by MeshXL are better", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 435, + 389, + 445 + ], + "spans": [ + { + "bbox": [ + 107, + 435, + 389, + 445 + ], + "type": "text", + "content": "aligned with human preference in terms of both geometry and designs.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 197, + 451, + 413, + 510 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 197, + 451, + 413, + 510 + ], + "spans": [ + { + "bbox": [ + 197, + 451, + 413, + 510 + ], + "type": "table", + "html": "
MethodsQuality↑Artistic↑Triangulation↑
PolyGen [53]2.532.723.15
GET3D [23]3.152.463.15
MeshXL3.963.453.72
Reals4.083.333.75
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Comparing to MeshGPT [66], MeshXL is an end-to-end trainable model", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 561, + 505, + 571 + ], + "spans": [ + { + "bbox": [ + 107, + 561, + 505, + 571 + ], + "type": "text", + "content": "that produces 3D meshes with next-coordinate prediction. We show in Tab. 3 that, MeshXL out-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 572, + 504, + 582 + ], + "spans": [ + { + "bbox": [ + 107, + 572, + 504, + 582 + ], + "type": "text", + "content": "performs MeshGPT with similar numbers of parameters. Furthermore, MeshXL can save the effort", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 583, + 493, + 594 + ], + "spans": [ + { + "bbox": [ + 107, + 583, + 493, + 594 + ], + "type": "text", + "content": "training a mesh autoencoder [66, 73], which further facilitates scaling up generative pre-training.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 599, + 506, + 656 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 107, + 601, + 504, + 610 + ], + "spans": [ + { + "bbox": [ + 107, + 601, + 504, + 610 + ], + "type": "text", + "content": "Shape Completion. To analysis whether our method is capable of producing diverse outputs, we ask", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 612, + 504, + 621 + ], + "spans": [ + { + "bbox": [ + 107, + 612, + 504, + 621 + ], + "type": "text", + "content": "MeshXL (1.3B) model to predict the whole object given some partial observations of the 3D mesh.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 623, + 504, + 632 + ], + "spans": [ + { + "bbox": [ + 107, + 623, + 504, + 632 + ], + "type": "text", + "content": "In practice, we use 50% of the object mesh as input, and ask the model to predict the rest 50% of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 633, + 504, + 643 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 504, + 643 + ], + "type": "text", + "content": "the 3D mesh. We illustrate completion examples on chairs and tables in Fig. 4. One can see that", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 645, + 463, + 654 + ], + "spans": [ + { + "bbox": [ + 107, + 645, + 463, + 654 + ], + "type": "text", + "content": "Mesh-XL is able to produce diverse outputs given the partial observation of the 3D mesh.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 660, + 504, + 695 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 661, + 504, + 672 + ], + "spans": [ + { + "bbox": [ + 107, + 661, + 504, + 672 + ], + "type": "text", + "content": "X -to-Mesh Generation. We showcases several conditional generation results in Fig. 5. We show", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 672, + 503, + 682 + ], + "spans": [ + { + "bbox": [ + 106, + 672, + 503, + 682 + ], + "type": "text", + "content": "that MeshXL can generate high-quality 3D meshes given the corresponding image or text as the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 684, + 176, + 693 + ], + "spans": [ + { + "bbox": [ + 107, + 684, + 176, + 693 + ], + "type": "text", + "content": "additional inputs.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 700, + 503, + 710 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 503, + 710 + ], + "type": "text", + "content": "Effectiveness of Model Sizes. To analyze whether large-scale pre-training a larger model benefits 3D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 712, + 504, + 721 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 504, + 721 + ], + "type": "text", + "content": "mesh generation, we evaluate MeshXL base models with different sizes on the Objaverse [17] dataset", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "page_number", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 302, + 742, + 309, + 751 + ], + "spans": [ + { + "bbox": [ + 302, + 742, + 309, + 751 + ], + "type": "text", + "content": "8", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7, + "para_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 70, + 504, + 308 + ], + "blocks": [ + { + "bbox": [ + 111, + 70, + 504, + 308 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 70, + 504, + 308 + ], + "spans": [ + { + "bbox": [ + 111, + 70, + 504, + 308 + ], + "type": "image", + "content": "Input\nCompleted Mesh\nGround Truth", + "image_path": "d06e184c553ec05435444e2274b7f39c38c8637fb0ffbb95840c2be6c331d410.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 315, + 504, + 339 + ], + "type": "image_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 318, + 503, + 326 + ], + "spans": [ + { + "bbox": [ + 107, + 318, + 503, + 326 + ], + "type": "text", + "content": "Figure 4: Evaluation of Partial Mesh Completion. Given some partial observation of the 3D mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 328, + 411, + 337 + ], + "spans": [ + { + "bbox": [ + 107, + 328, + 411, + 337 + ], + "type": "text", + "content": "(white), MeshXL is able to produce diverse object completion results (blue).", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_type": "text_image" + }, + { + "bbox": [ + 104, + 357, + 504, + 414 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "type": "table", + "bbox": [ + 197, + 451, + 413, + 510 + ], + "blocks": [ + { + "bbox": [ + 104, + 422, + 504, + 446 + ], + "type": "table_caption", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 423, + 504, + 433 + ], + "spans": [ + { + "bbox": [ + 107, + 423, + 504, + 433 + ], + "type": "text", + "content": "Table 4: User Study. Compared to baseline methods, the meshes generated by MeshXL are better", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 435, + 389, + 445 + ], + "spans": [ + { + "bbox": [ + 107, + 435, + 389, + 445 + ], + "type": "text", + "content": "aligned with human preference in terms of both geometry and designs.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 197, + 451, + 413, + 510 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 197, + 451, + 413, + 510 + ], + "spans": [ + { + "bbox": [ + 197, + 451, + 413, + 510 + ], + "type": "table", + "html": "
MethodsQuality↑Artistic↑Triangulation↑
PolyGen [53]2.532.723.15
GET3D [23]3.152.463.15
MeshXL3.963.453.72
Reals4.083.333.75
", + "image_path": "7be20ee8332f4b4a39b7aed0272e9dae1f72d2090462df67fa45e41de61a8007.jpg" + } + ] + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 528, + 201, + 540 + ], + "type": "title", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 529, + 200, + 539 + ], + "spans": [ + { + "bbox": [ + 107, + 529, + 200, + 539 + ], + "type": "text", + "content": "6.3 Ablation Studies", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 549, + 506, + 595 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 551, + 503, + 559 + ], + "spans": [ + { + "bbox": [ + 107, + 551, + 503, + 559 + ], + "type": "text", + "content": "Necessity of Mesh VQVAE. Comparing to MeshGPT [66], MeshXL is an end-to-end trainable model", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 561, + 505, + 571 + ], + "spans": [ + { + "bbox": [ + 107, + 561, + 505, + 571 + ], + "type": "text", + "content": "that produces 3D meshes with next-coordinate prediction. We show in Tab. 3 that, MeshXL out-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 572, + 504, + 582 + ], + "spans": [ + { + "bbox": [ + 107, + 572, + 504, + 582 + ], + "type": "text", + "content": "performs MeshGPT with similar numbers of parameters. Furthermore, MeshXL can save the effort", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 583, + 493, + 594 + ], + "spans": [ + { + "bbox": [ + 107, + 583, + 493, + 594 + ], + "type": "text", + "content": "training a mesh autoencoder [66, 73], which further facilitates scaling up generative pre-training.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 599, + 506, + 656 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 107, + 601, + 504, + 610 + ], + "spans": [ + { + "bbox": [ + 107, + 601, + 504, + 610 + ], + "type": "text", + "content": "Shape Completion. To analysis whether our method is capable of producing diverse outputs, we ask", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 612, + 504, + 621 + ], + "spans": [ + { + "bbox": [ + 107, + 612, + 504, + 621 + ], + "type": "text", + "content": "MeshXL (1.3B) model to predict the whole object given some partial observations of the 3D mesh.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 623, + 504, + 632 + ], + "spans": [ + { + "bbox": [ + 107, + 623, + 504, + 632 + ], + "type": "text", + "content": "In practice, we use 50% of the object mesh as input, and ask the model to predict the rest 50% of", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 633, + 504, + 643 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 504, + 643 + ], + "type": "text", + "content": "the 3D mesh. We illustrate completion examples on chairs and tables in Fig. 4. One can see that", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 645, + 463, + 654 + ], + "spans": [ + { + "bbox": [ + 107, + 645, + 463, + 654 + ], + "type": "text", + "content": "Mesh-XL is able to produce diverse outputs given the partial observation of the 3D mesh.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 660, + 504, + 695 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 661, + 504, + 672 + ], + "spans": [ + { + "bbox": [ + 107, + 661, + 504, + 672 + ], + "type": "text", + "content": "X -to-Mesh Generation. We showcases several conditional generation results in Fig. 5. We show", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 672, + 503, + 682 + ], + "spans": [ + { + "bbox": [ + 106, + 672, + 503, + 682 + ], + "type": "text", + "content": "that MeshXL can generate high-quality 3D meshes given the corresponding image or text as the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 684, + 176, + 693 + ], + "spans": [ + { + "bbox": [ + 107, + 684, + 176, + 693 + ], + "type": "text", + "content": "additional inputs.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 700, + 503, + 710 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 503, + 710 + ], + "type": "text", + "content": "Effectiveness of Model Sizes. To analyze whether large-scale pre-training a larger model benefits 3D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 712, + 504, + 721 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 504, + 721 + ], + "type": "text", + "content": "mesh generation, we evaluate MeshXL base models with different sizes on the Objaverse [17] dataset", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 559, + 504, + 570 + ], + "spans": [ + { + "bbox": [ + 106, + 559, + 504, + 570 + ], + "type": "text", + "content": "in Tab. 5. We observe that as the model size grows, the generated samples exhibits a closer 1-NNA to", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 571, + 484, + 582 + ], + "spans": [ + { + "bbox": [ + 107, + 571, + 484, + 582 + ], + "type": "text", + "content": "50%, a larger COV, and smaller JSD score, which indicates an improving diversity and quality.", + "score": 1.0, + "cross_page": true + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 79, + 504, + 277 + ], + "blocks": [ + { + "bbox": [ + 109, + 79, + 504, + 277 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 79, + 504, + 277 + ], + "spans": [ + { + "bbox": [ + 109, + 79, + 504, + 277 + ], + "type": "image", + "content": "```mermaid\ngraph LR\n subgraph Image\n A1[\"Image\"] --> B1[\"Generated\"]\n B1 --> C1[\"Ground Truth\"]\n end\n\n subgraph Text\n D1[\"Text: "A basic chair with four leges and an open back."\"]\n E1[\"Text: "4 legs, solid seat and backing."\"]\n F1[\"Text: "A basic looking square wooden table."\"]\n end\n\n subgraph Ground Truth\n G1[\"Ground Truth\"]\n H1[\"Ground Truth\"]\n I1[\"Ground Truth\"]\n end\n\n B1 -.-> C1\n C1 -.-> D1\n C1 -.-> E1\n C1 -.-> F1\n C1 -.-> F1\n C1 -.-> I1\n C1 -.-> I1\n```", + "image_path": "94cdc9b3c5ee464d5f15cdcfe4da92287cb1c8599f3bf67892456c268bdd3ed2.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 278, + 504, + 301 + ], + "type": "image_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 106, + 279, + 503, + 290 + ], + "spans": [ + { + "bbox": [ + 106, + 279, + 503, + 290 + ], + "type": "text", + "content": "Figure 5: Evaluation of X -to-mesh generation. We show that MeshXL can generate high-quality", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 291, + 401, + 300 + ], + "spans": [ + { + "bbox": [ + 107, + 291, + 401, + 300 + ], + "type": "text", + "content": "3D meshes given the corresponding image or text as the additional inputs.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_type": "flowchart" + }, + { + "type": "image", + "bbox": [ + 106, + 313, + 504, + 514 + ], + "blocks": [ + { + "bbox": [ + 106, + 313, + 504, + 514 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 313, + 504, + 514 + ], + "spans": [ + { + "bbox": [ + 106, + 313, + 504, + 514 + ], + "type": "image", + "content": "Generated Mesh\nTextured Mesh\nUV Map\nGenerated Mesh\nTextured Mesh\nUV Map", + "image_path": "0d0145de4d358ac6abbe978025ee1410f1a06e356a75c94e17ebed75daf318ad.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 517, + 504, + 540 + ], + "type": "image_caption", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 518, + 503, + 528 + ], + "spans": [ + { + "bbox": [ + 107, + 518, + 503, + 528 + ], + "type": "text", + "content": "Figure 6: Texture Generation for the Generated 3D Meshes. We adopt Paint3D [93] to generate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 529, + 291, + 538 + ], + "spans": [ + { + "bbox": [ + 107, + 529, + 291, + 538 + ], + "type": "text", + "content": "textures for 3D meshes produced by MeshXL.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 2, + "sub_type": "text_image" + }, + { + "bbox": [ + 104, + 559, + 504, + 583 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 106, + 559, + 504, + 570 + ], + "spans": [ + { + "bbox": [ + 106, + 559, + 504, + 570 + ], + "type": "text", + "content": "in Tab. 5. We observe that as the model size grows, the generated samples exhibits a closer 1-NNA to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 571, + 484, + 582 + ], + "spans": [ + { + "bbox": [ + 107, + 571, + 484, + 582 + ], + "type": "text", + "content": "50%, a larger COV, and smaller JSD score, which indicates an improving diversity and quality.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "type": "table", + "bbox": [ + 168, + 631, + 443, + 677 + ], + "blocks": [ + { + "bbox": [ + 104, + 597, + 506, + 631 + ], + "type": "table_caption", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 106, + 598, + 504, + 609 + ], + "spans": [ + { + "bbox": [ + 106, + 598, + 504, + 609 + ], + "type": "text", + "content": "Table 5: Effectiveness of Model Sizes on Objaverse. We observe that as the model size grows, the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 609, + 504, + 619 + ], + "spans": [ + { + "bbox": [ + 107, + 609, + 504, + 619 + ], + "type": "text", + "content": "generated meshes exhibit a closer 1-NNA to 50%, a larger COV and a smaller JSD, indicating better", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 621, + 190, + 631 + ], + "spans": [ + { + "bbox": [ + 107, + 621, + 190, + 631 + ], + "type": "text", + "content": "diversity and quality.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 168, + 631, + 443, + 677 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 168, + 631, + 443, + 677 + ], + "spans": [ + { + "bbox": [ + 168, + 631, + 443, + 677 + ], + "type": "table", + "html": "
MethodCOV↑MMD↓1-NNAJSD↓FID↓KID ↓
MeshXL (125M)39.765.2167.3426.0317.324.48
MeshXL (350M)40.795.2065.6823.7115.143.33
MeshXL (1.3B)42.864.1661.5620.9912.492.94
", + "image_path": "6cb4e5ae622dcf2dea00c2743b764c9c6a73ee80191f4942cbd03f97a3629408.jpg" + } + ] + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 689, + 504, + 723 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 107, + 689, + 504, + 700 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 504, + 700 + ], + "type": "text", + "content": "Texturing. We adopt Paint3D [93], a coarse-to-fine texture generation pipeline, to generate textures", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 701, + 504, + 710 + ], + "spans": [ + { + "bbox": [ + 107, + 701, + 504, + 710 + ], + "type": "text", + "content": "for the 3D meshes produced by MeshXL in Fig. 6. We show that 3D meshes produced by MeshXL", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 712, + 419, + 721 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 419, + 721 + ], + "type": "text", + "content": "can easily fit the existing texturing methods to produce high-quality 3D assets.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "page_number", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 302, + 742, + 308, + 751 + ], + "spans": [ + { + "bbox": [ + 302, + 742, + 308, + 751 + ], + "type": "text", + "content": "9", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8, + "para_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 79, + 504, + 277 + ], + "blocks": [ + { + "bbox": [ + 109, + 79, + 504, + 277 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 79, + 504, + 277 + ], + "spans": [ + { + "bbox": [ + 109, + 79, + 504, + 277 + ], + "type": "image", + "content": "```mermaid\ngraph LR\n subgraph Image\n A1[\"Image\"] --> B1[\"Generated\"]\n B1 --> C1[\"Ground Truth\"]\n end\n\n subgraph Text\n D1[\"Text: "A basic chair with four leges and an open back."\"]\n E1[\"Text: "4 legs, solid seat and backing."\"]\n F1[\"Text: "A basic looking square wooden table."\"]\n end\n\n subgraph Ground Truth\n G1[\"Ground Truth\"]\n H1[\"Ground Truth\"]\n I1[\"Ground Truth\"]\n end\n\n B1 -.-> C1\n C1 -.-> D1\n C1 -.-> E1\n C1 -.-> F1\n C1 -.-> F1\n C1 -.-> I1\n C1 -.-> I1\n```", + "image_path": "94cdc9b3c5ee464d5f15cdcfe4da92287cb1c8599f3bf67892456c268bdd3ed2.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 278, + 504, + 301 + ], + "type": "image_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 106, + 279, + 503, + 290 + ], + "spans": [ + { + "bbox": [ + 106, + 279, + 503, + 290 + ], + "type": "text", + "content": "Figure 5: Evaluation of X -to-mesh generation. We show that MeshXL can generate high-quality", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 291, + 401, + 300 + ], + "spans": [ + { + "bbox": [ + 107, + 291, + 401, + 300 + ], + "type": "text", + "content": "3D meshes given the corresponding image or text as the additional inputs.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_type": "flowchart" + }, + { + "type": "image", + "bbox": [ + 106, + 313, + 504, + 514 + ], + "blocks": [ + { + "bbox": [ + 106, + 313, + 504, + 514 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 313, + 504, + 514 + ], + "spans": [ + { + "bbox": [ + 106, + 313, + 504, + 514 + ], + "type": "image", + "content": "Generated Mesh\nTextured Mesh\nUV Map\nGenerated Mesh\nTextured Mesh\nUV Map", + "image_path": "0d0145de4d358ac6abbe978025ee1410f1a06e356a75c94e17ebed75daf318ad.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 517, + 504, + 540 + ], + "type": "image_caption", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 518, + 503, + 528 + ], + "spans": [ + { + "bbox": [ + 107, + 518, + 503, + 528 + ], + "type": "text", + "content": "Figure 6: Texture Generation for the Generated 3D Meshes. We adopt Paint3D [93] to generate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 529, + 291, + 538 + ], + "spans": [ + { + "bbox": [ + 107, + 529, + 291, + 538 + ], + "type": "text", + "content": "textures for 3D meshes produced by MeshXL.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 2, + "sub_type": "text_image" + }, + { + "bbox": [ + 104, + 559, + 504, + 583 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "type": "table", + "bbox": [ + 168, + 631, + 443, + 677 + ], + "blocks": [ + { + "bbox": [ + 104, + 597, + 506, + 631 + ], + "type": "table_caption", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 106, + 598, + 504, + 609 + ], + "spans": [ + { + "bbox": [ + 106, + 598, + 504, + 609 + ], + "type": "text", + "content": "Table 5: Effectiveness of Model Sizes on Objaverse. We observe that as the model size grows, the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 609, + 504, + 619 + ], + "spans": [ + { + "bbox": [ + 107, + 609, + 504, + 619 + ], + "type": "text", + "content": "generated meshes exhibit a closer 1-NNA to 50%, a larger COV and a smaller JSD, indicating better", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 621, + 190, + 631 + ], + "spans": [ + { + "bbox": [ + 107, + 621, + 190, + 631 + ], + "type": "text", + "content": "diversity and quality.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 168, + 631, + 443, + 677 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 168, + 631, + 443, + 677 + ], + "spans": [ + { + "bbox": [ + 168, + 631, + 443, + 677 + ], + "type": "table", + "html": "
MethodCOV↑MMD↓1-NNAJSD↓FID↓KID ↓
MeshXL (125M)39.765.2167.3426.0317.324.48
MeshXL (350M)40.795.2065.6823.7115.143.33
MeshXL (1.3B)42.864.1661.5620.9912.492.94
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We show that 3D meshes produced by MeshXL", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 712, + 419, + 721 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 419, + 721 + ], + "type": "text", + "content": "can easily fit the existing texturing methods to produce high-quality 3D assets.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 72, + 506, + 257 + ], + "blocks": [ + { + "bbox": [ + 111, + 72, + 506, + 257 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 72, + 506, + 257 + ], + "spans": [ + { + "bbox": [ + 111, + 72, + 506, + 257 + ], + "type": "image", + "content": "PolyGen\nGET3D\nMeshGPT\nMeshXL", + "image_path": "25d8b0ad0310574d3a5b0d0102818a9ac33b4b5aee0bf2849ed58541fd041bb1.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 268, + 504, + 301 + ], + "type": "image_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 269, + 504, + 279 + ], + "spans": [ + { + "bbox": [ + 107, + 269, + 504, + 279 + ], + "type": "text", + "content": "Figure 7: Qualitative comparison on the generated meshes. 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During", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 109, + 503, + 118 + ], + "spans": [ + { + "bbox": [ + 107, + 109, + 503, + 118 + ], + "type": "text", + "content": "sampling, MeshXL will generate 7,200 tokens for an 800-faced 3D mesh, which takes a relatively", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 120, + 504, + 129 + ], + "spans": [ + { + "bbox": [ + 107, + 120, + 504, + 129 + ], + "type": "text", + "content": "long time because of the auto-regressive process. As for future works, recent endeavors on the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 130, + 504, + 141 + ], + "spans": [ + { + "bbox": [ + 106, + 130, + 504, + 141 + ], + "type": "text", + "content": "RNN-related methods [6, 55, 26] and multiple tokens prediction for LLMs [24] might open up great", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 142, + 274, + 152 + ], + "spans": [ + { + "bbox": [ + 107, + 142, + 274, + 152 + ], + "type": "text", + "content": "opportunities in saving the inference cost.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 157, + 506, + 237 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 159, + 504, + 168 + ], + "spans": [ + { + "bbox": [ + 107, + 159, + 504, + 168 + ], + "type": "text", + "content": "Conclusion. 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We show", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 202, + 503, + 212 + ], + "spans": [ + { + "bbox": [ + 107, + 202, + 503, + 212 + ], + "type": "text", + "content": "that MeshXL performs better given larger-scale training data and increased parameters. Extensive", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 213, + 503, + 222 + ], + "spans": [ + { + "bbox": [ + 107, + 213, + 503, + 222 + ], + "type": "text", + "content": "results show our proposed MeshXL can not only generate high-quality 3D meshes, but also exhibits", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 224, + 408, + 234 + ], + "spans": [ + { + "bbox": [ + 107, + 224, + 408, + 234 + ], + "type": "text", + "content": "great potential serving as base models for conditional 3D assets generation.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 300, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 299, + 741, + 312, + 752 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 312, + 752 + ], + "type": "text", + "content": "13", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 12, + "para_blocks": [ + { + "bbox": [ + 105, + 71, + 350, + 85 + ], + "type": "title", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 106, + 72, + 348, + 84 + ], + "spans": [ + { + "bbox": [ + 106, + 72, + 348, + 84 + ], + "type": "text", + "content": "8 Limitations, Future Work, and Conclusions", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 96, + 504, + 152 + ], + "type": "text", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 106, + 97, + 503, + 108 + ], + "spans": [ + { + "bbox": [ + 106, + 97, + 503, + 108 + ], + "type": "text", + "content": "Limitations and Future Work. 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DatasetPre-trainingText-to-3D
TrainValTrainVal
ShapeNet [9]16,0011,75415,3841,728
3D-Future [22]1,603---
Objaverse [17]85,28285483,501820
Objaverse-XL [16]2,407,33715,2001,347,80213,579
Total2,510,22317,8081,446,67816,127
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HyperparametersMeshXL(125M)MeshXL(350M)MeshXL(1.3B)
# Layers122424
# Heads121632
d_{model}7681,0242,048
d_{FFN}3,0724,0968,192
OptimizerAdamW(\\beta_1=0.9, \\beta_2=0.999)
Learning rate1.0 \\times 10^{-4}1.0 \\times 10^{-4}1.0 \\times 10^{-4}
LR schedulerCosineCosineCosine
Weight decay0.10.10.1
Gradient Clip1.01.01.0
Number of GPUs81632
# GPU hrs (A100)1,9446,00023,232
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CategoryMethodsCOV↑MMD↓1-NNAJSD↓FID↓KID↓
ChairPolyGen [53]7.7916.0099.16228.8063.4943.73
GET3D [23]11.7015.9299.75155.2567.8442.10
MeshGPT [66]42.004.7569.5055.1639.528.97
MeshXL (125M)50.803.1156.559.6928.151.48
MeshXL (350M)50.803.1755.809.6628.291.39
MeshXL (1.3B)51.603.2355.809.489.121.84
TablePolyGen [53]44.003.3667.2025.0654.0814.96
GET3D [23]16.8010.3991.90226.9767.6534.62
MeshGPT [66]34.306.5175.0592.8853.757.75
MeshXL (125M)51.212.9657.9612.8242.550.92
MeshXL (350M)49.703.0756.1013.6443.431.27
MeshXL (1.3B)52.122.9256.8014.9322.292.03
BenchPolyGen [53]31.154.0183.2355.2570.5312.1
MeshGPT [66]34.922.2268.6557.3252.476.49
MeshXL (125M)54.371.6543.7516.4335.310.82
MeshXL (350M)53.371.6542.9615.4136.350.96
MeshXL (1.3B)56.551.6239.7815.5135.501.60
LampPolyGen [53]35.047.8775.4996.5765.1512.78
MeshGPT [66]41.594.9261.5961.8247.195.19
MeshXL (125M)55.865.0648.2443.4134.610.84
MeshXL (350M)53.524.1849.4134.8725.941.92
MeshXL (1.3B)51.954.8947.2741.8931.660.99
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MethodsQuality↑Artistic↑Triangulation↑
PolyGen [53]2.532.723.15
GET3D [23]3.152.463.15
MeshXL3.963.453.72
Reals4.083.333.75
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"score": 1.0 + }, + { + "type": "ocr_text", + "bbox": [ + 0.174, + 0.849, + 0.823, + 0.862 + ], + "text": "", + "score": 1.0 + }, + { + "type": "ocr_text", + "bbox": [ + 0.175, + 0.864, + 0.288, + 0.876 + ], + "text": "", + "score": 1.0 + }, + { + "type": "ocr_text", + "bbox": [ + 0.175, + 0.885, + 0.823, + 0.897 + ], + "text": "", + "score": 1.0 + }, + { + "type": "ocr_text", + "bbox": [ + 0.175, + 0.899, + 0.824, + 0.911 + ], + "text": "", + "score": 1.0 + }, + { + "type": "ocr_text", + "bbox": [ + 0.494, + 0.937, + 0.505, + 0.949 + ], + "text": "", + "score": 1.0 + } + ], + [ + { + "type": "image", + "bbox": [ + 0.179, + 0.101, + 0.825, + 0.35 + ], + "angle": 0, + "content": "```mermaid\ngraph LR\n subgraph Image\n A1[\"Image\"] --> B1[\"Generated\"]\n B1 --> C1[\"Ground Truth\"]\n end\n\n subgraph Text\n D1[\"Text: "A basic chair with four leges and an open back."\"]\n E1[\"Text: "4 legs, solid seat and backing."\"]\n F1[\"Text: "A basic looking square wooden table."\"]\n end\n\n subgraph Ground Truth\n G1[\"Ground Truth\"]\n H1[\"Ground Truth\"]\n I1[\"Ground Truth\"]\n end\n\n B1 -.-> C1\n C1 -.-> D1\n C1 -.-> E1\n C1 -.-> F1\n C1 -.-> F1\n C1 -.-> I1\n C1 -.-> I1\n```", + "sub_type": "flowchart" + }, + { + "type": "image_caption", + "bbox": [ + 0.172, + 0.352, + 0.825, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.174, + 0.396, + 0.825, + 0.65 + ], + "angle": 0, + "content": "Generated Mesh\nTextured Mesh\nUV Map\nGenerated Mesh\nTextured Mesh\nUV Map", + "sub_type": "text_image" + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.653, + 0.825, + 0.682 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.706, + 0.825, + 0.737 + ], + "angle": 0, + "content": null, + "merge_prev": false + }, + { + "type": "table_caption", + "bbox": [ + 0.171, + 0.755, + 0.827, + 0.797 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.275, + 0.797, + 0.724, + 0.856 + ], + "angle": 0, + "content": "
MethodCOV↑MMD↓1-NNAJSD↓FID↓KID ↓
MeshXL (125M)39.765.2167.3426.0317.324.48
MeshXL (350M)40.795.2065.6823.7115.143.33
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b/papers/markdown/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers/hybrid_auto/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers.md @@ -0,0 +1,541 @@ +# MESHANYTHING: ARTIST-CREATED MESH GENERA-TION WITH AUTOREGRESSIVE TRANSFORMERS + +Yiwen Chen1,2∗, Tong He2†, Di Huang2, Weicai Ye2, Sijin Chen3, Jiaxiang Tang4 Xin Chen5, Zhongang Cai6, Lei Yang6, Gang Yu7, Guosheng Lin1†, Chi Zhang8† 1S-Lab, Nanyang Technological University 2Shanghai AI Lab 3Fudan University 4Peking University 5University of Chinese Academy of Sciences 6SenseTime Research 7Stepfun 8Westlake University https://buaacyw.github.io/mesh-anything/ + +![](images/4c8a3616bc55f836a4dc48c40a287983e81006ea66f4e11701727c07112ba992.jpg) + +
+flowchart + +```mermaid +graph LR + A["Text Condition: A commode"] --> B["NeRF"] + B --> C["3D GS"] + C --> D["Image"] + D --> E["Dense Mesh"] + E --> F["Dense Mesh"] + F --> G["Dense Mesh"] + G --> H["Dense Mesh"] + H --> I["Point Cloud"] + J["Point Cloud"] --> K["Dense Mesh"] + K --> L["Dense Mesh"] + L --> M["Point Cloud"] +``` +
+ +Figure 1: MeshAnything converts any 3D representation into Artist-Created Meshes (AMs), i.e., meshes created by human artists. It can be combined with various 3D asset production pipelines, such as 3D reconstruction and generation, to transform their results into AMs that can be seamlessly applied in the 3D industry. + +## ABSTRACT + +Recently, 3D assets created via reconstruction and generation have matched the quality of manually crafted assets, highlighting their potential for replacement. However, this potential is largely unrealized because these assets always need to be converted to meshes for 3D industry applications, and the meshes produced by current mesh extraction methods are significantly inferior to Artist-Created Meshes (AMs), i.e., meshes created by human artists. Specifically, current mesh extraction methods rely on dense faces and ignore geometric features, leading to inefficiencies, complicated post-processing, and lower representation quality. To address these issues, we introduce MeshAnything, a model that treats mesh extraction as a generation problem, producing AMs aligned with specified shapes. By converting 3D assets in any 3D representation into AMs, MeshAnything can be integrated with various 3D asset production methods, thereby enhancing their application across the 3D industry. The architecture of MeshAnything comprises a VQ-VAE and a shape-conditioned decoder-only transformer. We first learn a mesh vocabulary using the VQ-VAE, then train the shape-conditioned decoderonly transformer on this vocabulary for shape-conditioned autoregressive mesh generation. Our extensive experiments show that our method generates AMs with hundreds of times fewer faces, significantly improving storage, rendering, and simulation efficiencies, while achieving precision comparable to previous methods. + +## 1 INTRODUCTION + +In recent years, the 3D community has experienced rapid advancements, with a variety of methods developed for automatically producing high-quality 3D assets. These methods, including 3D reconstruction Mildenhall et al. (2020); Yu et al. (2021); Barron et al. (2021; 2022); Kerbl et al. (2023b); Huang et al. (2024), 3D generation Poole et al. (2023); Liu et al. (2023a); Wang et al. (2023); Long et al. (2023); Sun et al. (2023); Hong et al. (2023); Tang et al. (2024); Xu et al. (2024); Wei et al. (2024), and scanning Daneshmand et al. (2018); Haleem & Javaid (2019); Haleem et al. (2022), can produce 3D assets with shape and color quality comparable to manually created ones. The success of these methods reveals the potential to replace manually created 3D models with automatically produced ones in the 3D industry, including applications in games, movies, and the metaverse, significantly reducing time and labor costs. + +However, this potential remains largely unrealized because the current 3D industry predominantly relies on mesh-based pipelines for their superior efficiency and controllability, while methods for producing 3D assets typically use alternative 3D representations to achieve optimal results across various scenarios. Therefore, substantial efforts Lorensen & Cline (1987); Chernyaev (1995); Lorensen & Cline (1998); Shen et al. (2021b); Chen et al. (2022); Shen et al. (2023) are devoted to converting other 3D representations into meshes and have achieved some success. Meshes produced by these methods approximate the shape quality of those created by human artists, which we refer to as Artist-Created Meshes (AMs), but they still fall short in addressing the aforementioned issues. + +This is because all meshes produced by these methods Lorensen & Cline (1987); Chernyaev (1995); Lorensen & Cline (1998); Shen et al. (2021b); Chen et al. (2022); Shen et al. (2023) exhibit significantly poorer topology quality compared to AMs. As shown in Fig. 2, these methods rely on dense faces to reconstruct 3D shapes, completely ignoring geometric characteristics. Using these meshes in the 3D industry leads to three significant problems: First, converted meshes typically contain several orders of magnitude more faces compared to AMs, leading to significant inefficiencies in storage, rendering, and simulation. Moreover, the converted meshes complicate post-processing and downstream tasks in the 3D pipeline. They significantly increase the challenge for human artists in optimizing these meshes due to their chaotic and inefficient topologies. Finally, previous methods struggle to represent sharp edges and flat surfaces, resulting in oversmoothing and bumpy artifacts as shown in Fig. 2. + +In this work, we aim to solve the aforementioned issues to facilitate the application of automatically generated 3D assets in the 3D industry. As mentioned earlier, all previous methods Lorensen & Cline (1987); Chernyaev (1995); Lorensen & Cline (1998); Shen et al. (2021b); Chen et al. (2022); Shen et al. (2023) extract 3D meshes with excessively dense faces in a reconstruction manner, which inherently cannot solve these issues. Therefore, we diverge from previous approaches by formulating mesh extraction as a generation problem for the first time: we teach models to generate Artist- + +![](images/9fa5b06a364431abe5830c26121adaca68b8bb5f0c40aa46d34f732c3aea7e4c.jpg) + +
+text_image + +Faces: 90k +Vertices: 45k +Marching Cubes +Faces: 33k +Vertices: 53k +Remesh-0.01 +Faces: 3.5k +Vertices: 6.7k +Remesh-0.03 +Faces: 1.1k +Vertices: 2.2k +Remesh-0.05 +Faces: 0.28k +Vertices: 0.57k +Remesh-0.10 +Faces: 0.64k +Vertices: 0.31k +MeshAnything +Faces: 200k +Vertices: 100k +Marching Cubes +Faces: 84k +Vertices: 132k +Remesh-0.01 +Faces: 7.4k +Vertices: 13k +Remesh-0.03 +Faces: 2k +Vertices: 3.9k +Remesh-0.05 +Faces: 0.46k +Vertices: 0.92k +Remesh-0.10 +Faces: 0.80k +Vertices: 0.47k +MeshAnything +
+ +Figure 2: Comparison with Marching Cubes Lorensen & Cline (1987) and Remesh Blender Development Team (2024). We apply Marching Cubes and MeshAnything to ground truth shapes and then apply remeshing to the Marching Cubes results with different voxel sizes. Existing methods extract meshes in a reconstruction manner, ignoring the geometric features of the object and producing dense meshes with poor topology. These methods fundamentally fail to capture sharp edges and flat surfaces, as shown in the zoomed-in figure. + +Created Meshes (AMs) that are aligned with the given 3D assets. The meshes generated by our methods mimic the shape and topology quality of those created by human artists. Consequently, our setting, namely Shape-Conditioned AM Generation, is fundamentally free from all previous issues, enabling seamless integration of the generated results into the 3D industry pipeline. + +However, training such a model presents significant challenges. The first challenge is constructing the dataset, as we need paired shape conditions and Artist-Created Meshes (AMs) for model training. The shape condition must be efficiently derived from as many diverse 3D representations as possible to serve as a condition during inference. Additionally, it must have sufficient precision to accurately represent 3D shapes and be efficiently processed into features that can be injected into the model. After weighing the trade-offs, we chose point clouds due to their explicit and continuous representation, ease of derivation from most 3D representations, and the availability of mature point cloud encoders Qi et al. (2017a;b); Zhao et al. (2024). + +We filter out high-quality AMs from Objaverse Deitke et al. (2023b;a) and ShapeNet Chang et al. (2015). When obtaining paired shape conditions, a naive approach would be to sample point clouds directly from AMs. However, this leads to poor results during inference because the sampled point clouds have excessive precision, while automatically produced 3D assets cannot provide point clouds of similar quality, causing a domain gap between training and inference. To address this issue, we intentionally corrupt the shape quality of AMs. We first extract the signed distance function from AMs Wang et al. (2022), convert it into a coarser mesh using Lorensen & Cline (1987), and then sample point clouds from this coarse mesh to narrow the domain gap in shape conditions between inference and training. + +Following Siddiqui et al. (2023), we use a VQ-VAE Van Den Oord et al. (2017) to learn a mesh vocabulary and train a decoder-only transformer Vaswani et al. (2017) on this vocabulary for mesh generation. To inject shape condition, we draw inspiration from the recent success of multimodal large language models (MLLM) Wu et al. (2023); Liu et al. (2024a), where image features encoded by pre-trained image encoders are projected into the token space of the large language models for efficient multimodal understanding. Similarly, we treat the mesh tokens obtained from the trained VQ-VAE as the language token in LLMs and use a pre-trained encoder Zhao et al. (2024) to encode the point clouds into shape features, which is later projected into the mesh token space. These shape tokens are placed at the beginning of the mesh token sequences, effectively serving as the shape conditions for next-token predictions. After predictions, these predicted mesh tokens are decoded back to meshes with the VQ-VAE decoder Siddiqui et al. (2023). + +To further enhance the quality of mesh generation, we develop a novel noise-resistant decoder for robust mesh decoding. Our observation is that as the decoder in the VQ-VAE Van Den Oord et al. (2017) is only trained with ground truth token sequences from the encoder, it could potentially lead to a domain gap when decoding the generated token sequences. To mitigate this problem, we inject the shape condition into the VQ-VAE decoder as auxiliary information for robust decoding and finetune it after the VQ-VAE training. This fine-tuning process involves adding noise to the mesh token sequences to simulate possible poor-quality token sequences from the decoder-only transformer, thus making the decoder robust to such poor-quality sequences. + +Finally, we introduce our model, MeshAnything, trained based on the aforementioned techniques. As shown in Fig. 1, MeshAnything can convert 3D assets across various 3D representations into AMs, thereby significantly facilitating their application. Furthermore, our extensive experiments demonstrate that our method generates AMs with significantly fewer faces and more refined topology, while achieving precision metrics that are close to or comparable with previous methods. + +In summary, our contributions are as follows: + +• We highlight one important reason why current automatically produced 3D assets cannot replace those created by human artists: current methods cannot convert these 3D assets into Artist-Created Meshes (AMs). To solve this issue, we propose a novel solution called Shape-Conditioned AM Generation, which aims to generate AMs aligned with given shapes. +• We introduce MeshAnything for Shape-Conditioned AM Generation. MeshAnything can be integrated with various 3D asset production methods, converting their results into AMs to facilitate their application in the 3D industry. +• We develop a novel noise-resistant decoder to enhance mesh generation quality. We inject the shape condition into the decoder as auxiliary information for robust decoding and fine-tune it using noised token sequences to narrow the domain gap between training and inference. +• Extensive experiments demonstrate that Shape-Conditioned Mesh Generation is a more suitable setting for mesh generation, and MeshAnything significantly surpasses previous mesh generation methods. + +## 2 RELATED WORKS + +## 2.1 MESH EXTRACTION + +Methods for extracting meshes from 3D models are numerous and have been a subject of research for decades. Following Shen et al. (2023), we categorize these methods into two main types: Isosurface Extraction Lorensen & Cline (1987); Bloomenthal (1988); Chernyaev (1995); Bloomenthal & Bajaj (1997); Lorensen & Cline (1998); Chen et al. (2022) and Gradient-Based Mesh Optimization Chen et al. (2019); Gao et al. (2020); Hanocka et al. (2020); Kato et al. (2018); Shen et al. (2021a); Liao et al. (2018); Shen et al. (2023). + +Traditional isosurface extraction methods Lorensen & Cline (1987; 1998); Chernyaev (1995); Doi & Koide (1991); Ju et al. (2002); Schaefer et al. (2007); Chen & Zhang (2021); Chen et al. (2022) focus on extracting a polygonal mesh that represents the level set of a scalar function, an area that has seen extensive study in various fields. The most popular method among them is Marching Cubes Lorensen & Cline (1987). It divides the space into cells, within which polygons are created to approximate the surface. Marching Cubes has been widely used for mesh extraction its robustness and simplicity. Recently, Chen & Zhang (2021) and Chen et al. (2022) introduce data-driven methods to determine the position of the extracted mesh based on the input field. + +Transitioning to more recent developments, the advent of machine learning has ushered in new techniques for generating 3D meshes Chen et al. (2019); Gao et al. (2020); Hanocka et al. (2020); Kato et al. (2018); Shen et al. (2021a); Liao et al. (2018); Shen et al. (2023). This line of work explores using neural networks to generate 3D meshes, where the network parameters are optimized through gradient-based methods under specific loss functions. Shen et al. (2021a) employs a differentiable Marching Tetrahedra layer for mesh extraction. Similar to Shen et al. (2021a), Shen et al. (2023) iteratively optimizes a 3D surface mesh by representing it as the isosurface of a scalar field. + +However, these approaches fundamentally differ from ours. They ignore the characteristics of the shape and inherently cannot produce meshes with efficient topology. In contrast, MeshAnything formulates mesh extraction as a generation problem for the first time, aiming to mimic human artists in mesh extraction and thereby generating Artist-Created Meshes (AMs) with hundreds of times fewer faces. + +## 2.2 3D MESH GENERATIONS + +3D mesh generation can be mainly divided into two categories: generating dense meshes similar to those produced by previous mesh extraction methods, and generating Artist-Created Meshes (AMs). + +The former category is currently the mainstream research focus. Methods such as Gao et al. (2022); Wei et al. (2024); Xu et al. (2024) directly generate meshes in a feed-forward manner, but because they produce dense meshes with low-quality topology similar to previous mesh extraction methods, they still encounter the same issues when applied in the 3D industry. + +Notably, numerous 3D generation methods Poole et al. (2023); Tang et al. (2023b); Wang et al. (2023); Chen et al. (2024b); Tang et al. (2023a); Yang et al. (2023); Hong et al. (2023); Fang et al. (2023); Chen et al. (2023a); Liu et al. (2024b); Shi et al. (2023); Li et al. (2023); Chen et al. (2023b; 2024c); Tang et al. (2024); Wang et al. (2024); Tochilkin et al. (2024) can also produce meshes. These methods first generate 3D assets and then convert them to dense meshes using mesh extraction methods like Lorensen & Cline (1987). Consequently, they face challenges when applied to the 3D industry due to their inefficient topology. + +Recently, several works have focused on the second category: generating Artist-Created Meshes(AMs) Nash et al. (2020); Alliegro et al. (2023); Siddiqui et al. (2023); Chen et al. (2024a). Although our approach also focuses on AM generation, it fundamentally differs from these methods. Since they lack shape conditioning, these methods must simultaneously learn the complex 3D shape distribution—which typically alone requires extensive training Hong et al. (2023); Tang et al. (2024)—and the topology distribution of AMs, leading to very challenging training processes. In contrast, our methods eliminate the challenge of learning the shape distribution, allowing the model to focus on learning the topology distribution. This not only significantly reduces training costs but also enhances the model’s application value. + +Among these methods, the most relevant to ours is MeshGPT Siddiqui et al. (2023), as we follow its architecture. Siddiqui et al. (2023) introduced a combination of a VQ-VAE Van Den Oord et al. (2017) and an autoregressive transformer architecture. It first learns a mesh vocabulary with the VQ-VAE and then trains the transformer on the learned vocabulary for mesh generation. However, MeshGPT’s results are limited to several categories in ShapeNet. MeshGPT requires a training GPU hours similar to ours, but our method can generalize to unlimited categories in Objaverse. As shown in Fig. 3, this is largely due to the difference in target complexity caused by MeshGPT needing to additionally learn the complex 3D shape distribution. + +## 3 SHAPE-CONDITIONED AM GENERATION + +In this section, we first introduce the formal formulation for Shape-Conditioned AM Generation and compare it with previous mesh generation settings Nash et al. (2020); Siddiqui et al. (2023); Alliegro et al. (2023). We show that it can achieve better performance and a broader range of applications compared to the settings in previous mesh generation methods, with significantly less training effort. + +![](images/aecc35c40ee63cf700f8e266846c83e8dfb32ed3aab02b0e0271258e64dac101.jpg) + +
+line + +| Training iterations | Shape-Conditioned | Image-Conditioned | Unconditional | +| --- | --- | --- | --- | +| 60k | ~2.0 | — | — | +| 80k | ~1.67 | ~1.98 | ~1.99 | +| 100k | ~1.56 | ~1.83 | ~1.86 | +| 120k | ~1.49 | ~1.74 | ~1.78 | +| 140k | ~1.46 | ~1.71 | ~1.75 | +| 160k | ~1.44 | ~1.70 | ~1.75 | +| 180k | ~1.43 | ~1.70 | ~1.75 | +| 200k | ~1.43 | ~1.69 | ~1.72 | +| 220k | ~1.42 | ~1.69 | ~1.73 | +
+ +(a) Training Perplexity (PPL) + +![](images/82c80d138141f010fa79e32343b04995c61f9dcd45f48b620653763fb4af129e.jpg) + +
+line + +| Training iterations | Shape-Conditioned (Validation PPL) | Image-Conditioned (Validation PPL) | Unconditional (Validation PPL) | +| --- | --- | --- | --- | +| 60k | ~2.0 | ~2.0 | ~2.0 | +| 80k | ~1.52 | ~1.75 | ~1.8 | +| 100k | ~1.44 | ~1.67 | ~1.72 | +| 120k | ~1.41 | ~1.63 | ~1.68 | +| 140k | ~1.39 | ~1.6 | ~1.65 | +| 160k | ~1.37 | ~1.59 | ~1.63 | +| 180k | ~1.36 | ~1.58 | ~1.61 | +| 200k | ~1.35 | ~1.57 | ~1.6 | +| 220k | ~1.34 | ~1.56 | ~1.59 | +
+ +(b) Validation Perplexity (PPL) +Figure 3: Training and validation perplexity (PPL) for the mesh generation model under different input conditions. All models are trained with the same settings as detailed in Section 5.2. The training and validation PPL of shape-conditioned mesh generation is significantly lower than that of unconditional and image-conditioned mesh generation. This indicates that the training burden of shape-conditioned mesh generation is much lower since it avoids learning the complex 3D shape distribution. + +Shape-Conditioned AM Generation targets to estimate a conditional distribution $p ( \mathcal { M } | S )$ . In this formula, M refers to the Artist-Created Mesh (AM), i.e., the mesh manually modeled by human artists. S refers to the 3D shape information that indicates the 3D shape to which M should align. The input form of S can be diverse, such as voxels or point clouds. Therefore, this versatility allows our method to be integrated with any 3D pipeline that outputs S, such as 3D reconstruction Mildenhall et al. (2020); Kerbl et al. (2023b), generation Poole et al. (2023); Hong et al. (2023), and scanning, making these methods more efficient for the 3D industry. + +Compared to existing AM generation work, they directly estimate the distribution $p ( \mathcal { M } | \mathcal { C } )$ , where C denotes conditions such as images, text or empty sets for unconditional generation. However, estimating $p ( \mathcal { M } | \mathcal { C } )$ requires an understanding of both the underlying shape, i.e., S, and complex topological structures M. Given this, we made the following approximation: + +$$ +p (\mathcal {M} | \mathcal {C}) \approx p (\mathcal {M}, \mathcal {S} | \mathcal {C}). \tag {1} +$$ + +According to the chain rule, we have: + +$$ +p (\mathcal {M}, \mathcal {S} | \mathcal {C}) = p (\mathcal {M} | \mathcal {S}, \mathcal {C}) \cdot p (\mathcal {S} | \mathcal {C}). \tag {2} +$$ + +For distribution $p ( \mathcal { M } | \mathcal { S } , \mathcal { C } )$ , given that S is a much stronger and more direct condition than C, we can make the following approximation: + +$$ +p (\mathcal {M} | \mathcal {S}, \mathcal {C}) \approx p (\mathcal {M} | \mathcal {S}). \tag {3} +$$ + +Combining 1, 2 and 3: + +$$ +p (\mathcal {M} | \mathcal {C}) \approx p (\mathcal {M} | \mathcal {S}) \cdot p (\mathcal {S} | \mathcal {C}), \tag {4} +$$ + +in which $p ( \mathcal { M } | S )$ is the focus of our shape-conditioned mesh generation. As shown in Fig. 3, estimating $p ( \mathcal { M } | S )$ is much more simpler than $p ( \mathcal { M } | \mathcal { C } )$ , proving that our setting is much easier to train than settings in privous methods. + +As for p(S|C), In the 3D community, numerous large models Team (2024); Tang et al. (2024); Xu et al. (2024); Siddiqui et al. (2023) aim to estimate using various 3D representations and demonstrate excellent results. Besides, some single scene 3D asset production methods Mildenhall et al. (2020); Kerbl et al. (2023b); Barron et al. (2021; 2022); Poole et al. (2023); Liu et al. (2023b); Sun et al. (2023) can also provide samples from this distribution. By integrating our framework with these existing methods, we can leverage their capabilities to enhance our mesh generation process. This integration allows for a more resource-efficient way to estimate $p ( \mathcal { M } | \mathcal { C } )$ , significantly reducing the complexity and resources required compared to previous methods. + +![](images/ed7acb9369bfcc2c48faff57b105d6db318c21dfbb1b16f91c12ef6419bebbfe.jpg) + +
+flowchart + +```mermaid +graph LR + A["Training"] --> B["VQ Encoder"] + B --> C["Artist-Created Mesh"] + C --> D["Sample from surface"] + D --> E["Inference"] + E --> F["NeRF 3D GS"] + F --> G["Sample"] + G --> H["Point Cloud"] + H --> I["Feature"] + I --> J["Mesh Autoregressive Transformer"] + J --> K["..."] + K -.-> L["Cross-Entropy Loss"] + L --> M["Cross-Entropy Loss"] + M --> N["Cross-Entropy Loss"] + N --> O["Cross-Entropy Loss"] + O --> P["VQ Decoder"] + P --> Q["Generated Mesh"] +``` +
+ +Figure 4: Pipeline Overview. We introduce MeshAnything, an autoregressive transformer capable of generating Artist-Created Meshes that adhere to given 3D shapes. During training, we inject point clouds features into a decoder-only transformer and supervise it using token sequences derived from the Artist-Created meshes. After training, MeshAnything takes point clouds sampled from various 3D representations as input and generates aligned Artist-Created meshes. + +## 4 METHOD + +In this section, we detail our shape condition strategy in Section 4.1. After that, we provide a detailed description for MeshAnything, which consists of a VQVAE with our newly proposed noise-resistant decoder (Section 4.2) and a shape-conditioned autoregressive transformer (Section 4.3). + +## 4.1 SHAPE ENCODING FOR CONDITIONAL GENERATION + +We begin by describing our shape condition strategy. MeshAnything targets learning p(M|S), so we need to pair each mesh M with a corresponding S, i.e., the shape condition. Choosing an appropriate 3D representation for S is non-trivial and should satisfy the following conditions: + +1. It should be easily extracted from various 3D representations. This ensures that the trained models can be integrated with a wide range of 3D asset production pipelines Mildenhall et al. (2020); Kerbl et al. (2023b); Hong et al. (2023); Poole et al. (2023); Tang et al. (2024). +2. It should be suitable for data augmentation to prevent overfitting. To ensure the effectiveness of S during training, any data augmentation applied to M must be equivalently applicable to S. +3. It should be efficiently and conveniently input into the model as a condition. To ensure the model comprehends the shape information and to maintain efficient training, S must be easily and effectively encoded into features. + +Considering the first and second points, S should be in an explicit representation. Further considering the third point, the main explicit 3D representations that can be easily encoded as features are voxels and point clouds. Both representations are suitable, but voxels typically require a high resolution to accurately represent shapes, and processing high-resolution voxels into features is computationally expensive. Additionally, voxels, being a discrete representation, are less precise for data augmentation compared to point clouds. Therefore, we chose point clouds as the representation for S. To enhance the expressive power of the point clouds, we also include normals into the point cloud representation. + +To obtain point clouds from the ground truth mesh for training, we could simply sample point clouds directly from the surface of M. However, this would create problems during inference: the surfaces of automatically generated 3D assets are often rougher than those of AMs. For example, in AMs, we would sample a series of points on a flat plane, whereas automatically generated 3D assets would have uneven surfaces, causing a domain gap between training and inference. + +Therefore, we need to ensure that S extracted from the ground truth M during training has a similar domain to the S extracted during inference. To bring their domains closer, we intentionally construct coarse meshes from AMs. We first extract the signed distance function from M with Wang et al. (2022), then convert it into a relatively coarse mesh using Marching Cubes Lorensen & Cline (1987) to destroy the ground truth topology. Finally, we sample point cloud and its normals from the coarse mesh. This approach also helps to avoid overfitting, as AMs typically have fewer faces, and each face can often sample multiple points. The network can easily recognize the ground truth topology by determining whether the points lie on the same plane. + +Since almost all 3D representations can be converted into a coarse mesh using Marching Cubes Lorensen & Cline (1987) or sampled into point clouds, this ensures that the domain of S is consistent during both training and inference. We pair the point clouds extracted as S with M to create a data item $\big \{ ( { \mathcal { M } } _ { i } , { \mathcal { S } } _ { i } ) \big \} $ i for training. + +## 4.2 VQ-VAE WITH NOISE-RESISTANT DECODER + +Following MeshGPT Siddiqui et al. (2023), we first train a VQ-VAE Van Den Oord et al. (2017) to learn a vocabulary of geometric embeddings for better transformer Vaswani et al. (2017) learning. Different to MeshGPT, which uses graph convolutional networks Wu et al. (2019) and ResNet He et al. (2016) as the encoder and decoder respectively, we employ transformers with identical structures for both the encoder and decoder. When training VQ-VAE, meshes are discretized and input as a sequence of triangle faces: + +$$ +\mathcal {M} := (f _ {1}, f _ {2}, f _ {3}, \dots , f _ {N}), \tag {5} +$$ + +where $f _ { i }$ is the coordinates of the vertices of each face, and N is the number of faces in M. The encoder E then extracts a feature vector for each face: + +$$ +\mathcal {Z} = (z _ {1}, z _ {2}, \dots , z _ {N}) = E (\mathcal {M}), \tag {6} +$$ + +where $z _ { i }$ is the feature vector for $f _ { i }$ . + +The extracted faces are then quantized into quantized features T with codebook B: + +$$ +\mathcal {T} = R Q (\mathcal {Z}; \mathcal {B}) \tag {7} +$$ + +Finally, the reconstructed mesh is decoded from $\tau$ with decoder D by predicting the logits for each vertex’s coordinates: + +$$ +\hat {\mathcal {M}} = D (\mathcal {Z}) \tag {8} +$$ + +The VQ-VAE is trained end-to-end with cross-entropy loss on the predicted vertex coordinate logits and the commitment loss of vector quantization Van Den Oord et al. (2017). After the training of VQ-VAE, the encoder-decoder of VQ-VAE is treated as a tokenizer and detokenizer for autoregressive transformer training. + +However, as shown in Fig. 7, there are possible imperfections in the generation results. To address this issue, given our setting of Shape-Conditioned AM Generation, the VQ-VAE decoder can also take the shape condition as input. Small imperfections in the token sequences generated by the transformer can potentially be corrected by a shape-aware decoder. Therefore, after completing the vanilla VQ-VAE training, we add an additional decoder fine-tuning stage, where we inject the shape information into the transformer decoder. Then we add random Gumbel noise to the codebook sampling logits to simulate the potential imperfections in the token sequences generated by the transformer during inference. The decoder is then updated independently with the same crossentropy loss to train it to produce refined meshes even when facing imperfect token sequences. Our experiments in Tab. 3 and Tab. 4 show that our method effectively enhances the decoder’s noise resistance and mesh generation quality. + +## 4.3 SHAPE-CONDITIONED AUTOREGRESSIVE TRANSFORMER + +To add shape condition to the transformer, inspired by the success of multimodal large language models Wu et al. (2023); Liu et al. (2024a); Xu et al. (2023); Guo et al. (2023), we first encode the point cloud into a fixed-length token sequence with a point cloud encoder P and then concatenate it to the front of the embedding sequence from T VQ-VAE as the final input embedding sequence for the transformer: + +$$ +\mathcal {T} ^ {\prime} = \operatorname{concat} (\mathcal {P} (\mathcal {S}), \mathcal {T}) \tag {9} +$$ + +where $\tau ^ { \prime }$ is the training input for the transformer. + +We borrow a pretrained point encoder from Zhao et al. (2024) and add a linear projection layer to project its output feature to the same latent space as $\tau$ . During training, the original point encoder from Zhao et al. (2024) is frozen; we only update the newly added projection layer and the autoregressive transformer with cross-entropy loss. + +Table 1: Comparison of Mesh Generation Methods. As shown in the left table, compared to the baseline Artist-Created Mesh Generation method, the meshes generated by MeshAnything are better aligned with human preferences. In the right table, we compare MeshAnything with mesh extraction baselines, and it received the most votes. For detailed settings, please refer to Section 5.4. + +
MethodShape↑Topology↑
PolyGen12.7%11.1%
MeshGPT24.1%28.2%
MeshAnything63.2%60.7%
+ +
MethodShape↑Topology↑
MarchingCubes38.1%10.2%
Shape As Points17.3%6.2%
MeshAnything44.6%83.6%
+ +During inference, we input ${ \mathcal { P } } ( S )$ to the transformer and require it to generate the subsequent sequence, Tˆ . $\hat { \tau }$ is then input to the noise-resistant decoder to reconstruct meshes: + +$$ +\hat {\mathcal {M}} = D (\hat {\mathcal {T}}) \tag {10} +$$ + +where $\hat { \mathcal { M } }$ is the final generated AM. + +We use the standard next-token prediction loss to train shape-conditioned transformers. For each sequence, we add a token after the point cloud tokens and a token after the mesh tokens to identify the end of a 3D mesh. + +## 5 EXPERIMENTS + +## 5.1 DATA PREPARATION + +Data Selection. Existing AM generation works are limited to a few categories. However, our method targets to operate on general shapes. MeshAnything is trained on a combined dataset of Objaverse Deitke et al. (2023b) and ShapeNet Chang et al. (2015), selected for their complementary characteristics. We chose Objaverse because it contains a large number of AMs without category limitations. On the other hand, ShapeNet offers higher data quality within limited categories. + +We filter out meshes with more than 800 faces from both datasets. Additionally, we manually filtered out low quality meshes. Our final filtered dataset consists of 51k meshes from Objaverse and 5k meshes from ShapeNet. We randomly select 10% of this dataset as the evaluation dataset, with the remaining 90% used as the training set for all our experiments. + +Data Processing and Augmentation. Following the strategies of PolyGen Nash et al. (2020) and MeshGPT Siddiqui et al. (2023), we order faces by their lowest vertex index, then by the next lowest, and so on. Vertices are sorted in ascending order based on their z-y-x coordinates, where z represents the vertical axis. Within each face, we permute the indices to ensure the lowest index comes first. During training, we apply on-the-fly scaling, shifting, and rotation augmentations, normalizing each mesh to a unit bounding box from −0.5 to 0.5. + +## 5.2 IMPLEMENTATION DETAILS + +The encoder and decoder of VQ-VAE both use the encoder of BERT Devlin et al. (2018), while we choose OPT-350M Zhang et al. (2022) as our autoregressive transformer architecture. The residual vector quantization Zeghidour et al. (2021) depth is set to 3, with a codebook size of 8,192. + +Our point encoder is based on the pretrained point encoder from Zhao et al. (2024), which has been trained on Objaverse and thus can handle general shapes. This point encoder outputs a fixedlength token sequence of 257 tokens, with 256 tokens primarily containing shape information and an additional head token containing semantic information about the shape. We sample 4096 points for each point cloud. + +The training batch size for both the VQ-VAE and the transformer is set to 8 per GPU. The VQ-VAE is trained on 8 A100 GPUs for 12 hours, after which we separately finetune the decoder part of the VQ-VAE into a noise-resistant decoder, as detailed in Section 4.2. Following this, the transformer is trained on 8 A100 GPUs for 4 days. + +Table 2: Quantitative Comparisons with Prior Arts on Objaverse. MeshAnything significantly outperforms prior methods across all metrics. MMD, KID are scaled by 103. + +
MethodCOV↑MMD↓1-NNA↓FID↓KID↓
PolyGen23.26.2288.248.827.7
MeshGPT41.73.8367.325.16.11
MeshAnything53.12.7255.714.51.89
+ +## 5.3 QUALITATIVE EXPERIMENTS + +As shown in Fig. 1, MeshAnything effectively generates AMs from various 3D representations. In our experiments, we use Rodin Team (2024) as the text-to-3D and image-to-3D method, and employ Mildenhall et al. (2020) and Kerbl et al. (2023a) as the 3D reconstruction pipeline to obtain the corresponding NeRF and Gaussian Splatting models. For additional qualitative results, please refer to A.2 combined with other 3D asset production pipelines. + +## 5.4 QUANTITATIVE EXPERIMENTS + +From the generative model perspective, MeshAnything is a shape-conditioned mesh generation model. From the mesh extraction perspective, it extracts artist-created meshes from point clouds. Consequently, we compare MeshAnything with both types of methods. Additional experiments can be found in Appendix Section A.2. + +User Study. As shown in Tab. 1, we conducted two user studies, comparing with mesh generation baselines Nash et al. (2020); Siddiqui et al. (2023) and mesh extraction baselines Lorensen & Cline (1987); Peng et al. (2021), respectively. The mesh generation baselines are trained on ShapeNet, and to ensure a fair comparison, we retrained them on Objaverse using the same transformer model as MeshAnything. Since the mesh generation baselines are all unconditional mesh generation methods, whereas MeshAnything is a shape-conditioned mesh generation method, we sampled shapes randomly from the evaluation set of Objaverse as inputs for MeshAnything, while for the baseline methods, we performed random sampling directly. + +In the mesh extraction baseline, since our method can also be viewed as a point cloud to mesh approach, we included Peng et al. (2021), a point cloud to mesh method, as a baseline. Additionally, we optimized the results from the mesh extraction baseline using the Blender remesh method Blender Development Team (2024) to simplify the topology. + +We collected 30 results from each method and asked users to vote for the best one in terms of shape quality and topology quality. A total of 41 users participated, providing 1,230 valid comparisons. Both user studies demonstrated the superiority of our method. The only difference between the retrained MeshGPT and MeshAnything is whether they are shape-conditioned, further proving the advantages of the shape-conditioned mesh generation setting. + +Metrics. We follow the metric setting of Chen et al. (2022); Siddiqui et al. (2023). We detail this setting in Appendix Section. A.1. + +Comparison with Mesh Generation Pipelines. We use the same retrained models from the user study for comparison. As shown in Tab. 2, MeshAnything significantly outperforms prior methods Nash et al. (2020); Siddiqui et al. (2023), indicating that it’s superior in both the shape and topology quality. Since the only difference between the retrained MeshGPT and MeshAnything is the inclusion of shape conditioning, the superior performance of MeshAnything further demonstrates that Shape-Conditioned Mesh Generation is a more suitable setting for mesh generation. + +## 6 CONCLUSION + +In this work, we propose a novel setting for improved mesh extraction and mesh generation, namely Shape-Conditioned Artist-Created Mesh (AM) Generation. Following this setting, we introduce MeshAnything, a model capable of generating AMs that adhere to given 3D assets. MeshAnything can convert 3D assets in any 3D representation into AMs and thus can be integrated with diverse 3D asset production methods to facilitate their application in the 3D industry. Furthermore, we introduce a noise-resistant decoder architecture to enhance the generation quality, enabling the model to handle low-quality token sequences produced by autoregressive transformers. Lastly, extensive experiments demonstrate the superior performance of our method, highlighting its potential to scale up for 3D industry application and its advantage over previous methods. + +## REFERENCES + +Antonio Alliegro, Yawar Siddiqui, Tatiana Tommasi, and Matthias Nießner. Polydiff: Generating 3d polygonal meshes with diffusion models. arXiv preprint arXiv:2312.11417, 2023. +Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 5855–5864, 2021. +Jonathan T. Barron, Ben Mildenhall, Dor Verbin, Pratul P. Srinivasan, and Peter Hedman. 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IEEE/ACM Transactions on Audio, Speech, and Language Processing, 30:495–507, 2021. +Susan Zhang, Stephen Roller, Naman Goyal, Mikel Artetxe, Moya Chen, Shuohui Chen, Christopher Dewan, Mona Diab, Xian Li, Xi Victoria Lin, et al. Opt: Open pre-trained transformer language models. arXiv preprint arXiv:2205.01068, 2022. +Zibo Zhao, Wen Liu, Xin Chen, Xianfang Zeng, Rui Wang, Pei Cheng, Bin Fu, Tao Chen, Gang Yu, and Shenghua Gao. Michelangelo: Conditional 3d shape generation based on shape-image-text aligned latent representation. Advances in Neural Information Processing Systems, 36, 2024. + +A APPENDIX +![](images/7ab65c46fed251beed13c7e66df489ff073504f84d285a2b7c7eda53b00ac28c.jpg) + +
+natural_image + +Collection of 3D wireframe models and 3D mesh designs including point cloud, image, and dense mesh (no text or symbols) +
+ +Figure 5: Additional qualitative results of MeshAnything. As shown, MeshAnything can be integrated with various 3D production pipelines to achieve highly controllable mesh generation. + +![](images/862aeab2050e05c2e08496535a396d53ce14ba0421ede1b90aa189a88547daac.jpg) + +
+text_image + +Point Cloud Condition +Image Condition +Image Condition +(a) +312 faces +Ours +518 faces +GT +612 faces +Ours +529 faces +GT +(b) +(c) +
+ +Figure 6: Qualitative Results. (a) further demonstrates our capability to achieve highly controllable mesh generation when combined with 3D asset production pipelines. Besides, we compare our reseults with ground truth in (b) and (c). In (b), MeshAnything generates meshes with better topology and fewer faces than the ground truth. In (c), we produce meshes with a completely different topology while achieving a similar shape, proving that our method does not simply overfit but understands how to construct meshes using efficient topology. + +![](images/eb9f539a645e6b2e3c176b61b49ba88020584ef19f05df2c9ea2f6addf7bca86.jpg) + +
+text_image + +W.O. Noise-Resistant Decoder +Ours +W.O. Noise-Resistant Decoder +Ours +W.O. Noise-Resistant Decoder +Ours +
+ +Figure 7: Ablation on Noise-Resistant Decoder. The decoder-only transformer may generate lowquality token sequences, and the decoder of VQ-VAE would typically produce flawed meshes based on these sequences. In contrast, our Noise-Resistant Decoder, aided by shape conditions, has the ability to resist these low-quality token sequences, producing higher-quality meshes. + +## A.1 METRICS + +We follow the evaluation metric setting of Siddiqui et al. (2023) in mesh generation experiments and the setting of Chen et al. (2022) in mesh extraction experiments. + +We quantitatively evaluate mesh quality by uniformly sampling 100K points from the faces of both the ground truth meshes and the predicted meshes, and then computing a set of metrics to assess various aspects of the reconstruction. + +Table 3: Reconstruction Performance under Different Noise Levels with and without Noise-Resistant (NR) Decoder. Please refer to A.1 for metrics explanation. + +
Noise Level $\mathbf{CD}(\times 10^{-2})\downarrow$ $\mathbf{ECD}(\times 10^{-2})\downarrow$ $\mathbf{NC}\uparrow$
W/O NRW/ NRW/O NRW/ NRW/O NRW/ NR
0.00.0110.0070.0350.0230.9870.993
0.10.1870.0280.6130.1380.9730.991
0.51.1670.6392.5381.3290.9640.981
1.02.1311.7984.3172.3160.9520.969
+ +Table 4: Ablation on Noise-Resistant (NR) Decoder for the Quality of Mesh Generation. + +
Method $\mathbf{CD}↓$ $(×10^{-2})$ $\mathbf{ECD}↓$ $(×10^{-2})$ $\mathbf{NC}↑$
W/O NR2.4236.4140.883
W/ NR2.2566.2450.902
+ +For mesh extraction, we report the following metrics: Chamfer Distance (CD) to evaluate the overall quality of a reconstructed mesh; Edge Chamfer Distance (ECD) to assess the preservation of sharp edges by sampling points near sharp edges and corners; and Normal Consistency (NC) to evaluate the quality of the surface normals. Additionally, we report the number of mesh vertices (#V) and the number of mesh faces (#F). We also provide the ratio of the estimated number of vertices to the ground truth number of vertices (#V R) and the same ratio for faces (#F R). + +For mesh generation, Coverage (COV) captures the diversity of generated meshes and is sensitive to mode dropping, but it does not reflect the quality of the results. Minimum Matching Distance (MMD) measures the average distance between the reference set and their nearest neighbors in the generated set, though it lacks sensitivity to low-quality outputs. The 1-Nearest Neighbor Accuracy (1-NNA) assesses both quality and diversity between the generated and reference sets. To evaluate topology quality, we render the ground truth meshes and generated meshes with their wireframes visualized. We then employ Frechet Inception Distance (FID) and Kernel Inception Distance (KID) on rendered images. MMD, and KID scores are scaled by a factor of 103. + +## A.2 EXPERIMENTS + +Additional Qualitative Experiments We present more qualitative results of MeshAnything here. As shown in Fig. 5 and Fig. 6, MeshAnything effectively generates AMs from various 3D representations. When integrated with different 3D assets production pipelines, our method effectively achieves mesh generation with diverse conditions. + +Next, Fig. 6 demonstrates that MeshAnything does not simply overfit but understands how to generate meshes with efficient topology that conform to the given shape. To prove this, we use manuallycreated meshes as ground truth and use their shapes as conditions to test whether our model can generate meshes with comparable topology. To effectively use the ground truth as conditions, we first convert them into dense meshes using Marching Cubes Lorensen & Cline (1987) to disrupt their face structure. Then, we sample point clouds with normals from the dense meshes to serve as shape conditions. The experimental results in Fig. 6 show that MeshAnything is capable of generating meshes comparable to or even surpassing those modeled by human artists, exhibiting diverse and strong 3D modeling capabilities. + +Comparison with mesh extraction baselines. Our method is related to various mesh extraction methods Lorensen & Cline (1987); Chen & Zhang (2021); Chen et al. (2022); Shen et al. (2023); Peng et al. (2021) since we also convert other 3D representations into meshes. However, it is important to note that previous approaches are reconstruction-like methods that produce dense meshes, while our approach is generative, creating Artist-Created Meshes (AMs) that are significantly more complex to produce than dense meshes. Therefore, strictly speaking, our method cannot be considered the same as these reconstruction-based mesh extraction methods. The main purpose of this comparison is to use these mesh extraction methods as a reference for evaluating the quality of the meshes generated by MeshAnything in terms of shape. We compare MeshAnything with Lorensen & Cline (1987); Shen et al. (2023); Peng et al. (2021). Among these, MarchingCubes is the most popular mesh extraction method, FlexiCubes represents the state-of-the-art in mesh extraction, and Shape as Points is the leading method for extracting mesh from point cloud. + +Table 5: Quantitative evaluation with mesh extraction baselines. MC, FC, SAP refer to Marching Cubes Lorensen & Cline (1987), FlexiCubes Shen et al. (2023), and Shape As Points Peng et al. (2021), respectively. Please refer to A.1 for metrics explanation. + +
Method $\mathbf{CD}\downarrow$ $(\times 10^{-2})$ $\mathbf{ECD}\downarrow$ $(\times 10^{-2})$ $\mathbf{NC}\uparrow$ $\#V\downarrow$ $(\times 10^{3})$ $\#F\downarrow$ $(\times 10^{3})$ $\mathbf{V\_R}\downarrow$ $\mathbf{F\_R}\downarrow$
(a) Marching Cubes1.5326.7330.95473.22146.0440.2462.2
(b) MC+Remesh (0.005)2.1747.8130.912127.8167.9748.1534.6
(c) MC+Remesh (0.010)2.0837.5780.92939.0141.78225.4132.3
(d) MC+Remesh (0.030)2.9158.3290.8635.8484.41034.3814.05
(e) MC+Remesh (0.050)4.1798.1380.8142.2991.53813.644.920
(f) MC+Remesh (0.100)7.31210.7710.7480.6250.3593.7351.149
(g) FC1.1906.1210.96759.12121.1378.2391.1
(h) FC+Remesh (0.010)1.8616.9400.93337.9840.19205.5124.2
(i) SAP1.7717.1120.93979.12152.3481.2489.3
(j) SAP+Remesh (0.010)2.3677.8620.92539.1742.87239.1136.6
(k) MeshAnything2.2566.2450.9020.1720.3180.8880.871
+ +We also combined these methods with the remesh technique to test whether they could significantly reduce the number of faces while maintaining shape quality. We used Blender Remesh in voxel mode Community (2018); Blender Development Team (2024), specifically using Blender version 4.1, as the remesh method. Since our evaluation dataset includes non-watertight meshes, we first extract the signed distance fields (SDF) of all ground truth meshes using Wang et al. (2022), which can handle non-watertight meshes. We then apply Marching Cubes with a resolution of 128 on these SDFs. Next, we apply Blender remesh Blender Development Team (2024) with different voxel sizes to the Marching Cubes results, as both the remesh method and our approach are capable of simplifying topology. Additionally, the Marching Cubes result is used as the shape condition input to MeshAnything to obtain our results. The settings of Shen et al. (2023) and Peng et al. (2021) follow their papers. + +As shown in Tab. 5, we found that these methods require hundreds of times more faces to achieve results comparable to our method. Comparing (a), (g), (i) and (k), our method lags in Chamfer Distance (CD) and Normal Consistency (NC), mainly due to our method’s inherent failure cases as a generative model, which makes it less robust than these reconstruction-based mesh extraction methods. When comparing with remesh methods, we observe that they incur a high cost to achieve a face count similar to ours. Comparing (f) and (k), we find that even when remesh methods achieve a comparable face count, the number of vertices is still several times higher than ours, indicating that the topology efficiency of remesh methods is far inferior to ours, as they completely ignore the shape characteristics of the 3D assets. It’s important to note that the metrics in mesh etraction can only indicate the quality of shape alignment, which do not effectively reflect the topological advantages of our method. Additionally, we surprisingly find that our method can produce results with fewer faces than the ground truth, demonstrating that MeshAnything is not overfitting to the data but instead learns an efficient topology representation, occasionally surpassing the ground truth meshes. + +Ablations on Noise-Resistant Conditional Decoder. We perform ablation experiments to verify the effectiveness of the Noise-Resistant Decoder. We begin with a VQ-VAE trained without any noise or conditioning. We then perform ablation between two settings: one where the decoder remains unchanged and unaware of the shape condition, and another where the shape condition is injected into the transformer, as described in Section 4.2. Next, we randomly sample a noise from gumbel distribution and add it to codebook sampling logits during the vector quantization process to simulate the potential low-quality token sequences generated by the transformer. We control the noise level by scaling the added noise. + +Table 6: Experiments on the Impact of Input Point Cloud Quality on Generated Results. + +
Method $\mathbf{CD}↓$ $(×10^{-2})$ $\mathbf{ECD}↓$ $(×10^{-2})$ $\mathbf{NC}↑$ $#V↓$ $(×10^{3})$ $#F↓$ $(×10^{3})$ $V\_R↓$ $F\_R↓$
(a) Noise scale 0.0052.3516.4120.8970.1750.3210.8950.880
(b) Noise scale 0.0202.9806.9700.8810.1800.3300.9010.910
(c) Noise scale 0.0504.9108.5560.7550.1620.2840.8110.802
(d) Rodin2.5526.6220.8330.1850.3420.9190.923
(e) $MeshAnything$ 2.2566.2450.9020.1720.3180.8880.871
+ +After training both models for enough epochs, we test their performance to the same level of noise. As shown in Tab. 3, as the intensity of the added noise increases, the Noise-Resistant Decoder with shape condition clearly achieves better reconstruction results. This indicates that the shape condition helps the decoder identify and correct imperfections in the input token sequences. + +Next, we verify whether the Noise-Resistant Decoder indeed enhances the transformer’s performance during inference. The test method used dense meshes derived from corrupted GT meshes as the condition for generating new meshes. The generated meshes were then assessed for shape alignment with the conditional shape. As shown in Tab. 4, the model with Noise-Resistant Decoder achieved better results. + +Experiments on the Impact of Input Point Cloud Quality on Generated Results. MeshAnything takes point clouds as input, and its robustness to point cloud quality determines its versatility across various applications. We design two experiments to evaluate its tolerance to input point cloud quality: First, keeping the other evaluation settings unchanged, we apply Gaussian noise to the input point cloud coordinates and normals. Specifically, for each point, we randomly sample Gaussian noise from a standard distribution, scale it by a noise factor, and add it to the point’s coordinates. The same approach is applied to the normals, but normalization is applied after adding the noise. Second, we use Rodin’s generation result as the ground truth mesh, sample point clouds from this mesh as input, and evaluate the deviation between the generated result and the ground truth. + +As shown in Tab. 6, MeshAnything did not experience a significant performance drop in (a) and (b), demonstrating resilience to noise in the point cloud, with a noticeable performance decrease only in (c). It is important to note that the input point cloud is normalized to the range [-1,1], and the noise scale in (c) is already quite large. The experiment in (d) further demonstrates that MeshAnything can tolerate generated point clouds and effectively integrate with 3D generation models. + +## A.3 LIMITATIONS + +Our method cannot generate meshes that exceed the maximum face count limit, so it cannot convert large scenes and particularly complex objects into meshes. Additionally, due to its generative nature, our method is not as stable as reconstruction-based mesh extraction methods like Lorensen & Cline (1987); Shen et al. (2023). + +## A.4 SOCIAL IMPACT + +Our method points to a promising approach for the automatically generation of Artist-Created Meshes, which has the potential to significantly reduce labor costs in the 3D industry, thereby facilitating advancements in industries such as gaming, film, and the metaverse. However, the reduced cost of obtaining 3D Artist-Created meshes could also lead to potential criminal activities. \ No newline at end of file diff --git a/papers/markdown/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers/hybrid_auto/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers_content_list.json b/papers/markdown/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers/hybrid_auto/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..3e6bc54df8bd99d0c3a6145d5fd0fd88581716fb --- /dev/null +++ b/papers/markdown/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers/hybrid_auto/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers_content_list.json @@ -0,0 +1,1983 @@ +[ + { + "type": "text", + "text": "MESHANYTHING: ARTIST-CREATED MESH GENERA-TION WITH AUTOREGRESSIVE TRANSFORMERS", + "text_level": 1, + "bbox": [ + 171, + 99, + 823, + 146 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yiwen Chen1,2∗, Tong He2†, Di Huang2, Weicai Ye2, Sijin Chen3, Jiaxiang Tang4 Xin Chen5, Zhongang Cai6, Lei Yang6, Gang Yu7, Guosheng Lin1†, Chi Zhang8† 1S-Lab, Nanyang Technological University 2Shanghai AI Lab 3Fudan University 4Peking University 5University of Chinese Academy of Sciences 6SenseTime Research 7Stepfun 8Westlake University https://buaacyw.github.io/mesh-anything/", + "bbox": [ + 187, + 169, + 776, + 257 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4c8a3616bc55f836a4dc48c40a287983e81006ea66f4e11701727c07112ba992.jpg", + "image_caption": [ + "Figure 1: MeshAnything converts any 3D representation into Artist-Created Meshes (AMs), i.e., meshes created by human artists. It can be combined with various 3D asset production pipelines, such as 3D reconstruction and generation, to transform their results into AMs that can be seamlessly applied in the 3D industry." + ], + "image_footnote": [], + "content": "```mermaid\ngraph LR\n A[\"Text Condition: A commode\"] --> B[\"NeRF\"]\n B --> C[\"3D GS\"]\n C --> D[\"Image\"]\n D --> E[\"Dense Mesh\"]\n E --> F[\"Dense Mesh\"]\n F --> G[\"Dense Mesh\"]\n G --> H[\"Dense Mesh\"]\n H --> I[\"Point Cloud\"]\n J[\"Point Cloud\"] --> K[\"Dense Mesh\"]\n K --> L[\"Dense Mesh\"]\n L --> M[\"Point Cloud\"]\n```", + "sub_type": "flowchart", + "bbox": [ + 173, + 284, + 826, + 728 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ABSTRACT", + "text_level": 2, + "bbox": [ + 450, + 815, + 547, + 830 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, 3D assets created via reconstruction and generation have matched the quality of manually crafted assets, highlighting their potential for replacement. However, this potential is largely unrealized because these assets always need to be converted to meshes for 3D industry applications, and the meshes produced by current mesh extraction methods are significantly inferior to Artist-Created Meshes (AMs), i.e., meshes created by human artists. Specifically, current mesh extraction methods rely on dense faces and ignore geometric features, leading to inefficiencies, complicated post-processing, and lower representation quality. To address these issues, we introduce MeshAnything, a model that treats mesh extraction as a generation problem, producing AMs aligned with specified shapes. By converting 3D assets in any 3D representation into AMs, MeshAnything can be integrated with various 3D asset production methods, thereby enhancing their application across the 3D industry. The architecture of MeshAnything comprises a VQ-VAE and a shape-conditioned decoder-only transformer. We first learn a mesh vocabulary using the VQ-VAE, then train the shape-conditioned decoderonly transformer on this vocabulary for shape-conditioned autoregressive mesh generation. Our extensive experiments show that our method generates AMs with hundreds of times fewer faces, significantly improving storage, rendering, and simulation efficiencies, while achieving precision comparable to previous methods.", + "bbox": [ + 228, + 845, + 767, + 890 + ], + "page_idx": 0 + }, + { + "type": "aside_text", + "text": "arXiv:2406.10163v2 [cs.CV] 9 Oct 2024", + "bbox": [ + 22, + 270, + 58, + 700 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "∗Work done during a research internship at Shanghai AI Lab.", + "bbox": [ + 189, + 896, + 555, + 910 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding Authors.", + "bbox": [ + 192, + 910, + 344, + 924 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1", + "bbox": [ + 493, + 948, + 503, + 959 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 228, + 103, + 767, + 339 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1 INTRODUCTION", + "text_level": 2, + "bbox": [ + 173, + 369, + 336, + 383 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent years, the 3D community has experienced rapid advancements, with a variety of methods developed for automatically producing high-quality 3D assets. These methods, including 3D reconstruction Mildenhall et al. (2020); Yu et al. (2021); Barron et al. (2021; 2022); Kerbl et al. (2023b); Huang et al. (2024), 3D generation Poole et al. (2023); Liu et al. (2023a); Wang et al. (2023); Long et al. (2023); Sun et al. (2023); Hong et al. (2023); Tang et al. (2024); Xu et al. (2024); Wei et al. (2024), and scanning Daneshmand et al. (2018); Haleem & Javaid (2019); Haleem et al. (2022), can produce 3D assets with shape and color quality comparable to manually created ones. The success of these methods reveals the potential to replace manually created 3D models with automatically produced ones in the 3D industry, including applications in games, movies, and the metaverse, significantly reducing time and labor costs.", + "bbox": [ + 169, + 402, + 826, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, this potential remains largely unrealized because the current 3D industry predominantly relies on mesh-based pipelines for their superior efficiency and controllability, while methods for producing 3D assets typically use alternative 3D representations to achieve optimal results across various scenarios. Therefore, substantial efforts Lorensen & Cline (1987); Chernyaev (1995); Lorensen & Cline (1998); Shen et al. (2021b); Chen et al. (2022); Shen et al. (2023) are devoted to converting other 3D representations into meshes and have achieved some success. Meshes produced by these methods approximate the shape quality of those created by human artists, which we refer to as Artist-Created Meshes (AMs), but they still fall short in addressing the aforementioned issues.", + "bbox": [ + 169, + 547, + 823, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This is because all meshes produced by these methods Lorensen & Cline (1987); Chernyaev (1995); Lorensen & Cline (1998); Shen et al. (2021b); Chen et al. (2022); Shen et al. (2023) exhibit significantly poorer topology quality compared to AMs. As shown in Fig. 2, these methods rely on dense faces to reconstruct 3D shapes, completely ignoring geometric characteristics. Using these meshes in the 3D industry leads to three significant problems: First, converted meshes typically contain several orders of magnitude more faces compared to AMs, leading to significant inefficiencies in storage, rendering, and simulation. Moreover, the converted meshes complicate post-processing and downstream tasks in the 3D pipeline. They significantly increase the challenge for human artists in optimizing these meshes due to their chaotic and inefficient topologies. Finally, previous methods struggle to represent sharp edges and flat surfaces, resulting in oversmoothing and bumpy artifacts as shown in Fig. 2.", + "bbox": [ + 169, + 680, + 823, + 834 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we aim to solve the aforementioned issues to facilitate the application of automatically generated 3D assets in the 3D industry. As mentioned earlier, all previous methods Lorensen & Cline (1987); Chernyaev (1995); Lorensen & Cline (1998); Shen et al. (2021b); Chen et al. (2022); Shen et al. (2023) extract 3D meshes with excessively dense faces in a reconstruction manner, which inherently cannot solve these issues. Therefore, we diverge from previous approaches by formulating mesh extraction as a generation problem for the first time: we teach models to generate Artist-", + "bbox": [ + 169, + 840, + 823, + 925 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2", + "bbox": [ + 493, + 948, + 504, + 959 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9fa5b06a364431abe5830c26121adaca68b8bb5f0c40aa46d34f732c3aea7e4c.jpg", + "image_caption": [ + "Figure 2: Comparison with Marching Cubes Lorensen & Cline (1987) and Remesh Blender Development Team (2024). We apply Marching Cubes and MeshAnything to ground truth shapes and then apply remeshing to the Marching Cubes results with different voxel sizes. Existing methods extract meshes in a reconstruction manner, ignoring the geometric features of the object and producing dense meshes with poor topology. These methods fundamentally fail to capture sharp edges and flat surfaces, as shown in the zoomed-in figure." + ], + "image_footnote": [], + "content": "Faces: 90k\nVertices: 45k\nMarching Cubes\nFaces: 33k\nVertices: 53k\nRemesh-0.01\nFaces: 3.5k\nVertices: 6.7k\nRemesh-0.03\nFaces: 1.1k\nVertices: 2.2k\nRemesh-0.05\nFaces: 0.28k\nVertices: 0.57k\nRemesh-0.10\nFaces: 0.64k\nVertices: 0.31k\nMeshAnything\nFaces: 200k\nVertices: 100k\nMarching Cubes\nFaces: 84k\nVertices: 132k\nRemesh-0.01\nFaces: 7.4k\nVertices: 13k\nRemesh-0.03\nFaces: 2k\nVertices: 3.9k\nRemesh-0.05\nFaces: 0.46k\nVertices: 0.92k\nRemesh-0.10\nFaces: 0.80k\nVertices: 0.47k\nMeshAnything", + "sub_type": "text_image", + "bbox": [ + 176, + 99, + 823, + 429 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Created Meshes (AMs) that are aligned with the given 3D assets. The meshes generated by our methods mimic the shape and topology quality of those created by human artists. Consequently, our setting, namely Shape-Conditioned AM Generation, is fundamentally free from all previous issues, enabling seamless integration of the generated results into the 3D industry pipeline.", + "bbox": [ + 169, + 554, + 823, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, training such a model presents significant challenges. The first challenge is constructing the dataset, as we need paired shape conditions and Artist-Created Meshes (AMs) for model training. The shape condition must be efficiently derived from as many diverse 3D representations as possible to serve as a condition during inference. Additionally, it must have sufficient precision to accurately represent 3D shapes and be efficiently processed into features that can be injected into the model. After weighing the trade-offs, we chose point clouds due to their explicit and continuous representation, ease of derivation from most 3D representations, and the availability of mature point cloud encoders Qi et al. (2017a;b); Zhao et al. (2024).", + "bbox": [ + 169, + 617, + 823, + 729 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We filter out high-quality AMs from Objaverse Deitke et al. (2023b;a) and ShapeNet Chang et al. (2015). When obtaining paired shape conditions, a naive approach would be to sample point clouds directly from AMs. However, this leads to poor results during inference because the sampled point clouds have excessive precision, while automatically produced 3D assets cannot provide point clouds of similar quality, causing a domain gap between training and inference. To address this issue, we intentionally corrupt the shape quality of AMs. We first extract the signed distance function from AMs Wang et al. (2022), convert it into a coarser mesh using Lorensen & Cline (1987), and then sample point clouds from this coarse mesh to narrow the domain gap in shape conditions between inference and training.", + "bbox": [ + 169, + 734, + 823, + 862 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Following Siddiqui et al. (2023), we use a VQ-VAE Van Den Oord et al. (2017) to learn a mesh vocabulary and train a decoder-only transformer Vaswani et al. (2017) on this vocabulary for mesh generation. To inject shape condition, we draw inspiration from the recent success of multimodal large language models (MLLM) Wu et al. (2023); Liu et al. (2024a), where image features encoded by pre-trained image encoders are projected into the token space of the large language models for efficient multimodal understanding. Similarly, we treat the mesh tokens obtained from the trained VQ-VAE as the language token in LLMs and use a pre-trained encoder Zhao et al. (2024) to encode the point clouds into shape features, which is later projected into the mesh token space. These shape tokens are placed at the beginning of the mesh token sequences, effectively serving as the shape conditions for next-token predictions. After predictions, these predicted mesh tokens are decoded back to meshes with the VQ-VAE decoder Siddiqui et al. (2023).", + "bbox": [ + 169, + 867, + 823, + 925 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3", + "bbox": [ + 493, + 948, + 503, + 959 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "", + "bbox": [ + 169, + 104, + 823, + 202 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To further enhance the quality of mesh generation, we develop a novel noise-resistant decoder for robust mesh decoding. Our observation is that as the decoder in the VQ-VAE Van Den Oord et al. (2017) is only trained with ground truth token sequences from the encoder, it could potentially lead to a domain gap when decoding the generated token sequences. To mitigate this problem, we inject the shape condition into the VQ-VAE decoder as auxiliary information for robust decoding and finetune it after the VQ-VAE training. This fine-tuning process involves adding noise to the mesh token sequences to simulate possible poor-quality token sequences from the decoder-only transformer, thus making the decoder robust to such poor-quality sequences.", + "bbox": [ + 169, + 208, + 826, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we introduce our model, MeshAnything, trained based on the aforementioned techniques. As shown in Fig. 1, MeshAnything can convert 3D assets across various 3D representations into AMs, thereby significantly facilitating their application. Furthermore, our extensive experiments demonstrate that our method generates AMs with significantly fewer faces and more refined topology, while achieving precision metrics that are close to or comparable with previous methods.", + "bbox": [ + 169, + 325, + 823, + 397 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In summary, our contributions are as follows:", + "bbox": [ + 171, + 402, + 472, + 417 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "• We highlight one important reason why current automatically produced 3D assets cannot replace those created by human artists: current methods cannot convert these 3D assets into Artist-Created Meshes (AMs). To solve this issue, we propose a novel solution called Shape-Conditioned AM Generation, which aims to generate AMs aligned with given shapes.", + "• We introduce MeshAnything for Shape-Conditioned AM Generation. MeshAnything can be integrated with various 3D asset production methods, converting their results into AMs to facilitate their application in the 3D industry.", + "• We develop a novel noise-resistant decoder to enhance mesh generation quality. We inject the shape condition into the decoder as auxiliary information for robust decoding and fine-tune it using noised token sequences to narrow the domain gap between training and inference.", + "• Extensive experiments demonstrate that Shape-Conditioned Mesh Generation is a more suitable setting for mesh generation, and MeshAnything significantly surpasses previous mesh generation methods." + ], + "bbox": [ + 215, + 431, + 823, + 664 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2 RELATED WORKS", + "text_level": 2, + "bbox": [ + 171, + 688, + 354, + 704 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.1 MESH EXTRACTION", + "text_level": 2, + "bbox": [ + 171, + 722, + 354, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Methods for extracting meshes from 3D models are numerous and have been a subject of research for decades. Following Shen et al. (2023), we categorize these methods into two main types: Isosurface Extraction Lorensen & Cline (1987); Bloomenthal (1988); Chernyaev (1995); Bloomenthal & Bajaj (1997); Lorensen & Cline (1998); Chen et al. (2022) and Gradient-Based Mesh Optimization Chen et al. (2019); Gao et al. (2020); Hanocka et al. (2020); Kato et al. (2018); Shen et al. (2021a); Liao et al. (2018); Shen et al. (2023).", + "bbox": [ + 169, + 750, + 823, + 834 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Traditional isosurface extraction methods Lorensen & Cline (1987; 1998); Chernyaev (1995); Doi & Koide (1991); Ju et al. (2002); Schaefer et al. (2007); Chen & Zhang (2021); Chen et al. (2022) focus on extracting a polygonal mesh that represents the level set of a scalar function, an area that has seen extensive study in various fields. The most popular method among them is Marching Cubes Lorensen & Cline (1987). It divides the space into cells, within which polygons are created to approximate the surface. Marching Cubes has been widely used for mesh extraction its robustness and simplicity. Recently, Chen & Zhang (2021) and Chen et al. (2022) introduce data-driven methods to determine the position of the extracted mesh based on the input field.", + "bbox": [ + 169, + 839, + 826, + 925 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4", + "bbox": [ + 493, + 948, + 504, + 959 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "", + "bbox": [ + 169, + 103, + 823, + 133 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Transitioning to more recent developments, the advent of machine learning has ushered in new techniques for generating 3D meshes Chen et al. (2019); Gao et al. (2020); Hanocka et al. (2020); Kato et al. (2018); Shen et al. (2021a); Liao et al. (2018); Shen et al. (2023). This line of work explores using neural networks to generate 3D meshes, where the network parameters are optimized through gradient-based methods under specific loss functions. Shen et al. (2021a) employs a differentiable Marching Tetrahedra layer for mesh extraction. Similar to Shen et al. (2021a), Shen et al. (2023) iteratively optimizes a 3D surface mesh by representing it as the isosurface of a scalar field.", + "bbox": [ + 169, + 138, + 826, + 238 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, these approaches fundamentally differ from ours. They ignore the characteristics of the shape and inherently cannot produce meshes with efficient topology. In contrast, MeshAnything formulates mesh extraction as a generation problem for the first time, aiming to mimic human artists in mesh extraction and thereby generating Artist-Created Meshes (AMs) with hundreds of times fewer faces.", + "bbox": [ + 169, + 243, + 826, + 313 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "2.2 3D MESH GENERATIONS", + "text_level": 2, + "bbox": [ + 171, + 334, + 390, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3D mesh generation can be mainly divided into two categories: generating dense meshes similar to those produced by previous mesh extraction methods, and generating Artist-Created Meshes (AMs).", + "bbox": [ + 169, + 363, + 823, + 392 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The former category is currently the mainstream research focus. Methods such as Gao et al. (2022); Wei et al. (2024); Xu et al. (2024) directly generate meshes in a feed-forward manner, but because they produce dense meshes with low-quality topology similar to previous mesh extraction methods, they still encounter the same issues when applied in the 3D industry.", + "bbox": [ + 169, + 398, + 823, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Notably, numerous 3D generation methods Poole et al. (2023); Tang et al. (2023b); Wang et al. (2023); Chen et al. (2024b); Tang et al. (2023a); Yang et al. (2023); Hong et al. (2023); Fang et al. (2023); Chen et al. (2023a); Liu et al. (2024b); Shi et al. (2023); Li et al. (2023); Chen et al. (2023b; 2024c); Tang et al. (2024); Wang et al. (2024); Tochilkin et al. (2024) can also produce meshes. These methods first generate 3D assets and then convert them to dense meshes using mesh extraction methods like Lorensen & Cline (1987). Consequently, they face challenges when applied to the 3D industry due to their inefficient topology.", + "bbox": [ + 169, + 460, + 825, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Recently, several works have focused on the second category: generating Artist-Created Meshes(AMs) Nash et al. (2020); Alliegro et al. (2023); Siddiqui et al. (2023); Chen et al. (2024a). Although our approach also focuses on AM generation, it fundamentally differs from these methods. Since they lack shape conditioning, these methods must simultaneously learn the complex 3D shape distribution—which typically alone requires extensive training Hong et al. (2023); Tang et al. (2024)—and the topology distribution of AMs, leading to very challenging training processes. In contrast, our methods eliminate the challenge of learning the shape distribution, allowing the model to focus on learning the topology distribution. This not only significantly reduces training costs but also enhances the model’s application value.", + "bbox": [ + 169, + 565, + 826, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Among these methods, the most relevant to ours is MeshGPT Siddiqui et al. (2023), as we follow its architecture. Siddiqui et al. (2023) introduced a combination of a VQ-VAE Van Den Oord et al. (2017) and an autoregressive transformer architecture. It first learns a mesh vocabulary with the VQ-VAE and then trains the transformer on the learned vocabulary for mesh generation. However, MeshGPT’s results are limited to several categories in ShapeNet. MeshGPT requires a training GPU hours similar to ours, but our method can generalize to unlimited categories in Objaverse. As shown in Fig. 3, this is largely due to the difference in target complexity caused by MeshGPT needing to additionally learn the complex 3D shape distribution.", + "bbox": [ + 169, + 696, + 825, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3 SHAPE-CONDITIONED AM GENERATION", + "text_level": 2, + "bbox": [ + 171, + 833, + 547, + 849 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first introduce the formal formulation for Shape-Conditioned AM Generation and compare it with previous mesh generation settings Nash et al. (2020); Siddiqui et al. (2023); Alliegro et al. (2023). We show that it can achieve better performance and a broader range of applications compared to the settings in previous mesh generation methods, with significantly less training effort.", + "bbox": [ + 169, + 867, + 823, + 925 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5", + "bbox": [ + 493, + 948, + 504, + 959 + ], + "page_idx": 4 + }, + { + "type": "chart", + "img_path": "images/aecc35c40ee63cf700f8e266846c83e8dfb32ed3aab02b0e0271258e64dac101.jpg", + "content": "| Training iterations | Shape-Conditioned | Image-Conditioned | Unconditional |\n| --- | --- | --- | --- |\n| 60k | ~2.0 | — | — |\n| 80k | ~1.67 | ~1.98 | ~1.99 |\n| 100k | ~1.56 | ~1.83 | ~1.86 |\n| 120k | ~1.49 | ~1.74 | ~1.78 |\n| 140k | ~1.46 | ~1.71 | ~1.75 |\n| 160k | ~1.44 | ~1.70 | ~1.75 |\n| 180k | ~1.43 | ~1.70 | ~1.75 |\n| 200k | ~1.43 | ~1.69 | ~1.72 |\n| 220k | ~1.42 | ~1.69 | ~1.73 |", + "chart_caption": [ + "(a) Training Perplexity (PPL)" + ], + "chart_footnote": [], + "sub_type": "line", + "bbox": [ + 184, + 111, + 442, + 268 + ], + "page_idx": 5 + }, + { + "type": "chart", + "img_path": "images/82c80d138141f010fa79e32343b04995c61f9dcd45f48b620653763fb4af129e.jpg", + "content": "| Training iterations | Shape-Conditioned (Validation PPL) | Image-Conditioned (Validation PPL) | Unconditional (Validation PPL) |\n| --- | --- | --- | --- |\n| 60k | ~2.0 | ~2.0 | ~2.0 |\n| 80k | ~1.52 | ~1.75 | ~1.8 |\n| 100k | ~1.44 | ~1.67 | ~1.72 |\n| 120k | ~1.41 | ~1.63 | ~1.68 |\n| 140k | ~1.39 | ~1.6 | ~1.65 |\n| 160k | ~1.37 | ~1.59 | ~1.63 |\n| 180k | ~1.36 | ~1.58 | ~1.61 |\n| 200k | ~1.35 | ~1.57 | ~1.6 |\n| 220k | ~1.34 | ~1.56 | ~1.59 |", + "chart_caption": [ + "(b) Validation Perplexity (PPL)", + "Figure 3: Training and validation perplexity (PPL) for the mesh generation model under different input conditions. All models are trained with the same settings as detailed in Section 5.2. The training and validation PPL of shape-conditioned mesh generation is significantly lower than that of unconditional and image-conditioned mesh generation. This indicates that the training burden of shape-conditioned mesh generation is much lower since it avoids learning the complex 3D shape distribution." + ], + "chart_footnote": [], + "sub_type": "line", + "bbox": [ + 540, + 112, + 797, + 268 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Shape-Conditioned AM Generation targets to estimate a conditional distribution $p ( \\mathcal { M } | S )$ . In this formula, M refers to the Artist-Created Mesh (AM), i.e., the mesh manually modeled by human artists. S refers to the 3D shape information that indicates the 3D shape to which M should align. The input form of S can be diverse, such as voxels or point clouds. Therefore, this versatility allows our method to be integrated with any 3D pipeline that outputs S, such as 3D reconstruction Mildenhall et al. (2020); Kerbl et al. (2023b), generation Poole et al. (2023); Hong et al. (2023), and scanning, making these methods more efficient for the 3D industry.", + "bbox": [ + 169, + 419, + 823, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared to existing AM generation work, they directly estimate the distribution $p ( \\mathcal { M } | \\mathcal { C } )$ , where C denotes conditions such as images, text or empty sets for unconditional generation. However, estimating $p ( \\mathcal { M } | \\mathcal { C } )$ requires an understanding of both the underlying shape, i.e., S, and complex topological structures M. Given this, we made the following approximation:", + "bbox": [ + 169, + 523, + 823, + 580 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "$$\np (\\mathcal {M} | \\mathcal {C}) \\approx p (\\mathcal {M}, \\mathcal {S} | \\mathcal {C}). \\tag {1}\n$$", + "text_format": "latex", + "bbox": [ + 416, + 602, + 823, + 618 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "According to the chain rule, we have:", + "bbox": [ + 171, + 622, + 419, + 636 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "$$\np (\\mathcal {M}, \\mathcal {S} | \\mathcal {C}) = p (\\mathcal {M} | \\mathcal {S}, \\mathcal {C}) \\cdot p (\\mathcal {S} | \\mathcal {C}). \\tag {2}\n$$", + "text_format": "latex", + "bbox": [ + 379, + 643, + 823, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For distribution $p ( \\mathcal { M } | \\mathcal { S } , \\mathcal { C } )$ , given that S is a much stronger and more direct condition than C, we can make the following approximation:", + "bbox": [ + 169, + 667, + 823, + 698 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "$$\np (\\mathcal {M} | \\mathcal {S}, \\mathcal {C}) \\approx p (\\mathcal {M} | \\mathcal {S}). \\tag {3}\n$$", + "text_format": "latex", + "bbox": [ + 416, + 705, + 823, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Combining 1, 2 and 3:", + "bbox": [ + 171, + 728, + 321, + 743 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "$$\np (\\mathcal {M} | \\mathcal {C}) \\approx p (\\mathcal {M} | \\mathcal {S}) \\cdot p (\\mathcal {S} | \\mathcal {C}), \\tag {4}\n$$", + "text_format": "latex", + "bbox": [ + 397, + 742, + 823, + 760 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "in which $p ( \\mathcal { M } | S )$ is the focus of our shape-conditioned mesh generation. As shown in Fig. 3, estimating $p ( \\mathcal { M } | S )$ is much more simpler than $p ( \\mathcal { M } | \\mathcal { C } )$ , proving that our setting is much easier to train than settings in privous methods.", + "bbox": [ + 169, + 763, + 823, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As for p(S|C), In the 3D community, numerous large models Team (2024); Tang et al. (2024); Xu et al. (2024); Siddiqui et al. (2023) aim to estimate using various 3D representations and demonstrate excellent results. Besides, some single scene 3D asset production methods Mildenhall et al. (2020); Kerbl et al. (2023b); Barron et al. (2021; 2022); Poole et al. (2023); Liu et al. (2023b); Sun et al. (2023) can also provide samples from this distribution. By integrating our framework with these existing methods, we can leverage their capabilities to enhance our mesh generation process. This integration allows for a more resource-efficient way to estimate $p ( \\mathcal { M } | \\mathcal { C } )$ , significantly reducing the complexity and resources required compared to previous methods.", + "bbox": [ + 169, + 811, + 825, + 925 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6", + "bbox": [ + 493, + 948, + 503, + 959 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ed7acb9369bfcc2c48faff57b105d6db318c21dfbb1b16f91c12ef6419bebbfe.jpg", + "image_caption": [ + "Figure 4: Pipeline Overview. We introduce MeshAnything, an autoregressive transformer capable of generating Artist-Created Meshes that adhere to given 3D shapes. During training, we inject point clouds features into a decoder-only transformer and supervise it using token sequences derived from the Artist-Created meshes. After training, MeshAnything takes point clouds sampled from various 3D representations as input and generates aligned Artist-Created meshes." + ], + "image_footnote": [], + "content": "```mermaid\ngraph LR\n A[\"Training\"] --> B[\"VQ Encoder\"]\n B --> C[\"Artist-Created Mesh\"]\n C --> D[\"Sample from surface\"]\n D --> E[\"Inference\"]\n E --> F[\"NeRF 3D GS\"]\n F --> G[\"Sample\"]\n G --> H[\"Point Cloud\"]\n H --> I[\"Feature\"]\n I --> J[\"Mesh Autoregressive Transformer\"]\n J --> K[\"...\"]\n K -.-> L[\"Cross-Entropy Loss\"]\n L --> M[\"Cross-Entropy Loss\"]\n M --> N[\"Cross-Entropy Loss\"]\n N --> O[\"Cross-Entropy Loss\"]\n O --> P[\"VQ Decoder\"]\n P --> Q[\"Generated Mesh\"]\n```", + "sub_type": "flowchart", + "bbox": [ + 181, + 102, + 816, + 199 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4 METHOD", + "text_level": 2, + "bbox": [ + 171, + 311, + 282, + 327 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we detail our shape condition strategy in Section 4.1. After that, we provide a detailed description for MeshAnything, which consists of a VQVAE with our newly proposed noise-resistant decoder (Section 4.2) and a shape-conditioned autoregressive transformer (Section 4.3).", + "bbox": [ + 169, + 345, + 823, + 388 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1 SHAPE ENCODING FOR CONDITIONAL GENERATION", + "text_level": 2, + "bbox": [ + 171, + 407, + 576, + 420 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We begin by describing our shape condition strategy. MeshAnything targets learning p(M|S), so we need to pair each mesh M with a corresponding S, i.e., the shape condition. Choosing an appropriate 3D representation for S is non-trivial and should satisfy the following conditions:", + "bbox": [ + 169, + 434, + 823, + 477 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. It should be easily extracted from various 3D representations. This ensures that the trained models can be integrated with a wide range of 3D asset production pipelines Mildenhall et al. (2020); Kerbl et al. (2023b); Hong et al. (2023); Poole et al. (2023); Tang et al. (2024).", + "2. It should be suitable for data augmentation to prevent overfitting. To ensure the effectiveness of S during training, any data augmentation applied to M must be equivalently applicable to S.", + "3. It should be efficiently and conveniently input into the model as a condition. To ensure the model comprehends the shape information and to maintain efficient training, S must be easily and effectively encoded into features." + ], + "bbox": [ + 207, + 489, + 825, + 631 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Considering the first and second points, S should be in an explicit representation. Further considering the third point, the main explicit 3D representations that can be easily encoded as features are voxels and point clouds. Both representations are suitable, but voxels typically require a high resolution to accurately represent shapes, and processing high-resolution voxels into features is computationally expensive. Additionally, voxels, being a discrete representation, are less precise for data augmentation compared to point clouds. Therefore, we chose point clouds as the representation for S. To enhance the expressive power of the point clouds, we also include normals into the point cloud representation.", + "bbox": [ + 169, + 645, + 823, + 756 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To obtain point clouds from the ground truth mesh for training, we could simply sample point clouds directly from the surface of M. However, this would create problems during inference: the surfaces of automatically generated 3D assets are often rougher than those of AMs. For example, in AMs, we would sample a series of points on a flat plane, whereas automatically generated 3D assets would have uneven surfaces, causing a domain gap between training and inference.", + "bbox": [ + 169, + 763, + 823, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Therefore, we need to ensure that S extracted from the ground truth M during training has a similar domain to the S extracted during inference. To bring their domains closer, we intentionally construct coarse meshes from AMs. We first extract the signed distance function from M with Wang et al. (2022), then convert it into a relatively coarse mesh using Marching Cubes Lorensen & Cline (1987) to destroy the ground truth topology. Finally, we sample point cloud and its normals from the coarse mesh. This approach also helps to avoid overfitting, as AMs typically have fewer faces, and each face can often sample multiple points. The network can easily recognize the ground truth topology by determining whether the points lie on the same plane.", + "bbox": [ + 169, + 840, + 825, + 925 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "", + "bbox": [ + 493, + 948, + 503, + 959 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 169, + 104, + 823, + 133 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Since almost all 3D representations can be converted into a coarse mesh using Marching Cubes Lorensen & Cline (1987) or sampled into point clouds, this ensures that the domain of S is consistent during both training and inference. We pair the point clouds extracted as S with M to create a data item $\\big \\{ ( { \\mathcal { M } } _ { i } , { \\mathcal { S } } _ { i } ) \\big \\} $ i for training.", + "bbox": [ + 169, + 138, + 823, + 196 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2 VQ-VAE WITH NOISE-RESISTANT DECODER", + "text_level": 2, + "bbox": [ + 171, + 210, + 529, + 226 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Following MeshGPT Siddiqui et al. (2023), we first train a VQ-VAE Van Den Oord et al. (2017) to learn a vocabulary of geometric embeddings for better transformer Vaswani et al. (2017) learning. Different to MeshGPT, which uses graph convolutional networks Wu et al. (2019) and ResNet He et al. (2016) as the encoder and decoder respectively, we employ transformers with identical structures for both the encoder and decoder. When training VQ-VAE, meshes are discretized and input as a sequence of triangle faces:", + "bbox": [ + 169, + 237, + 823, + 321 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {M} := (f _ {1}, f _ {2}, f _ {3}, \\dots , f _ {N}), \\tag {5}\n$$", + "text_format": "latex", + "bbox": [ + 405, + 324, + 823, + 340 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $f _ { i }$ is the coordinates of the vertices of each face, and N is the number of faces in M. The encoder E then extracts a feature vector for each face:", + "bbox": [ + 169, + 342, + 823, + 371 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {Z} = (z _ {1}, z _ {2}, \\dots , z _ {N}) = E (\\mathcal {M}), \\tag {6}\n$$", + "text_format": "latex", + "bbox": [ + 388, + 375, + 823, + 391 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $z _ { i }$ is the feature vector for $f _ { i }$ .", + "bbox": [ + 171, + 393, + 410, + 409 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The extracted faces are then quantized into quantized features T with codebook B:", + "bbox": [ + 171, + 415, + 718, + 430 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {T} = R Q (\\mathcal {Z}; \\mathcal {B}) \\tag {7}\n$$", + "text_format": "latex", + "bbox": [ + 442, + 433, + 823, + 449 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, the reconstructed mesh is decoded from $\\tau$ with decoder D by predicting the logits for each vertex’s coordinates:", + "bbox": [ + 169, + 459, + 823, + 486 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "$$\n\\hat {\\mathcal {M}} = D (\\mathcal {Z}) \\tag {8}\n$$", + "text_format": "latex", + "bbox": [ + 454, + 486, + 823, + 502 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The VQ-VAE is trained end-to-end with cross-entropy loss on the predicted vertex coordinate logits and the commitment loss of vector quantization Van Den Oord et al. (2017). After the training of VQ-VAE, the encoder-decoder of VQ-VAE is treated as a tokenizer and detokenizer for autoregressive transformer training.", + "bbox": [ + 169, + 503, + 825, + 559 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "However, as shown in Fig. 7, there are possible imperfections in the generation results. To address this issue, given our setting of Shape-Conditioned AM Generation, the VQ-VAE decoder can also take the shape condition as input. Small imperfections in the token sequences generated by the transformer can potentially be corrected by a shape-aware decoder. Therefore, after completing the vanilla VQ-VAE training, we add an additional decoder fine-tuning stage, where we inject the shape information into the transformer decoder. Then we add random Gumbel noise to the codebook sampling logits to simulate the potential imperfections in the token sequences generated by the transformer during inference. The decoder is then updated independently with the same crossentropy loss to train it to produce refined meshes even when facing imperfect token sequences. Our experiments in Tab. 3 and Tab. 4 show that our method effectively enhances the decoder’s noise resistance and mesh generation quality.", + "bbox": [ + 169, + 566, + 825, + 719 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3 SHAPE-CONDITIONED AUTOREGRESSIVE TRANSFORMER", + "text_level": 2, + "bbox": [ + 171, + 734, + 612, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To add shape condition to the transformer, inspired by the success of multimodal large language models Wu et al. (2023); Liu et al. (2024a); Xu et al. (2023); Guo et al. (2023), we first encode the point cloud into a fixed-length token sequence with a point cloud encoder P and then concatenate it to the front of the embedding sequence from T VQ-VAE as the final input embedding sequence for the transformer:", + "bbox": [ + 169, + 761, + 823, + 829 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "$$\n\\mathcal {T} ^ {\\prime} = \\operatorname{concat} (\\mathcal {P} (\\mathcal {S}), \\mathcal {T}) \\tag {9}\n$$", + "text_format": "latex", + "bbox": [ + 419, + 830, + 823, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $\\tau ^ { \\prime }$ is the training input for the transformer.", + "bbox": [ + 171, + 845, + 500, + 861 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We borrow a pretrained point encoder from Zhao et al. (2024) and add a linear projection layer to project its output feature to the same latent space as $\\tau$ . During training, the original point encoder from Zhao et al. (2024) is frozen; we only update the newly added projection layer and the autoregressive transformer with cross-entropy loss.", + "bbox": [ + 169, + 868, + 825, + 925 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8", + "bbox": [ + 493, + 948, + 504, + 959 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a587e59902d48906bf018b70b34312d4b3280f44f16e87918959ca0a92f84164.jpg", + "table_caption": [ + "Table 1: Comparison of Mesh Generation Methods. As shown in the left table, compared to the baseline Artist-Created Mesh Generation method, the meshes generated by MeshAnything are better aligned with human preferences. In the right table, we compare MeshAnything with mesh extraction baselines, and it received the most votes. For detailed settings, please refer to Section 5.4." + ], + "table_footnote": [], + "table_body": "
MethodShape↑Topology↑
PolyGen12.7%11.1%
MeshGPT24.1%28.2%
MeshAnything63.2%60.7%
", + "bbox": [ + 179, + 167, + 460, + 241 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/0b2e63f9cc4b9269adf4e17a0403f2cecc8664a098b27bd19b69d8792431ebb8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodShape↑Topology↑
MarchingCubes38.1%10.2%
Shape As Points17.3%6.2%
MeshAnything44.6%83.6%
", + "bbox": [ + 526, + 167, + 818, + 241 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "During inference, we input ${ \\mathcal { P } } ( S )$ to the transformer and require it to generate the subsequent sequence, Tˆ . $\\hat { \\tau }$ is then input to the noise-resistant decoder to reconstruct meshes:", + "bbox": [ + 169, + 266, + 823, + 297 + ], + "page_idx": 8 + }, + { + "type": "equation", + "text": "$$\n\\hat {\\mathcal {M}} = D (\\hat {\\mathcal {T}}) \\tag {10}\n$$", + "text_format": "latex", + "bbox": [ + 454, + 305, + 823, + 324 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "where $\\hat { \\mathcal { M } }$ is the final generated AM.", + "bbox": [ + 171, + 332, + 413, + 348 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We use the standard next-token prediction loss to train shape-conditioned transformers. For each sequence, we add a token after the point cloud tokens and a token after the mesh tokens to identify the end of a 3D mesh.", + "bbox": [ + 169, + 354, + 823, + 397 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5 EXPERIMENTS", + "text_level": 2, + "bbox": [ + 171, + 417, + 326, + 431 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5.1 DATA PREPARATION", + "text_level": 2, + "bbox": [ + 171, + 449, + 356, + 462 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Data Selection. Existing AM generation works are limited to a few categories. However, our method targets to operate on general shapes. MeshAnything is trained on a combined dataset of Objaverse Deitke et al. (2023b) and ShapeNet Chang et al. (2015), selected for their complementary characteristics. We chose Objaverse because it contains a large number of AMs without category limitations. On the other hand, ShapeNet offers higher data quality within limited categories.", + "bbox": [ + 169, + 474, + 823, + 546 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We filter out meshes with more than 800 faces from both datasets. Additionally, we manually filtered out low quality meshes. Our final filtered dataset consists of 51k meshes from Objaverse and 5k meshes from ShapeNet. We randomly select 10% of this dataset as the evaluation dataset, with the remaining 90% used as the training set for all our experiments.", + "bbox": [ + 169, + 551, + 823, + 609 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Data Processing and Augmentation. Following the strategies of PolyGen Nash et al. (2020) and MeshGPT Siddiqui et al. (2023), we order faces by their lowest vertex index, then by the next lowest, and so on. Vertices are sorted in ascending order based on their z-y-x coordinates, where z represents the vertical axis. Within each face, we permute the indices to ensure the lowest index comes first. During training, we apply on-the-fly scaling, shifting, and rotation augmentations, normalizing each mesh to a unit bounding box from −0.5 to 0.5.", + "bbox": [ + 169, + 614, + 823, + 699 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5.2 IMPLEMENTATION DETAILS", + "text_level": 2, + "bbox": [ + 171, + 715, + 406, + 729 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The encoder and decoder of VQ-VAE both use the encoder of BERT Devlin et al. (2018), while we choose OPT-350M Zhang et al. (2022) as our autoregressive transformer architecture. The residual vector quantization Zeghidour et al. (2021) depth is set to 3, with a codebook size of 8,192.", + "bbox": [ + 169, + 741, + 823, + 785 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Our point encoder is based on the pretrained point encoder from Zhao et al. (2024), which has been trained on Objaverse and thus can handle general shapes. This point encoder outputs a fixedlength token sequence of 257 tokens, with 256 tokens primarily containing shape information and an additional head token containing semantic information about the shape. We sample 4096 points for each point cloud.", + "bbox": [ + 169, + 790, + 823, + 861 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The training batch size for both the VQ-VAE and the transformer is set to 8 per GPU. The VQ-VAE is trained on 8 A100 GPUs for 12 hours, after which we separately finetune the decoder part of the VQ-VAE into a noise-resistant decoder, as detailed in Section 4.2. Following this, the transformer is trained on 8 A100 GPUs for 4 days.", + "bbox": [ + 169, + 867, + 823, + 924 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "9", + "bbox": [ + 493, + 948, + 503, + 959 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/cbf54f8daa7c24b2a3d45e6d3135a4ff3686aa78f4c49f65629cd4b147f96acd.jpg", + "table_caption": [ + "Table 2: Quantitative Comparisons with Prior Arts on Objaverse. MeshAnything significantly outperforms prior methods across all metrics. MMD, KID are scaled by 103." + ], + "table_footnote": [], + "table_body": "
MethodCOV↑MMD↓1-NNA↓FID↓KID↓
PolyGen23.26.2288.248.827.7
MeshGPT41.73.8367.325.16.11
MeshAnything53.12.7255.714.51.89
", + "bbox": [ + 274, + 140, + 718, + 213 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "5.3 QUALITATIVE EXPERIMENTS", + "text_level": 2, + "bbox": [ + 171, + 237, + 415, + 253 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "As shown in Fig. 1, MeshAnything effectively generates AMs from various 3D representations. In our experiments, we use Rodin Team (2024) as the text-to-3D and image-to-3D method, and employ Mildenhall et al. (2020) and Kerbl et al. (2023a) as the 3D reconstruction pipeline to obtain the corresponding NeRF and Gaussian Splatting models. For additional qualitative results, please refer to A.2 combined with other 3D asset production pipelines.", + "bbox": [ + 169, + 263, + 823, + 335 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "5.4 QUANTITATIVE EXPERIMENTS", + "text_level": 2, + "bbox": [ + 171, + 349, + 426, + 364 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "From the generative model perspective, MeshAnything is a shape-conditioned mesh generation model. From the mesh extraction perspective, it extracts artist-created meshes from point clouds. Consequently, we compare MeshAnything with both types of methods. Additional experiments can be found in Appendix Section A.2.", + "bbox": [ + 169, + 376, + 823, + 434 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "User Study. As shown in Tab. 1, we conducted two user studies, comparing with mesh generation baselines Nash et al. (2020); Siddiqui et al. (2023) and mesh extraction baselines Lorensen & Cline (1987); Peng et al. (2021), respectively. The mesh generation baselines are trained on ShapeNet, and to ensure a fair comparison, we retrained them on Objaverse using the same transformer model as MeshAnything. Since the mesh generation baselines are all unconditional mesh generation methods, whereas MeshAnything is a shape-conditioned mesh generation method, we sampled shapes randomly from the evaluation set of Objaverse as inputs for MeshAnything, while for the baseline methods, we performed random sampling directly.", + "bbox": [ + 169, + 439, + 823, + 551 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "In the mesh extraction baseline, since our method can also be viewed as a point cloud to mesh approach, we included Peng et al. (2021), a point cloud to mesh method, as a baseline. Additionally, we optimized the results from the mesh extraction baseline using the Blender remesh method Blender Development Team (2024) to simplify the topology.", + "bbox": [ + 169, + 556, + 823, + 614 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "We collected 30 results from each method and asked users to vote for the best one in terms of shape quality and topology quality. A total of 41 users participated, providing 1,230 valid comparisons. Both user studies demonstrated the superiority of our method. The only difference between the retrained MeshGPT and MeshAnything is whether they are shape-conditioned, further proving the advantages of the shape-conditioned mesh generation setting.", + "bbox": [ + 169, + 619, + 823, + 691 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Metrics. We follow the metric setting of Chen et al. (2022); Siddiqui et al. (2023). We detail this setting in Appendix Section. A.1.", + "bbox": [ + 169, + 696, + 823, + 726 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Comparison with Mesh Generation Pipelines. We use the same retrained models from the user study for comparison. As shown in Tab. 2, MeshAnything significantly outperforms prior methods Nash et al. (2020); Siddiqui et al. (2023), indicating that it’s superior in both the shape and topology quality. Since the only difference between the retrained MeshGPT and MeshAnything is the inclusion of shape conditioning, the superior performance of MeshAnything further demonstrates that Shape-Conditioned Mesh Generation is a more suitable setting for mesh generation.", + "bbox": [ + 169, + 732, + 823, + 816 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "6 CONCLUSION", + "text_level": 2, + "bbox": [ + 171, + 837, + 318, + 852 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "In this work, we propose a novel setting for improved mesh extraction and mesh generation, namely Shape-Conditioned Artist-Created Mesh (AM) Generation. Following this setting, we introduce MeshAnything, a model capable of generating AMs that adhere to given 3D assets. MeshAnything can convert 3D assets in any 3D representation into AMs and thus can be integrated with diverse 3D asset production methods to facilitate their application in the 3D industry. Furthermore, we introduce a noise-resistant decoder architecture to enhance the generation quality, enabling the model to handle low-quality token sequences produced by autoregressive transformers. Lastly, extensive experiments demonstrate the superior performance of our method, highlighting its potential to scale up for 3D industry application and its advantage over previous methods.", + "bbox": [ + 169, + 867, + 823, + 925 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10", + "bbox": [ + 490, + 946, + 508, + 959 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "", + "bbox": [ + 169, + 103, + 825, + 175 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "REFERENCES", + "text_level": 2, + "bbox": [ + 173, + 194, + 287, + 209 + ], + "page_idx": 10 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "Antonio Alliegro, Yawar Siddiqui, Tatiana Tommasi, and Matthias Nießner. 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Advances in Neural Information Processing Systems, 36, 2024." + ], + "bbox": [ + 169, + 217, + 826, + 924 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11", + "bbox": [ + 490, + 948, + 506, + 959 + ], + "page_idx": 10 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [], + "bbox": [ + 166, + 99, + 834, + 928 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "12", + "bbox": [ + 490, + 948, + 508, + 959 + ], + "page_idx": 11 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [], + "bbox": [ + 168, + 99, + 828, + 926 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "13", + "bbox": [ + 490, + 948, + 508, + 959 + ], + "page_idx": 12 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [], + "bbox": [ + 168, + 99, + 828, + 925 + ], + "page_idx": 13 + }, + { + "type": "page_number", + "text": "14", + "bbox": [ + 490, + 948, + 508, + 959 + ], + "page_idx": 13 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [], + "bbox": [ + 165, + 98, + 828, + 497 + ], + "page_idx": 14 + }, + { + "type": "page_number", + "text": "15", + "bbox": [ + 490, + 946, + 508, + 959 + ], + "page_idx": 14 + }, + { + "type": "image", + "img_path": "images/7ab65c46fed251beed13c7e66df489ff073504f84d285a2b7c7eda53b00ac28c.jpg", + "image_caption": [ + "A APPENDIX", + "Figure 5: Additional qualitative results of MeshAnything. As shown, MeshAnything can be integrated with various 3D production pipelines to achieve highly controllable mesh generation." + ], + "image_footnote": [], + "content": "Collection of 3D wireframe models and 3D mesh designs including point cloud, image, and dense mesh (no text or symbols)", + "sub_type": "natural_image", + "bbox": [ + 183, + 138, + 823, + 316 + ], + "page_idx": 15 + }, + { + "type": "image", + "img_path": "images/862aeab2050e05c2e08496535a396d53ce14ba0421ede1b90aa189a88547daac.jpg", + "image_caption": [ + "Figure 6: Qualitative Results. (a) further demonstrates our capability to achieve highly controllable mesh generation when combined with 3D asset production pipelines. Besides, we compare our reseults with ground truth in (b) and (c). In (b), MeshAnything generates meshes with better topology and fewer faces than the ground truth. In (c), we produce meshes with a completely different topology while achieving a similar shape, proving that our method does not simply overfit but understands how to construct meshes using efficient topology." + ], + "image_footnote": [], + "content": "Point Cloud Condition\nImage Condition\nImage Condition\n(a)\n312 faces\nOurs\n518 faces\nGT\n612 faces\nOurs\n529 faces\nGT\n(b)\n(c)", + "sub_type": "text_image", + "bbox": [ + 178, + 378, + 826, + 526 + ], + "page_idx": 15 + }, + { + "type": "image", + "img_path": "images/eb9f539a645e6b2e3c176b61b49ba88020584ef19f05df2c9ea2f6addf7bca86.jpg", + "image_caption": [ + "Figure 7: Ablation on Noise-Resistant Decoder. The decoder-only transformer may generate lowquality token sequences, and the decoder of VQ-VAE would typically produce flawed meshes based on these sequences. In contrast, our Noise-Resistant Decoder, aided by shape conditions, has the ability to resist these low-quality token sequences, producing higher-quality meshes." + ], + "image_footnote": [], + "content": "W.O. Noise-Resistant Decoder\nOurs\nW.O. Noise-Resistant Decoder\nOurs\nW.O. Noise-Resistant Decoder\nOurs", + "sub_type": "text_image", + "bbox": [ + 181, + 643, + 816, + 726 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "A.1 METRICS", + "text_level": 2, + "bbox": [ + 171, + 821, + 284, + 833 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "We follow the evaluation metric setting of Siddiqui et al. (2023) in mesh generation experiments and the setting of Chen et al. (2022) in mesh extraction experiments.", + "bbox": [ + 169, + 845, + 823, + 875 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "We quantitatively evaluate mesh quality by uniformly sampling 100K points from the faces of both the ground truth meshes and the predicted meshes, and then computing a set of metrics to assess various aspects of the reconstruction.", + "bbox": [ + 169, + 881, + 823, + 924 + ], + "page_idx": 15 + }, + { + "type": "page_number", + "text": "16", + "bbox": [ + 490, + 948, + 508, + 959 + ], + "page_idx": 15 + }, + { + "type": "table", + "img_path": "images/0f72e96f0ce4abc9816ff609fb6b53f38a109b826510443cc8109a04076fc291.jpg", + "table_caption": [ + "Table 3: Reconstruction Performance under Different Noise Levels with and without Noise-Resistant (NR) Decoder. Please refer to A.1 for metrics explanation." + ], + "table_footnote": [], + "table_body": "
Noise Level $\\mathbf{CD}(\\times 10^{-2})\\downarrow$ $\\mathbf{ECD}(\\times 10^{-2})\\downarrow$ $\\mathbf{NC}\\uparrow$
W/O NRW/ NRW/O NRW/ NRW/O NRW/ NR
0.00.0110.0070.0350.0230.9870.993
0.10.1870.0280.6130.1380.9730.991
0.51.1670.6392.5381.3290.9640.981
1.02.1311.7984.3172.3160.9520.969
", + "bbox": [ + 228, + 140, + 767, + 247 + ], + "page_idx": 16 + }, + { + "type": "table", + "img_path": "images/4c8edf4f1e0648c2ebb129bfe07d83d794970f16251239b451977c0b2d640628.jpg", + "table_caption": [ + "Table 4: Ablation on Noise-Resistant (NR) Decoder for the Quality of Mesh Generation." + ], + "table_footnote": [], + "table_body": "
Method $\\mathbf{CD}↓$ $(×10^{-2})$ $\\mathbf{ECD}↓$ $(×10^{-2})$ $\\mathbf{NC}↑$
W/O NR2.4236.4140.883
W/ NR2.2566.2450.902
", + "bbox": [ + 354, + 286, + 638, + 359 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "For mesh extraction, we report the following metrics: Chamfer Distance (CD) to evaluate the overall quality of a reconstructed mesh; Edge Chamfer Distance (ECD) to assess the preservation of sharp edges by sampling points near sharp edges and corners; and Normal Consistency (NC) to evaluate the quality of the surface normals. Additionally, we report the number of mesh vertices (#V) and the number of mesh faces (#F). We also provide the ratio of the estimated number of vertices to the ground truth number of vertices (#V R) and the same ratio for faces (#F R).", + "bbox": [ + 169, + 383, + 823, + 469 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "For mesh generation, Coverage (COV) captures the diversity of generated meshes and is sensitive to mode dropping, but it does not reflect the quality of the results. Minimum Matching Distance (MMD) measures the average distance between the reference set and their nearest neighbors in the generated set, though it lacks sensitivity to low-quality outputs. The 1-Nearest Neighbor Accuracy (1-NNA) assesses both quality and diversity between the generated and reference sets. To evaluate topology quality, we render the ground truth meshes and generated meshes with their wireframes visualized. We then employ Frechet Inception Distance (FID) and Kernel Inception Distance (KID) on rendered images. MMD, and KID scores are scaled by a factor of 103.", + "bbox": [ + 169, + 474, + 826, + 587 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "A.2 EXPERIMENTS", + "text_level": 2, + "bbox": [ + 171, + 604, + 318, + 618 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "Additional Qualitative Experiments We present more qualitative results of MeshAnything here. As shown in Fig. 5 and Fig. 6, MeshAnything effectively generates AMs from various 3D representations. When integrated with different 3D assets production pipelines, our method effectively achieves mesh generation with diverse conditions.", + "bbox": [ + 169, + 631, + 823, + 686 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "Next, Fig. 6 demonstrates that MeshAnything does not simply overfit but understands how to generate meshes with efficient topology that conform to the given shape. To prove this, we use manuallycreated meshes as ground truth and use their shapes as conditions to test whether our model can generate meshes with comparable topology. To effectively use the ground truth as conditions, we first convert them into dense meshes using Marching Cubes Lorensen & Cline (1987) to disrupt their face structure. Then, we sample point clouds with normals from the dense meshes to serve as shape conditions. The experimental results in Fig. 6 show that MeshAnything is capable of generating meshes comparable to or even surpassing those modeled by human artists, exhibiting diverse and strong 3D modeling capabilities.", + "bbox": [ + 169, + 694, + 826, + 820 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "Comparison with mesh extraction baselines. Our method is related to various mesh extraction methods Lorensen & Cline (1987); Chen & Zhang (2021); Chen et al. (2022); Shen et al. (2023); Peng et al. (2021) since we also convert other 3D representations into meshes. However, it is important to note that previous approaches are reconstruction-like methods that produce dense meshes, while our approach is generative, creating Artist-Created Meshes (AMs) that are significantly more complex to produce than dense meshes. Therefore, strictly speaking, our method cannot be considered the same as these reconstruction-based mesh extraction methods. The main purpose of this comparison is to use these mesh extraction methods as a reference for evaluating the quality of the meshes generated by MeshAnything in terms of shape. We compare MeshAnything with Lorensen & Cline (1987); Shen et al. (2023); Peng et al. (2021). Among these, MarchingCubes is the most popular mesh extraction method, FlexiCubes represents the state-of-the-art in mesh extraction, and Shape as Points is the leading method for extracting mesh from point cloud.", + "bbox": [ + 169, + 825, + 826, + 925 + ], + "page_idx": 16 + }, + { + "type": "page_number", + "text": "17", + "bbox": [ + 490, + 946, + 508, + 959 + ], + "page_idx": 16 + }, + { + "type": "table", + "img_path": "images/570664b3881998a3dd6868c6ee55bf8d42bd6333a7d525ab86e65793864941da.jpg", + "table_caption": [ + "Table 5: Quantitative evaluation with mesh extraction baselines. MC, FC, SAP refer to Marching Cubes Lorensen & Cline (1987), FlexiCubes Shen et al. (2023), and Shape As Points Peng et al. (2021), respectively. Please refer to A.1 for metrics explanation." + ], + "table_footnote": [], + "table_body": "
Method $\\mathbf{CD}\\downarrow$ $(\\times 10^{-2})$ $\\mathbf{ECD}\\downarrow$ $(\\times 10^{-2})$ $\\mathbf{NC}\\uparrow$ $\\#V\\downarrow$ $(\\times 10^{3})$ $\\#F\\downarrow$ $(\\times 10^{3})$ $\\mathbf{V\\_R}\\downarrow$ $\\mathbf{F\\_R}\\downarrow$
(a) Marching Cubes1.5326.7330.95473.22146.0440.2462.2
(b) MC+Remesh (0.005)2.1747.8130.912127.8167.9748.1534.6
(c) MC+Remesh (0.010)2.0837.5780.92939.0141.78225.4132.3
(d) MC+Remesh (0.030)2.9158.3290.8635.8484.41034.3814.05
(e) MC+Remesh (0.050)4.1798.1380.8142.2991.53813.644.920
(f) MC+Remesh (0.100)7.31210.7710.7480.6250.3593.7351.149
(g) FC1.1906.1210.96759.12121.1378.2391.1
(h) FC+Remesh (0.010)1.8616.9400.93337.9840.19205.5124.2
(i) SAP1.7717.1120.93979.12152.3481.2489.3
(j) SAP+Remesh (0.010)2.3677.8620.92539.1742.87239.1136.6
(k) MeshAnything2.2566.2450.9020.1720.3180.8880.871
", + "bbox": [ + 183, + 152, + 810, + 339 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "", + "bbox": [ + 169, + 375, + 823, + 445 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "We also combined these methods with the remesh technique to test whether they could significantly reduce the number of faces while maintaining shape quality. We used Blender Remesh in voxel mode Community (2018); Blender Development Team (2024), specifically using Blender version 4.1, as the remesh method. Since our evaluation dataset includes non-watertight meshes, we first extract the signed distance fields (SDF) of all ground truth meshes using Wang et al. (2022), which can handle non-watertight meshes. We then apply Marching Cubes with a resolution of 128 on these SDFs. Next, we apply Blender remesh Blender Development Team (2024) with different voxel sizes to the Marching Cubes results, as both the remesh method and our approach are capable of simplifying topology. Additionally, the Marching Cubes result is used as the shape condition input to MeshAnything to obtain our results. The settings of Shen et al. (2023) and Peng et al. (2021) follow their papers.", + "bbox": [ + 169, + 450, + 826, + 604 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "As shown in Tab. 5, we found that these methods require hundreds of times more faces to achieve results comparable to our method. Comparing (a), (g), (i) and (k), our method lags in Chamfer Distance (CD) and Normal Consistency (NC), mainly due to our method’s inherent failure cases as a generative model, which makes it less robust than these reconstruction-based mesh extraction methods. When comparing with remesh methods, we observe that they incur a high cost to achieve a face count similar to ours. Comparing (f) and (k), we find that even when remesh methods achieve a comparable face count, the number of vertices is still several times higher than ours, indicating that the topology efficiency of remesh methods is far inferior to ours, as they completely ignore the shape characteristics of the 3D assets. It’s important to note that the metrics in mesh etraction can only indicate the quality of shape alignment, which do not effectively reflect the topological advantages of our method. Additionally, we surprisingly find that our method can produce results with fewer faces than the ground truth, demonstrating that MeshAnything is not overfitting to the data but instead learns an efficient topology representation, occasionally surpassing the ground truth meshes.", + "bbox": [ + 169, + 611, + 826, + 805 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Ablations on Noise-Resistant Conditional Decoder. We perform ablation experiments to verify the effectiveness of the Noise-Resistant Decoder. We begin with a VQ-VAE trained without any noise or conditioning. We then perform ablation between two settings: one where the decoder remains unchanged and unaware of the shape condition, and another where the shape condition is injected into the transformer, as described in Section 4.2. Next, we randomly sample a noise from gumbel distribution and add it to codebook sampling logits during the vector quantization process to simulate the potential low-quality token sequences generated by the transformer. We control the noise level by scaling the added noise.", + "bbox": [ + 169, + 811, + 826, + 925 + ], + "page_idx": 17 + }, + { + "type": "page_number", + "text": "18", + "bbox": [ + 490, + 948, + 508, + 959 + ], + "page_idx": 17 + }, + { + "type": "table", + "img_path": "images/e9773db60cbbbf34982b211de9fb22c88377fbfb0429f74b9c5324bd472f3c08.jpg", + "table_caption": [ + "Table 6: Experiments on the Impact of Input Point Cloud Quality on Generated Results." + ], + "table_footnote": [], + "table_body": "
Method $\\mathbf{CD}↓$ $(×10^{-2})$ $\\mathbf{ECD}↓$ $(×10^{-2})$ $\\mathbf{NC}↑$ $#V↓$ $(×10^{3})$ $#F↓$ $(×10^{3})$ $V\\_R↓$ $F\\_R↓$
(a) Noise scale 0.0052.3516.4120.8970.1750.3210.8950.880
(b) Noise scale 0.0202.9806.9700.8810.1800.3300.9010.910
(c) Noise scale 0.0504.9108.5560.7550.1620.2840.8110.802
(d) Rodin2.5526.6220.8330.1850.3420.9190.923
(e) $MeshAnything$ 2.2566.2450.9020.1720.3180.8880.871
", + "bbox": [ + 196, + 125, + 799, + 229 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "After training both models for enough epochs, we test their performance to the same level of noise. As shown in Tab. 3, as the intensity of the added noise increases, the Noise-Resistant Decoder with shape condition clearly achieves better reconstruction results. This indicates that the shape condition helps the decoder identify and correct imperfections in the input token sequences.", + "bbox": [ + 169, + 242, + 823, + 301 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Next, we verify whether the Noise-Resistant Decoder indeed enhances the transformer’s performance during inference. The test method used dense meshes derived from corrupted GT meshes as the condition for generating new meshes. The generated meshes were then assessed for shape alignment with the conditional shape. As shown in Tab. 4, the model with Noise-Resistant Decoder achieved better results.", + "bbox": [ + 169, + 306, + 823, + 376 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Experiments on the Impact of Input Point Cloud Quality on Generated Results. MeshAnything takes point clouds as input, and its robustness to point cloud quality determines its versatility across various applications. We design two experiments to evaluate its tolerance to input point cloud quality: First, keeping the other evaluation settings unchanged, we apply Gaussian noise to the input point cloud coordinates and normals. Specifically, for each point, we randomly sample Gaussian noise from a standard distribution, scale it by a noise factor, and add it to the point’s coordinates. The same approach is applied to the normals, but normalization is applied after adding the noise. Second, we use Rodin’s generation result as the ground truth mesh, sample point clouds from this mesh as input, and evaluate the deviation between the generated result and the ground truth.", + "bbox": [ + 169, + 382, + 826, + 508 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "As shown in Tab. 6, MeshAnything did not experience a significant performance drop in (a) and (b), demonstrating resilience to noise in the point cloud, with a noticeable performance decrease only in (c). It is important to note that the input point cloud is normalized to the range [-1,1], and the noise scale in (c) is already quite large. The experiment in (d) further demonstrates that MeshAnything can tolerate generated point clouds and effectively integrate with 3D generation models.", + "bbox": [ + 169, + 513, + 825, + 585 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "A.3 LIMITATIONS", + "text_level": 2, + "bbox": [ + 171, + 601, + 312, + 614 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Our method cannot generate meshes that exceed the maximum face count limit, so it cannot convert large scenes and particularly complex objects into meshes. Additionally, due to its generative nature, our method is not as stable as reconstruction-based mesh extraction methods like Lorensen & Cline (1987); Shen et al. (2023).", + "bbox": [ + 169, + 627, + 823, + 684 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "A.4 SOCIAL IMPACT", + "text_level": 2, + "bbox": [ + 171, + 700, + 331, + 714 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Our method points to a promising approach for the automatically generation of Artist-Created Meshes, which has the potential to significantly reduce labor costs in the 3D industry, thereby facilitating advancements in industries such as gaming, film, and the metaverse. However, the reduced cost of obtaining 3D Artist-Created meshes could also lead to potential criminal activities.", + "bbox": [ + 169, + 726, + 825, + 784 + ], + "page_idx": 18 + }, + { + "type": "page_number", + "text": "19", + "bbox": [ + 490, + 946, + 508, + 959 + ], + "page_idx": 18 + } +] \ No newline at end of file diff --git a/papers/markdown/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers/hybrid_auto/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers_content_list_v2.json b/papers/markdown/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers/hybrid_auto/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers_content_list_v2.json new file mode 100644 index 0000000000000000000000000000000000000000..98064bdf72744edc7b6201fed1550e07d22447bb --- /dev/null +++ b/papers/markdown/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers/hybrid_auto/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers_content_list_v2.json @@ -0,0 +1,3738 @@ +[ + [ + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "MESHANYTHING: ARTIST-CREATED MESH GENERA-TION WITH AUTOREGRESSIVE TRANSFORMERS" + } + ], + "level": 1 + }, + "bbox": [ + 171, + 99, + 823, + 146 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Yiwen Chen1,2∗, Tong He2†, Di Huang2, Weicai Ye2, Sijin Chen3, Jiaxiang Tang4 Xin Chen5, Zhongang Cai6, Lei Yang6, Gang Yu7, Guosheng Lin1†, Chi Zhang8† 1S-Lab, Nanyang Technological University 2Shanghai AI Lab 3Fudan University 4Peking University 5University of Chinese Academy of Sciences 6SenseTime Research 7Stepfun 8Westlake University https://buaacyw.github.io/mesh-anything/" + } + ] + }, + "bbox": [ + 187, + 169, + 776, + 257 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/4c8a3616bc55f836a4dc48c40a287983e81006ea66f4e11701727c07112ba992.jpg" + }, + "content": "```mermaid\ngraph LR\n A[\"Text Condition: A commode\"] --> B[\"NeRF\"]\n B --> C[\"3D GS\"]\n C --> D[\"Image\"]\n D --> E[\"Dense Mesh\"]\n E --> F[\"Dense Mesh\"]\n F --> G[\"Dense Mesh\"]\n G --> H[\"Dense Mesh\"]\n H --> I[\"Point Cloud\"]\n J[\"Point Cloud\"] --> K[\"Dense Mesh\"]\n K --> L[\"Dense Mesh\"]\n L --> M[\"Point Cloud\"]\n```", + "image_caption": [ + { + "type": "text", + "content": "Figure 1: MeshAnything converts any 3D representation into Artist-Created Meshes (AMs), i.e., meshes created by human artists. It can be combined with various 3D asset production pipelines, such as 3D reconstruction and generation, to transform their results into AMs that can be seamlessly applied in the 3D industry." + } + ], + "image_footnote": [] + }, + "sub_type": "flowchart", + "bbox": [ + 173, + 284, + 826, + 728 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "ABSTRACT" + } + ], + "level": 2 + }, + "bbox": [ + 450, + 815, + 547, + 830 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Recently, 3D assets created via reconstruction and generation have matched the quality of manually crafted assets, highlighting their potential for replacement. However, this potential is largely unrealized because these assets always need to be converted to meshes for 3D industry applications, and the meshes produced by current mesh extraction methods are significantly inferior to Artist-Created Meshes (AMs), i.e., meshes created by human artists. Specifically, current mesh extraction methods rely on dense faces and ignore geometric features, leading to inefficiencies, complicated post-processing, and lower representation quality. To address these issues, we introduce MeshAnything, a model that treats mesh extraction as a generation problem, producing AMs aligned with specified shapes. By converting 3D assets in any 3D representation into AMs, MeshAnything can be integrated with various 3D asset production methods, thereby enhancing their application across the 3D industry. The architecture of MeshAnything comprises a VQ-VAE and a shape-conditioned decoder-only transformer. We first learn a mesh vocabulary using the VQ-VAE, then train the shape-conditioned decoderonly transformer on this vocabulary for shape-conditioned autoregressive mesh generation. Our extensive experiments show that our method generates AMs with hundreds of times fewer faces, significantly improving storage, rendering, and simulation efficiencies, while achieving precision comparable to previous methods." + } + ] + }, + "bbox": [ + 228, + 845, + 767, + 890 + ] + }, + { + "type": "page_aside_text", + "content": { + "page_aside_text_content": [ + { + "type": "text", + "content": "arXiv:2406.10163v2 [cs.CV] 9 Oct 2024" + } + ] + }, + "bbox": [ + 22, + 270, + 58, + 700 + ] + }, + { + "type": "page_footnote", + "content": { + "page_footnote_content": [ + { + "type": "text", + "content": "∗Work done during a research internship at Shanghai AI Lab." + } + ] + }, + "bbox": [ + 189, + 896, + 555, + 910 + ] + }, + { + "type": "page_footnote", + "content": { + "page_footnote_content": [ + { + "type": "text", + "content": "†Corresponding Authors." + } + ] + }, + "bbox": [ + 192, + 910, + 344, + 924 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "1" + } + ] + }, + "bbox": [ + 493, + 948, + 503, + 959 + ] + } + ], + [ + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 228, + 103, + 767, + 339 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "1 INTRODUCTION" + } + ], + "level": 2 + }, + "bbox": [ + 173, + 369, + 336, + 383 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In recent years, the 3D community has experienced rapid advancements, with a variety of methods developed for automatically producing high-quality 3D assets. These methods, including 3D reconstruction Mildenhall et al. (2020); Yu et al. (2021); Barron et al. (2021; 2022); Kerbl et al. (2023b); Huang et al. (2024), 3D generation Poole et al. (2023); Liu et al. (2023a); Wang et al. (2023); Long et al. (2023); Sun et al. (2023); Hong et al. (2023); Tang et al. (2024); Xu et al. (2024); Wei et al. (2024), and scanning Daneshmand et al. (2018); Haleem & Javaid (2019); Haleem et al. (2022), can produce 3D assets with shape and color quality comparable to manually created ones. The success of these methods reveals the potential to replace manually created 3D models with automatically produced ones in the 3D industry, including applications in games, movies, and the metaverse, significantly reducing time and labor costs." + } + ] + }, + "bbox": [ + 169, + 402, + 826, + 542 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "However, this potential remains largely unrealized because the current 3D industry predominantly relies on mesh-based pipelines for their superior efficiency and controllability, while methods for producing 3D assets typically use alternative 3D representations to achieve optimal results across various scenarios. Therefore, substantial efforts Lorensen & Cline (1987); Chernyaev (1995); Lorensen & Cline (1998); Shen et al. (2021b); Chen et al. (2022); Shen et al. (2023) are devoted to converting other 3D representations into meshes and have achieved some success. Meshes produced by these methods approximate the shape quality of those created by human artists, which we refer to as Artist-Created Meshes (AMs), but they still fall short in addressing the aforementioned issues." + } + ] + }, + "bbox": [ + 169, + 547, + 823, + 672 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "This is because all meshes produced by these methods Lorensen & Cline (1987); Chernyaev (1995); Lorensen & Cline (1998); Shen et al. (2021b); Chen et al. (2022); Shen et al. (2023) exhibit significantly poorer topology quality compared to AMs. As shown in Fig. 2, these methods rely on dense faces to reconstruct 3D shapes, completely ignoring geometric characteristics. Using these meshes in the 3D industry leads to three significant problems: First, converted meshes typically contain several orders of magnitude more faces compared to AMs, leading to significant inefficiencies in storage, rendering, and simulation. Moreover, the converted meshes complicate post-processing and downstream tasks in the 3D pipeline. They significantly increase the challenge for human artists in optimizing these meshes due to their chaotic and inefficient topologies. Finally, previous methods struggle to represent sharp edges and flat surfaces, resulting in oversmoothing and bumpy artifacts as shown in Fig. 2." + } + ] + }, + "bbox": [ + 169, + 680, + 823, + 834 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In this work, we aim to solve the aforementioned issues to facilitate the application of automatically generated 3D assets in the 3D industry. As mentioned earlier, all previous methods Lorensen & Cline (1987); Chernyaev (1995); Lorensen & Cline (1998); Shen et al. (2021b); Chen et al. (2022); Shen et al. (2023) extract 3D meshes with excessively dense faces in a reconstruction manner, which inherently cannot solve these issues. Therefore, we diverge from previous approaches by formulating mesh extraction as a generation problem for the first time: we teach models to generate Artist-" + } + ] + }, + "bbox": [ + 169, + 840, + 823, + 925 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "2" + } + ] + }, + "bbox": [ + 493, + 948, + 504, + 959 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/9fa5b06a364431abe5830c26121adaca68b8bb5f0c40aa46d34f732c3aea7e4c.jpg" + }, + "content": "Faces: 90k\nVertices: 45k\nMarching Cubes\nFaces: 33k\nVertices: 53k\nRemesh-0.01\nFaces: 3.5k\nVertices: 6.7k\nRemesh-0.03\nFaces: 1.1k\nVertices: 2.2k\nRemesh-0.05\nFaces: 0.28k\nVertices: 0.57k\nRemesh-0.10\nFaces: 0.64k\nVertices: 0.31k\nMeshAnything\nFaces: 200k\nVertices: 100k\nMarching Cubes\nFaces: 84k\nVertices: 132k\nRemesh-0.01\nFaces: 7.4k\nVertices: 13k\nRemesh-0.03\nFaces: 2k\nVertices: 3.9k\nRemesh-0.05\nFaces: 0.46k\nVertices: 0.92k\nRemesh-0.10\nFaces: 0.80k\nVertices: 0.47k\nMeshAnything", + "image_caption": [ + { + "type": "text", + "content": "Figure 2: Comparison with Marching Cubes Lorensen & Cline (1987) and Remesh Blender Development Team (2024). We apply Marching Cubes and MeshAnything to ground truth shapes and then apply remeshing to the Marching Cubes results with different voxel sizes. Existing methods extract meshes in a reconstruction manner, ignoring the geometric features of the object and producing dense meshes with poor topology. These methods fundamentally fail to capture sharp edges and flat surfaces, as shown in the zoomed-in figure." + } + ], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 176, + 99, + 823, + 429 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Created Meshes (AMs) that are aligned with the given 3D assets. The meshes generated by our methods mimic the shape and topology quality of those created by human artists. Consequently, our setting, namely Shape-Conditioned AM Generation, is fundamentally free from all previous issues, enabling seamless integration of the generated results into the 3D industry pipeline." + } + ] + }, + "bbox": [ + 169, + 554, + 823, + 612 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "However, training such a model presents significant challenges. The first challenge is constructing the dataset, as we need paired shape conditions and Artist-Created Meshes (AMs) for model training. The shape condition must be efficiently derived from as many diverse 3D representations as possible to serve as a condition during inference. Additionally, it must have sufficient precision to accurately represent 3D shapes and be efficiently processed into features that can be injected into the model. After weighing the trade-offs, we chose point clouds due to their explicit and continuous representation, ease of derivation from most 3D representations, and the availability of mature point cloud encoders Qi et al. (2017a;b); Zhao et al. (2024)." + } + ] + }, + "bbox": [ + 169, + 617, + 823, + 729 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We filter out high-quality AMs from Objaverse Deitke et al. (2023b;a) and ShapeNet Chang et al. (2015). When obtaining paired shape conditions, a naive approach would be to sample point clouds directly from AMs. However, this leads to poor results during inference because the sampled point clouds have excessive precision, while automatically produced 3D assets cannot provide point clouds of similar quality, causing a domain gap between training and inference. To address this issue, we intentionally corrupt the shape quality of AMs. We first extract the signed distance function from AMs Wang et al. (2022), convert it into a coarser mesh using Lorensen & Cline (1987), and then sample point clouds from this coarse mesh to narrow the domain gap in shape conditions between inference and training." + } + ] + }, + "bbox": [ + 169, + 734, + 823, + 862 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Following Siddiqui et al. (2023), we use a VQ-VAE Van Den Oord et al. (2017) to learn a mesh vocabulary and train a decoder-only transformer Vaswani et al. (2017) on this vocabulary for mesh generation. To inject shape condition, we draw inspiration from the recent success of multimodal large language models (MLLM) Wu et al. (2023); Liu et al. (2024a), where image features encoded by pre-trained image encoders are projected into the token space of the large language models for efficient multimodal understanding. Similarly, we treat the mesh tokens obtained from the trained VQ-VAE as the language token in LLMs and use a pre-trained encoder Zhao et al. (2024) to encode the point clouds into shape features, which is later projected into the mesh token space. These shape tokens are placed at the beginning of the mesh token sequences, effectively serving as the shape conditions for next-token predictions. After predictions, these predicted mesh tokens are decoded back to meshes with the VQ-VAE decoder Siddiqui et al. (2023)." + } + ] + }, + "bbox": [ + 169, + 867, + 823, + 925 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "3" + } + ] + }, + "bbox": [ + 493, + 948, + 503, + 959 + ] + } + ], + [ + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 169, + 104, + 823, + 202 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "To further enhance the quality of mesh generation, we develop a novel noise-resistant decoder for robust mesh decoding. Our observation is that as the decoder in the VQ-VAE Van Den Oord et al. (2017) is only trained with ground truth token sequences from the encoder, it could potentially lead to a domain gap when decoding the generated token sequences. To mitigate this problem, we inject the shape condition into the VQ-VAE decoder as auxiliary information for robust decoding and finetune it after the VQ-VAE training. This fine-tuning process involves adding noise to the mesh token sequences to simulate possible poor-quality token sequences from the decoder-only transformer, thus making the decoder robust to such poor-quality sequences." + } + ] + }, + "bbox": [ + 169, + 208, + 826, + 321 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Finally, we introduce our model, MeshAnything, trained based on the aforementioned techniques. As shown in Fig. 1, MeshAnything can convert 3D assets across various 3D representations into AMs, thereby significantly facilitating their application. Furthermore, our extensive experiments demonstrate that our method generates AMs with significantly fewer faces and more refined topology, while achieving precision metrics that are close to or comparable with previous methods." + } + ] + }, + "bbox": [ + 169, + 325, + 823, + 397 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In summary, our contributions are as follows:" + } + ] + }, + "bbox": [ + 171, + 402, + 472, + 417 + ] + }, + { + "type": "list", + "content": { + "list_type": "text_list", + "list_items": [ + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "• We highlight one important reason why current automatically produced 3D assets cannot replace those created by human artists: current methods cannot convert these 3D assets into Artist-Created Meshes (AMs). To solve this issue, we propose a novel solution called Shape-Conditioned AM Generation, which aims to generate AMs aligned with given shapes." + } + ] + }, + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "• We introduce MeshAnything for Shape-Conditioned AM Generation. MeshAnything can be integrated with various 3D asset production methods, converting their results into AMs to facilitate their application in the 3D industry." + } + ] + }, + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "• We develop a novel noise-resistant decoder to enhance mesh generation quality. We inject the shape condition into the decoder as auxiliary information for robust decoding and fine-tune it using noised token sequences to narrow the domain gap between training and inference." + } + ] + }, + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "• Extensive experiments demonstrate that Shape-Conditioned Mesh Generation is a more suitable setting for mesh generation, and MeshAnything significantly surpasses previous mesh generation methods." + } + ] + } + ] + }, + "bbox": [ + 215, + 431, + 823, + 664 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "2 RELATED WORKS" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 688, + 354, + 704 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "2.1 MESH EXTRACTION" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 722, + 354, + 736 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Methods for extracting meshes from 3D models are numerous and have been a subject of research for decades. Following Shen et al. (2023), we categorize these methods into two main types: Isosurface Extraction Lorensen & Cline (1987); Bloomenthal (1988); Chernyaev (1995); Bloomenthal & Bajaj (1997); Lorensen & Cline (1998); Chen et al. (2022) and Gradient-Based Mesh Optimization Chen et al. (2019); Gao et al. (2020); Hanocka et al. (2020); Kato et al. (2018); Shen et al. (2021a); Liao et al. (2018); Shen et al. (2023)." + } + ] + }, + "bbox": [ + 169, + 750, + 823, + 834 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Traditional isosurface extraction methods Lorensen & Cline (1987; 1998); Chernyaev (1995); Doi & Koide (1991); Ju et al. (2002); Schaefer et al. (2007); Chen & Zhang (2021); Chen et al. (2022) focus on extracting a polygonal mesh that represents the level set of a scalar function, an area that has seen extensive study in various fields. The most popular method among them is Marching Cubes Lorensen & Cline (1987). It divides the space into cells, within which polygons are created to approximate the surface. Marching Cubes has been widely used for mesh extraction its robustness and simplicity. Recently, Chen & Zhang (2021) and Chen et al. (2022) introduce data-driven methods to determine the position of the extracted mesh based on the input field." + } + ] + }, + "bbox": [ + 169, + 839, + 826, + 925 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "4" + } + ] + }, + "bbox": [ + 493, + 948, + 504, + 959 + ] + } + ], + [ + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 169, + 103, + 823, + 133 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Transitioning to more recent developments, the advent of machine learning has ushered in new techniques for generating 3D meshes Chen et al. (2019); Gao et al. (2020); Hanocka et al. (2020); Kato et al. (2018); Shen et al. (2021a); Liao et al. (2018); Shen et al. (2023). This line of work explores using neural networks to generate 3D meshes, where the network parameters are optimized through gradient-based methods under specific loss functions. Shen et al. (2021a) employs a differentiable Marching Tetrahedra layer for mesh extraction. Similar to Shen et al. (2021a), Shen et al. (2023) iteratively optimizes a 3D surface mesh by representing it as the isosurface of a scalar field." + } + ] + }, + "bbox": [ + 169, + 138, + 826, + 238 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "However, these approaches fundamentally differ from ours. They ignore the characteristics of the shape and inherently cannot produce meshes with efficient topology. In contrast, MeshAnything formulates mesh extraction as a generation problem for the first time, aiming to mimic human artists in mesh extraction and thereby generating Artist-Created Meshes (AMs) with hundreds of times fewer faces." + } + ] + }, + "bbox": [ + 169, + 243, + 826, + 313 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "2.2 3D MESH GENERATIONS" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 334, + 390, + 349 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "3D mesh generation can be mainly divided into two categories: generating dense meshes similar to those produced by previous mesh extraction methods, and generating Artist-Created Meshes (AMs)." + } + ] + }, + "bbox": [ + 169, + 363, + 823, + 392 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The former category is currently the mainstream research focus. Methods such as Gao et al. (2022); Wei et al. (2024); Xu et al. (2024) directly generate meshes in a feed-forward manner, but because they produce dense meshes with low-quality topology similar to previous mesh extraction methods, they still encounter the same issues when applied in the 3D industry." + } + ] + }, + "bbox": [ + 169, + 398, + 823, + 455 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Notably, numerous 3D generation methods Poole et al. (2023); Tang et al. (2023b); Wang et al. (2023); Chen et al. (2024b); Tang et al. (2023a); Yang et al. (2023); Hong et al. (2023); Fang et al. (2023); Chen et al. (2023a); Liu et al. (2024b); Shi et al. (2023); Li et al. (2023); Chen et al. (2023b; 2024c); Tang et al. (2024); Wang et al. (2024); Tochilkin et al. (2024) can also produce meshes. These methods first generate 3D assets and then convert them to dense meshes using mesh extraction methods like Lorensen & Cline (1987). Consequently, they face challenges when applied to the 3D industry due to their inefficient topology." + } + ] + }, + "bbox": [ + 169, + 460, + 825, + 559 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Recently, several works have focused on the second category: generating Artist-Created Meshes(AMs) Nash et al. (2020); Alliegro et al. (2023); Siddiqui et al. (2023); Chen et al. (2024a). Although our approach also focuses on AM generation, it fundamentally differs from these methods. Since they lack shape conditioning, these methods must simultaneously learn the complex 3D shape distribution—which typically alone requires extensive training Hong et al. (2023); Tang et al. (2024)—and the topology distribution of AMs, leading to very challenging training processes. In contrast, our methods eliminate the challenge of learning the shape distribution, allowing the model to focus on learning the topology distribution. This not only significantly reduces training costs but also enhances the model’s application value." + } + ] + }, + "bbox": [ + 169, + 565, + 826, + 691 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Among these methods, the most relevant to ours is MeshGPT Siddiqui et al. (2023), as we follow its architecture. Siddiqui et al. (2023) introduced a combination of a VQ-VAE Van Den Oord et al. (2017) and an autoregressive transformer architecture. It first learns a mesh vocabulary with the VQ-VAE and then trains the transformer on the learned vocabulary for mesh generation. However, MeshGPT’s results are limited to several categories in ShapeNet. MeshGPT requires a training GPU hours similar to ours, but our method can generalize to unlimited categories in Objaverse. As shown in Fig. 3, this is largely due to the difference in target complexity caused by MeshGPT needing to additionally learn the complex 3D shape distribution." + } + ] + }, + "bbox": [ + 169, + 696, + 825, + 809 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "3 SHAPE-CONDITIONED AM GENERATION" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 833, + 547, + 849 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In this section, we first introduce the formal formulation for Shape-Conditioned AM Generation and compare it with previous mesh generation settings Nash et al. (2020); Siddiqui et al. (2023); Alliegro et al. (2023). We show that it can achieve better performance and a broader range of applications compared to the settings in previous mesh generation methods, with significantly less training effort." + } + ] + }, + "bbox": [ + 169, + 867, + 823, + 925 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "5" + } + ] + }, + "bbox": [ + 493, + 948, + 504, + 959 + ] + } + ], + [ + { + "type": "chart", + "content": { + "image_source": { + "path": "images/aecc35c40ee63cf700f8e266846c83e8dfb32ed3aab02b0e0271258e64dac101.jpg" + }, + "content": "| Training iterations | Shape-Conditioned | Image-Conditioned | Unconditional |\n| --- | --- | --- | --- |\n| 60k | ~2.0 | — | — |\n| 80k | ~1.67 | ~1.98 | ~1.99 |\n| 100k | ~1.56 | ~1.83 | ~1.86 |\n| 120k | ~1.49 | ~1.74 | ~1.78 |\n| 140k | ~1.46 | ~1.71 | ~1.75 |\n| 160k | ~1.44 | ~1.70 | ~1.75 |\n| 180k | ~1.43 | ~1.70 | ~1.75 |\n| 200k | ~1.43 | ~1.69 | ~1.72 |\n| 220k | ~1.42 | ~1.69 | ~1.73 |", + "chart_caption": [ + { + "type": "text", + "content": "(a) Training Perplexity (PPL)" + } + ], + "chart_footnote": [] + }, + "sub_type": "line", + "bbox": [ + 184, + 111, + 442, + 268 + ] + }, + { + "type": "chart", + "content": { + "image_source": { + "path": "images/82c80d138141f010fa79e32343b04995c61f9dcd45f48b620653763fb4af129e.jpg" + }, + "content": "| Training iterations | Shape-Conditioned (Validation PPL) | Image-Conditioned (Validation PPL) | Unconditional (Validation PPL) |\n| --- | --- | --- | --- |\n| 60k | ~2.0 | ~2.0 | ~2.0 |\n| 80k | ~1.52 | ~1.75 | ~1.8 |\n| 100k | ~1.44 | ~1.67 | ~1.72 |\n| 120k | ~1.41 | ~1.63 | ~1.68 |\n| 140k | ~1.39 | ~1.6 | ~1.65 |\n| 160k | ~1.37 | ~1.59 | ~1.63 |\n| 180k | ~1.36 | ~1.58 | ~1.61 |\n| 200k | ~1.35 | ~1.57 | ~1.6 |\n| 220k | ~1.34 | ~1.56 | ~1.59 |", + "chart_caption": [ + { + "type": "text", + "content": "(b) Validation Perplexity (PPL)" + }, + { + "type": "text", + "content": "Figure 3: Training and validation perplexity (PPL) for the mesh generation model under different input conditions. All models are trained with the same settings as detailed in Section 5.2. The training and validation PPL of shape-conditioned mesh generation is significantly lower than that of unconditional and image-conditioned mesh generation. This indicates that the training burden of shape-conditioned mesh generation is much lower since it avoids learning the complex 3D shape distribution." + } + ], + "chart_footnote": [] + }, + "sub_type": "line", + "bbox": [ + 540, + 112, + 797, + 268 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Shape-Conditioned AM Generation targets to estimate a conditional distribution " + }, + { + "type": "equation_inline", + "content": "p ( \\mathcal { M } | S )" + }, + { + "type": "text", + "content": ". In this formula, M refers to the Artist-Created Mesh (AM), i.e., the mesh manually modeled by human artists. S refers to the 3D shape information that indicates the 3D shape to which M should align. The input form of S can be diverse, such as voxels or point clouds. Therefore, this versatility allows our method to be integrated with any 3D pipeline that outputs S, such as 3D reconstruction Mildenhall et al. (2020); Kerbl et al. (2023b), generation Poole et al. (2023); Hong et al. (2023), and scanning, making these methods more efficient for the 3D industry." + } + ] + }, + "bbox": [ + 169, + 419, + 823, + 518 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Compared to existing AM generation work, they directly estimate the distribution " + }, + { + "type": "equation_inline", + "content": "p ( \\mathcal { M } | \\mathcal { C } )" + }, + { + "type": "text", + "content": ", where C denotes conditions such as images, text or empty sets for unconditional generation. However, estimating " + }, + { + "type": "equation_inline", + "content": "p ( \\mathcal { M } | \\mathcal { C } )" + }, + { + "type": "text", + "content": "requires an understanding of both the underlying shape, i.e., S, and complex topological structures M. Given this, we made the following approximation:" + } + ] + }, + "bbox": [ + 169, + 523, + 823, + 580 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "p (\\mathcal {M} | \\mathcal {C}) \\approx p (\\mathcal {M}, \\mathcal {S} | \\mathcal {C}). \\tag {1}", + "math_type": "latex", + "image_source": { + "path": "images/493a0c9d88aa65dcd239591329191f0301e4dc8b32e2e11b7d2da81339584820.jpg" + } + }, + "bbox": [ + 416, + 602, + 823, + 618 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "According to the chain rule, we have:" + } + ] + }, + "bbox": [ + 171, + 622, + 419, + 636 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "p (\\mathcal {M}, \\mathcal {S} | \\mathcal {C}) = p (\\mathcal {M} | \\mathcal {S}, \\mathcal {C}) \\cdot p (\\mathcal {S} | \\mathcal {C}). \\tag {2}", + "math_type": "latex", + "image_source": { + "path": "images/8bf78913402038647174d8a506688d62b1cd01fa3b660b42209a6e0a26a2d109.jpg" + } + }, + "bbox": [ + 379, + 643, + 823, + 662 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "For distribution " + }, + { + "type": "equation_inline", + "content": "p ( \\mathcal { M } | \\mathcal { S } , \\mathcal { C } )" + }, + { + "type": "text", + "content": ", given that S is a much stronger and more direct condition than C, we can make the following approximation:" + } + ] + }, + "bbox": [ + 169, + 667, + 823, + 698 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "p (\\mathcal {M} | \\mathcal {S}, \\mathcal {C}) \\approx p (\\mathcal {M} | \\mathcal {S}). \\tag {3}", + "math_type": "latex", + "image_source": { + "path": "images/692ba251dac9eba24e7bc0d46470586f9e081c12ae578e1c30704831cc446a96.jpg" + } + }, + "bbox": [ + 416, + 705, + 823, + 720 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Combining 1, 2 and 3:" + } + ] + }, + "bbox": [ + 171, + 728, + 321, + 743 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "p (\\mathcal {M} | \\mathcal {C}) \\approx p (\\mathcal {M} | \\mathcal {S}) \\cdot p (\\mathcal {S} | \\mathcal {C}), \\tag {4}", + "math_type": "latex", + "image_source": { + "path": "images/cab409b95b2f03f76571481178ea0ec0675bd3d29957f6ddcfd8c06a15828a9c.jpg" + } + }, + "bbox": [ + 397, + 742, + 823, + 760 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "in which " + }, + { + "type": "equation_inline", + "content": "p ( \\mathcal { M } | S )" + }, + { + "type": "text", + "content": "is the focus of our shape-conditioned mesh generation. As shown in Fig. 3, estimating " + }, + { + "type": "equation_inline", + "content": "p ( \\mathcal { M } | S )" + }, + { + "type": "text", + "content": "is much more simpler than " + }, + { + "type": "equation_inline", + "content": "p ( \\mathcal { M } | \\mathcal { C } )" + }, + { + "type": "text", + "content": ", proving that our setting is much easier to train than settings in privous methods." + } + ] + }, + "bbox": [ + 169, + 763, + 823, + 806 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "As for p(S|C), In the 3D community, numerous large models Team (2024); Tang et al. (2024); Xu et al. (2024); Siddiqui et al. (2023) aim to estimate using various 3D representations and demonstrate excellent results. Besides, some single scene 3D asset production methods Mildenhall et al. (2020); Kerbl et al. (2023b); Barron et al. (2021; 2022); Poole et al. (2023); Liu et al. (2023b); Sun et al. (2023) can also provide samples from this distribution. By integrating our framework with these existing methods, we can leverage their capabilities to enhance our mesh generation process. This integration allows for a more resource-efficient way to estimate " + }, + { + "type": "equation_inline", + "content": "p ( \\mathcal { M } | \\mathcal { C } )" + }, + { + "type": "text", + "content": ", significantly reducing the complexity and resources required compared to previous methods." + } + ] + }, + "bbox": [ + 169, + 811, + 825, + 925 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "6" + } + ] + }, + "bbox": [ + 493, + 948, + 503, + 959 + ] + } + ], + [ + { + "type": "image", + "content": { + "image_source": { + "path": "images/ed7acb9369bfcc2c48faff57b105d6db318c21dfbb1b16f91c12ef6419bebbfe.jpg" + }, + "content": "```mermaid\ngraph LR\n A[\"Training\"] --> B[\"VQ Encoder\"]\n B --> C[\"Artist-Created Mesh\"]\n C --> D[\"Sample from surface\"]\n D --> E[\"Inference\"]\n E --> F[\"NeRF 3D GS\"]\n F --> G[\"Sample\"]\n G --> H[\"Point Cloud\"]\n H --> I[\"Feature\"]\n I --> J[\"Mesh Autoregressive Transformer\"]\n J --> K[\"...\"]\n K -.-> L[\"Cross-Entropy Loss\"]\n L --> M[\"Cross-Entropy Loss\"]\n M --> N[\"Cross-Entropy Loss\"]\n N --> O[\"Cross-Entropy Loss\"]\n O --> P[\"VQ Decoder\"]\n P --> Q[\"Generated Mesh\"]\n```", + "image_caption": [ + { + "type": "text", + "content": "Figure 4: Pipeline Overview. We introduce MeshAnything, an autoregressive transformer capable of generating Artist-Created Meshes that adhere to given 3D shapes. During training, we inject point clouds features into a decoder-only transformer and supervise it using token sequences derived from the Artist-Created meshes. After training, MeshAnything takes point clouds sampled from various 3D representations as input and generates aligned Artist-Created meshes." + } + ], + "image_footnote": [] + }, + "sub_type": "flowchart", + "bbox": [ + 181, + 102, + 816, + 199 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "4 METHOD" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 311, + 282, + 327 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In this section, we detail our shape condition strategy in Section 4.1. After that, we provide a detailed description for MeshAnything, which consists of a VQVAE with our newly proposed noise-resistant decoder (Section 4.2) and a shape-conditioned autoregressive transformer (Section 4.3)." + } + ] + }, + "bbox": [ + 169, + 345, + 823, + 388 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "4.1 SHAPE ENCODING FOR CONDITIONAL GENERATION" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 407, + 576, + 420 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We begin by describing our shape condition strategy. MeshAnything targets learning p(M|S), so we need to pair each mesh M with a corresponding S, i.e., the shape condition. Choosing an appropriate 3D representation for S is non-trivial and should satisfy the following conditions:" + } + ] + }, + "bbox": [ + 169, + 434, + 823, + 477 + ] + }, + { + "type": "list", + "content": { + "list_type": "text_list", + "list_items": [ + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "1. It should be easily extracted from various 3D representations. This ensures that the trained models can be integrated with a wide range of 3D asset production pipelines Mildenhall et al. (2020); Kerbl et al. (2023b); Hong et al. (2023); Poole et al. (2023); Tang et al. (2024)." + } + ] + }, + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "2. It should be suitable for data augmentation to prevent overfitting. To ensure the effectiveness of S during training, any data augmentation applied to M must be equivalently applicable to S." + } + ] + }, + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "3. It should be efficiently and conveniently input into the model as a condition. To ensure the model comprehends the shape information and to maintain efficient training, S must be easily and effectively encoded into features." + } + ] + } + ] + }, + "bbox": [ + 207, + 489, + 825, + 631 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Considering the first and second points, S should be in an explicit representation. Further considering the third point, the main explicit 3D representations that can be easily encoded as features are voxels and point clouds. Both representations are suitable, but voxels typically require a high resolution to accurately represent shapes, and processing high-resolution voxels into features is computationally expensive. Additionally, voxels, being a discrete representation, are less precise for data augmentation compared to point clouds. Therefore, we chose point clouds as the representation for S. To enhance the expressive power of the point clouds, we also include normals into the point cloud representation." + } + ] + }, + "bbox": [ + 169, + 645, + 823, + 756 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "To obtain point clouds from the ground truth mesh for training, we could simply sample point clouds directly from the surface of M. However, this would create problems during inference: the surfaces of automatically generated 3D assets are often rougher than those of AMs. For example, in AMs, we would sample a series of points on a flat plane, whereas automatically generated 3D assets would have uneven surfaces, causing a domain gap between training and inference." + } + ] + }, + "bbox": [ + 169, + 763, + 823, + 834 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Therefore, we need to ensure that S extracted from the ground truth M during training has a similar domain to the S extracted during inference. To bring their domains closer, we intentionally construct coarse meshes from AMs. We first extract the signed distance function from M with Wang et al. (2022), then convert it into a relatively coarse mesh using Marching Cubes Lorensen & Cline (1987) to destroy the ground truth topology. Finally, we sample point cloud and its normals from the coarse mesh. This approach also helps to avoid overfitting, as AMs typically have fewer faces, and each face can often sample multiple points. The network can easily recognize the ground truth topology by determining whether the points lie on the same plane." + } + ] + }, + "bbox": [ + 169, + 840, + 825, + 925 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [] + }, + "bbox": [ + 493, + 948, + 503, + 959 + ] + } + ], + [ + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 169, + 104, + 823, + 133 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Since almost all 3D representations can be converted into a coarse mesh using Marching Cubes Lorensen & Cline (1987) or sampled into point clouds, this ensures that the domain of S is consistent during both training and inference. We pair the point clouds extracted as S with M to create a data item " + }, + { + "type": "equation_inline", + "content": "\\big \\{ ( { \\mathcal { M } } _ { i } , { \\mathcal { S } } _ { i } ) \\big \\} " + }, + { + "type": "text", + "content": "i for training." + } + ] + }, + "bbox": [ + 169, + 138, + 823, + 196 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "4.2 VQ-VAE WITH NOISE-RESISTANT DECODER" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 210, + 529, + 226 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Following MeshGPT Siddiqui et al. (2023), we first train a VQ-VAE Van Den Oord et al. (2017) to learn a vocabulary of geometric embeddings for better transformer Vaswani et al. (2017) learning. Different to MeshGPT, which uses graph convolutional networks Wu et al. (2019) and ResNet He et al. (2016) as the encoder and decoder respectively, we employ transformers with identical structures for both the encoder and decoder. When training VQ-VAE, meshes are discretized and input as a sequence of triangle faces:" + } + ] + }, + "bbox": [ + 169, + 237, + 823, + 321 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {M} := (f _ {1}, f _ {2}, f _ {3}, \\dots , f _ {N}), \\tag {5}", + "math_type": "latex", + "image_source": { + "path": "images/8b3af83c6847d00522a1cf4d60e8a888b539d980db8020833611eb2d5e4a1823.jpg" + } + }, + "bbox": [ + 405, + 324, + 823, + 340 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "where " + }, + { + "type": "equation_inline", + "content": "f _ { i }" + }, + { + "type": "text", + "content": "is the coordinates of the vertices of each face, and N is the number of faces in M. The encoder E then extracts a feature vector for each face:" + } + ] + }, + "bbox": [ + 169, + 342, + 823, + 371 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {Z} = (z _ {1}, z _ {2}, \\dots , z _ {N}) = E (\\mathcal {M}), \\tag {6}", + "math_type": "latex", + "image_source": { + "path": "images/eb94b31a6cc3560bc7a2e5c39c262dfb6e02e3e92552c8786ea39ab7c03e75fa.jpg" + } + }, + "bbox": [ + 388, + 375, + 823, + 391 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "where " + }, + { + "type": "equation_inline", + "content": "z _ { i }" + }, + { + "type": "text", + "content": "is the feature vector for " + }, + { + "type": "equation_inline", + "content": "f _ { i }" + }, + { + "type": "text", + "content": "." + } + ] + }, + "bbox": [ + 171, + 393, + 410, + 409 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The extracted faces are then quantized into quantized features T with codebook B:" + } + ] + }, + "bbox": [ + 171, + 415, + 718, + 430 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {T} = R Q (\\mathcal {Z}; \\mathcal {B}) \\tag {7}", + "math_type": "latex", + "image_source": { + "path": "images/16e09b6dd2e31fb7eceb29a6f3ef111263c24e02161513e3d50c9ec08ec5d9ce.jpg" + } + }, + "bbox": [ + 442, + 433, + 823, + 449 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Finally, the reconstructed mesh is decoded from " + }, + { + "type": "equation_inline", + "content": "\\tau" + }, + { + "type": "text", + "content": "with decoder D by predicting the logits for each vertex’s coordinates:" + } + ] + }, + "bbox": [ + 169, + 459, + 823, + 486 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\hat {\\mathcal {M}} = D (\\mathcal {Z}) \\tag {8}", + "math_type": "latex", + "image_source": { + "path": "images/37fde7830ed11ba68426389761e16f499627f0c6ebad5c302aa82cb752eb0fba.jpg" + } + }, + "bbox": [ + 454, + 486, + 823, + 502 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The VQ-VAE is trained end-to-end with cross-entropy loss on the predicted vertex coordinate logits and the commitment loss of vector quantization Van Den Oord et al. (2017). After the training of VQ-VAE, the encoder-decoder of VQ-VAE is treated as a tokenizer and detokenizer for autoregressive transformer training." + } + ] + }, + "bbox": [ + 169, + 503, + 825, + 559 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "However, as shown in Fig. 7, there are possible imperfections in the generation results. To address this issue, given our setting of Shape-Conditioned AM Generation, the VQ-VAE decoder can also take the shape condition as input. Small imperfections in the token sequences generated by the transformer can potentially be corrected by a shape-aware decoder. Therefore, after completing the vanilla VQ-VAE training, we add an additional decoder fine-tuning stage, where we inject the shape information into the transformer decoder. Then we add random Gumbel noise to the codebook sampling logits to simulate the potential imperfections in the token sequences generated by the transformer during inference. The decoder is then updated independently with the same crossentropy loss to train it to produce refined meshes even when facing imperfect token sequences. Our experiments in Tab. 3 and Tab. 4 show that our method effectively enhances the decoder’s noise resistance and mesh generation quality." + } + ] + }, + "bbox": [ + 169, + 566, + 825, + 719 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "4.3 SHAPE-CONDITIONED AUTOREGRESSIVE TRANSFORMER" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 734, + 612, + 750 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "To add shape condition to the transformer, inspired by the success of multimodal large language models Wu et al. (2023); Liu et al. (2024a); Xu et al. (2023); Guo et al. (2023), we first encode the point cloud into a fixed-length token sequence with a point cloud encoder P and then concatenate it to the front of the embedding sequence from T VQ-VAE as the final input embedding sequence for the transformer:" + } + ] + }, + "bbox": [ + 169, + 761, + 823, + 829 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\mathcal {T} ^ {\\prime} = \\operatorname{concat} (\\mathcal {P} (\\mathcal {S}), \\mathcal {T}) \\tag {9}", + "math_type": "latex", + "image_source": { + "path": "images/2aab9c62c96846b493f2510a53f4eef3cdf119891dda2a8cd383b2125d12d63f.jpg" + } + }, + "bbox": [ + 419, + 830, + 823, + 845 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "where " + }, + { + "type": "equation_inline", + "content": "\\tau ^ { \\prime }" + }, + { + "type": "text", + "content": "is the training input for the transformer." + } + ] + }, + "bbox": [ + 171, + 845, + 500, + 861 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We borrow a pretrained point encoder from Zhao et al. (2024) and add a linear projection layer to project its output feature to the same latent space as " + }, + { + "type": "equation_inline", + "content": "\\tau" + }, + { + "type": "text", + "content": ". During training, the original point encoder from Zhao et al. (2024) is frozen; we only update the newly added projection layer and the autoregressive transformer with cross-entropy loss." + } + ] + }, + "bbox": [ + 169, + 868, + 825, + 925 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "8" + } + ] + }, + "bbox": [ + 493, + 948, + 504, + 959 + ] + } + ], + [ + { + "type": "table", + "content": { + "image_source": { + "path": "images/a587e59902d48906bf018b70b34312d4b3280f44f16e87918959ca0a92f84164.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 1: Comparison of Mesh Generation Methods. As shown in the left table, compared to the baseline Artist-Created Mesh Generation method, the meshes generated by MeshAnything are better aligned with human preferences. In the right table, we compare MeshAnything with mesh extraction baselines, and it received the most votes. For detailed settings, please refer to Section 5.4." + } + ], + "table_footnote": [], + "html": "
MethodShape↑Topology↑
PolyGen12.7%11.1%
MeshGPT24.1%28.2%
MeshAnything63.2%60.7%
", + "table_type": "simple_table", + "table_nest_level": 1 + }, + "bbox": [ + 179, + 167, + 460, + 241 + ] + }, + { + "type": "table", + "content": { + "image_source": { + "path": "images/0b2e63f9cc4b9269adf4e17a0403f2cecc8664a098b27bd19b69d8792431ebb8.jpg" + }, + "table_caption": [], + "table_footnote": [], + "html": "
MethodShape↑Topology↑
MarchingCubes38.1%10.2%
Shape As Points17.3%6.2%
MeshAnything44.6%83.6%
", + "table_type": "simple_table", + "table_nest_level": 1 + }, + "bbox": [ + 526, + 167, + 818, + 241 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "During inference, we input " + }, + { + "type": "equation_inline", + "content": "{ \\mathcal { P } } ( S )" + }, + { + "type": "text", + "content": "to the transformer and require it to generate the subsequent sequence, Tˆ . " + }, + { + "type": "equation_inline", + "content": "\\hat { \\tau }" + }, + { + "type": "text", + "content": "is then input to the noise-resistant decoder to reconstruct meshes:" + } + ] + }, + "bbox": [ + 169, + 266, + 823, + 297 + ] + }, + { + "type": "equation_interline", + "content": { + "math_content": "\\hat {\\mathcal {M}} = D (\\hat {\\mathcal {T}}) \\tag {10}", + "math_type": "latex", + "image_source": { + "path": "images/8ba27f7b449c1719946af50c323edac722c3af931637cd89d02fc62c01759f50.jpg" + } + }, + "bbox": [ + 454, + 305, + 823, + 324 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "where " + }, + { + "type": "equation_inline", + "content": "\\hat { \\mathcal { M } }" + }, + { + "type": "text", + "content": "is the final generated AM." + } + ] + }, + "bbox": [ + 171, + 332, + 413, + 348 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We use the standard next-token prediction loss to train shape-conditioned transformers. For each sequence, we add a token after the point cloud tokens and a token after the mesh tokens to identify the end of a 3D mesh." + } + ] + }, + "bbox": [ + 169, + 354, + 823, + 397 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "5 EXPERIMENTS" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 417, + 326, + 431 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "5.1 DATA PREPARATION" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 449, + 356, + 462 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Data Selection. Existing AM generation works are limited to a few categories. However, our method targets to operate on general shapes. MeshAnything is trained on a combined dataset of Objaverse Deitke et al. (2023b) and ShapeNet Chang et al. (2015), selected for their complementary characteristics. We chose Objaverse because it contains a large number of AMs without category limitations. On the other hand, ShapeNet offers higher data quality within limited categories." + } + ] + }, + "bbox": [ + 169, + 474, + 823, + 546 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We filter out meshes with more than 800 faces from both datasets. Additionally, we manually filtered out low quality meshes. Our final filtered dataset consists of 51k meshes from Objaverse and 5k meshes from ShapeNet. We randomly select 10% of this dataset as the evaluation dataset, with the remaining 90% used as the training set for all our experiments." + } + ] + }, + "bbox": [ + 169, + 551, + 823, + 609 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Data Processing and Augmentation. Following the strategies of PolyGen Nash et al. (2020) and MeshGPT Siddiqui et al. (2023), we order faces by their lowest vertex index, then by the next lowest, and so on. Vertices are sorted in ascending order based on their z-y-x coordinates, where z represents the vertical axis. Within each face, we permute the indices to ensure the lowest index comes first. During training, we apply on-the-fly scaling, shifting, and rotation augmentations, normalizing each mesh to a unit bounding box from −0.5 to 0.5." + } + ] + }, + "bbox": [ + 169, + 614, + 823, + 699 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "5.2 IMPLEMENTATION DETAILS" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 715, + 406, + 729 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The encoder and decoder of VQ-VAE both use the encoder of BERT Devlin et al. (2018), while we choose OPT-350M Zhang et al. (2022) as our autoregressive transformer architecture. The residual vector quantization Zeghidour et al. (2021) depth is set to 3, with a codebook size of 8,192." + } + ] + }, + "bbox": [ + 169, + 741, + 823, + 785 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Our point encoder is based on the pretrained point encoder from Zhao et al. (2024), which has been trained on Objaverse and thus can handle general shapes. This point encoder outputs a fixedlength token sequence of 257 tokens, with 256 tokens primarily containing shape information and an additional head token containing semantic information about the shape. We sample 4096 points for each point cloud." + } + ] + }, + "bbox": [ + 169, + 790, + 823, + 861 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "The training batch size for both the VQ-VAE and the transformer is set to 8 per GPU. The VQ-VAE is trained on 8 A100 GPUs for 12 hours, after which we separately finetune the decoder part of the VQ-VAE into a noise-resistant decoder, as detailed in Section 4.2. Following this, the transformer is trained on 8 A100 GPUs for 4 days." + } + ] + }, + "bbox": [ + 169, + 867, + 823, + 924 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "9" + } + ] + }, + "bbox": [ + 493, + 948, + 503, + 959 + ] + } + ], + [ + { + "type": "table", + "content": { + "image_source": { + "path": "images/cbf54f8daa7c24b2a3d45e6d3135a4ff3686aa78f4c49f65629cd4b147f96acd.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 2: Quantitative Comparisons with Prior Arts on Objaverse. MeshAnything significantly outperforms prior methods across all metrics. MMD, KID are scaled by 103." + } + ], + "table_footnote": [], + "html": "
MethodCOV↑MMD↓1-NNA↓FID↓KID↓
PolyGen23.26.2288.248.827.7
MeshGPT41.73.8367.325.16.11
MeshAnything53.12.7255.714.51.89
", + "table_type": "simple_table", + "table_nest_level": 1 + }, + "bbox": [ + 274, + 140, + 718, + 213 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "5.3 QUALITATIVE EXPERIMENTS" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 237, + 415, + 253 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "As shown in Fig. 1, MeshAnything effectively generates AMs from various 3D representations. In our experiments, we use Rodin Team (2024) as the text-to-3D and image-to-3D method, and employ Mildenhall et al. (2020) and Kerbl et al. (2023a) as the 3D reconstruction pipeline to obtain the corresponding NeRF and Gaussian Splatting models. For additional qualitative results, please refer to A.2 combined with other 3D asset production pipelines." + } + ] + }, + "bbox": [ + 169, + 263, + 823, + 335 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "5.4 QUANTITATIVE EXPERIMENTS" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 349, + 426, + 364 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "From the generative model perspective, MeshAnything is a shape-conditioned mesh generation model. From the mesh extraction perspective, it extracts artist-created meshes from point clouds. Consequently, we compare MeshAnything with both types of methods. Additional experiments can be found in Appendix Section A.2." + } + ] + }, + "bbox": [ + 169, + 376, + 823, + 434 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "User Study. As shown in Tab. 1, we conducted two user studies, comparing with mesh generation baselines Nash et al. (2020); Siddiqui et al. (2023) and mesh extraction baselines Lorensen & Cline (1987); Peng et al. (2021), respectively. The mesh generation baselines are trained on ShapeNet, and to ensure a fair comparison, we retrained them on Objaverse using the same transformer model as MeshAnything. Since the mesh generation baselines are all unconditional mesh generation methods, whereas MeshAnything is a shape-conditioned mesh generation method, we sampled shapes randomly from the evaluation set of Objaverse as inputs for MeshAnything, while for the baseline methods, we performed random sampling directly." + } + ] + }, + "bbox": [ + 169, + 439, + 823, + 551 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In the mesh extraction baseline, since our method can also be viewed as a point cloud to mesh approach, we included Peng et al. (2021), a point cloud to mesh method, as a baseline. Additionally, we optimized the results from the mesh extraction baseline using the Blender remesh method Blender Development Team (2024) to simplify the topology." + } + ] + }, + "bbox": [ + 169, + 556, + 823, + 614 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We collected 30 results from each method and asked users to vote for the best one in terms of shape quality and topology quality. A total of 41 users participated, providing 1,230 valid comparisons. Both user studies demonstrated the superiority of our method. The only difference between the retrained MeshGPT and MeshAnything is whether they are shape-conditioned, further proving the advantages of the shape-conditioned mesh generation setting." + } + ] + }, + "bbox": [ + 169, + 619, + 823, + 691 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Metrics. We follow the metric setting of Chen et al. (2022); Siddiqui et al. (2023). We detail this setting in Appendix Section. A.1." + } + ] + }, + "bbox": [ + 169, + 696, + 823, + 726 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Comparison with Mesh Generation Pipelines. We use the same retrained models from the user study for comparison. As shown in Tab. 2, MeshAnything significantly outperforms prior methods Nash et al. (2020); Siddiqui et al. (2023), indicating that it’s superior in both the shape and topology quality. Since the only difference between the retrained MeshGPT and MeshAnything is the inclusion of shape conditioning, the superior performance of MeshAnything further demonstrates that Shape-Conditioned Mesh Generation is a more suitable setting for mesh generation." + } + ] + }, + "bbox": [ + 169, + 732, + 823, + 816 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "6 CONCLUSION" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 837, + 318, + 852 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "In this work, we propose a novel setting for improved mesh extraction and mesh generation, namely Shape-Conditioned Artist-Created Mesh (AM) Generation. Following this setting, we introduce MeshAnything, a model capable of generating AMs that adhere to given 3D assets. MeshAnything can convert 3D assets in any 3D representation into AMs and thus can be integrated with diverse 3D asset production methods to facilitate their application in the 3D industry. Furthermore, we introduce a noise-resistant decoder architecture to enhance the generation quality, enabling the model to handle low-quality token sequences produced by autoregressive transformers. Lastly, extensive experiments demonstrate the superior performance of our method, highlighting its potential to scale up for 3D industry application and its advantage over previous methods." + } + ] + }, + "bbox": [ + 169, + 867, + 823, + 925 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "10" + } + ] + }, + "bbox": [ + 490, + 946, + 508, + 959 + ] + } + ], + [ + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 169, + 103, + 825, + 175 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "REFERENCES" + } + ], + "level": 2 + }, + "bbox": [ + 173, + 194, + 287, + 209 + ] + }, + { + "type": "list", + "content": { + "list_type": "reference_list", + "list_items": [ + { + "item_type": "text", + "item_content": [ + { + "type": "text", + "content": "Antonio Alliegro, Yawar Siddiqui, Tatiana Tommasi, and Matthias Nießner. 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As shown, MeshAnything can be integrated with various 3D production pipelines to achieve highly controllable mesh generation." + } + ], + "image_footnote": [] + }, + "sub_type": "natural_image", + "bbox": [ + 183, + 138, + 823, + 316 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/862aeab2050e05c2e08496535a396d53ce14ba0421ede1b90aa189a88547daac.jpg" + }, + "content": "Point Cloud Condition\nImage Condition\nImage Condition\n(a)\n312 faces\nOurs\n518 faces\nGT\n612 faces\nOurs\n529 faces\nGT\n(b)\n(c)", + "image_caption": [ + { + "type": "text", + "content": "Figure 6: Qualitative Results. (a) further demonstrates our capability to achieve highly controllable mesh generation when combined with 3D asset production pipelines. Besides, we compare our reseults with ground truth in (b) and (c). In (b), MeshAnything generates meshes with better topology and fewer faces than the ground truth. In (c), we produce meshes with a completely different topology while achieving a similar shape, proving that our method does not simply overfit but understands how to construct meshes using efficient topology." + } + ], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 178, + 378, + 826, + 526 + ] + }, + { + "type": "image", + "content": { + "image_source": { + "path": "images/eb9f539a645e6b2e3c176b61b49ba88020584ef19f05df2c9ea2f6addf7bca86.jpg" + }, + "content": "W.O. Noise-Resistant Decoder\nOurs\nW.O. Noise-Resistant Decoder\nOurs\nW.O. Noise-Resistant Decoder\nOurs", + "image_caption": [ + { + "type": "text", + "content": "Figure 7: Ablation on Noise-Resistant Decoder. The decoder-only transformer may generate lowquality token sequences, and the decoder of VQ-VAE would typically produce flawed meshes based on these sequences. In contrast, our Noise-Resistant Decoder, aided by shape conditions, has the ability to resist these low-quality token sequences, producing higher-quality meshes." + } + ], + "image_footnote": [] + }, + "sub_type": "text_image", + "bbox": [ + 181, + 643, + 816, + 726 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "A.1 METRICS" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 821, + 284, + 833 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We follow the evaluation metric setting of Siddiqui et al. (2023) in mesh generation experiments and the setting of Chen et al. (2022) in mesh extraction experiments." + } + ] + }, + "bbox": [ + 169, + 845, + 823, + 875 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We quantitatively evaluate mesh quality by uniformly sampling 100K points from the faces of both the ground truth meshes and the predicted meshes, and then computing a set of metrics to assess various aspects of the reconstruction." + } + ] + }, + "bbox": [ + 169, + 881, + 823, + 924 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "16" + } + ] + }, + "bbox": [ + 490, + 948, + 508, + 959 + ] + } + ], + [ + { + "type": "table", + "content": { + "image_source": { + "path": "images/0f72e96f0ce4abc9816ff609fb6b53f38a109b826510443cc8109a04076fc291.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 3: Reconstruction Performance under Different Noise Levels with and without Noise-Resistant (NR) Decoder. Please refer to A.1 for metrics explanation." + } + ], + "table_footnote": [], + "html": "
Noise Level $\\mathbf{CD}(\\times 10^{-2})\\downarrow$ $\\mathbf{ECD}(\\times 10^{-2})\\downarrow$ $\\mathbf{NC}\\uparrow$
W/O NRW/ NRW/O NRW/ NRW/O NRW/ NR
0.00.0110.0070.0350.0230.9870.993
0.10.1870.0280.6130.1380.9730.991
0.51.1670.6392.5381.3290.9640.981
1.02.1311.7984.3172.3160.9520.969
", + "table_type": "complex_table", + "table_nest_level": 1 + }, + "bbox": [ + 228, + 140, + 767, + 247 + ] + }, + { + "type": "table", + "content": { + "image_source": { + "path": "images/4c8edf4f1e0648c2ebb129bfe07d83d794970f16251239b451977c0b2d640628.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 4: Ablation on Noise-Resistant (NR) Decoder for the Quality of Mesh Generation." + } + ], + "table_footnote": [], + "html": "
Method $\\mathbf{CD}↓$ $(×10^{-2})$ $\\mathbf{ECD}↓$ $(×10^{-2})$ $\\mathbf{NC}↑$
W/O NR2.4236.4140.883
W/ NR2.2566.2450.902
", + "table_type": "simple_table", + "table_nest_level": 1 + }, + "bbox": [ + 354, + 286, + 638, + 359 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "For mesh extraction, we report the following metrics: Chamfer Distance (CD) to evaluate the overall quality of a reconstructed mesh; Edge Chamfer Distance (ECD) to assess the preservation of sharp edges by sampling points near sharp edges and corners; and Normal Consistency (NC) to evaluate the quality of the surface normals. Additionally, we report the number of mesh vertices (#V) and the number of mesh faces (#F). We also provide the ratio of the estimated number of vertices to the ground truth number of vertices (#V R) and the same ratio for faces (#F R)." + } + ] + }, + "bbox": [ + 169, + 383, + 823, + 469 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "For mesh generation, Coverage (COV) captures the diversity of generated meshes and is sensitive to mode dropping, but it does not reflect the quality of the results. Minimum Matching Distance (MMD) measures the average distance between the reference set and their nearest neighbors in the generated set, though it lacks sensitivity to low-quality outputs. The 1-Nearest Neighbor Accuracy (1-NNA) assesses both quality and diversity between the generated and reference sets. To evaluate topology quality, we render the ground truth meshes and generated meshes with their wireframes visualized. We then employ Frechet Inception Distance (FID) and Kernel Inception Distance (KID) on rendered images. MMD, and KID scores are scaled by a factor of 103." + } + ] + }, + "bbox": [ + 169, + 474, + 826, + 587 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "A.2 EXPERIMENTS" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 604, + 318, + 618 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Additional Qualitative Experiments We present more qualitative results of MeshAnything here. As shown in Fig. 5 and Fig. 6, MeshAnything effectively generates AMs from various 3D representations. When integrated with different 3D assets production pipelines, our method effectively achieves mesh generation with diverse conditions." + } + ] + }, + "bbox": [ + 169, + 631, + 823, + 686 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Next, Fig. 6 demonstrates that MeshAnything does not simply overfit but understands how to generate meshes with efficient topology that conform to the given shape. To prove this, we use manuallycreated meshes as ground truth and use their shapes as conditions to test whether our model can generate meshes with comparable topology. To effectively use the ground truth as conditions, we first convert them into dense meshes using Marching Cubes Lorensen & Cline (1987) to disrupt their face structure. Then, we sample point clouds with normals from the dense meshes to serve as shape conditions. The experimental results in Fig. 6 show that MeshAnything is capable of generating meshes comparable to or even surpassing those modeled by human artists, exhibiting diverse and strong 3D modeling capabilities." + } + ] + }, + "bbox": [ + 169, + 694, + 826, + 820 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Comparison with mesh extraction baselines. Our method is related to various mesh extraction methods Lorensen & Cline (1987); Chen & Zhang (2021); Chen et al. (2022); Shen et al. (2023); Peng et al. (2021) since we also convert other 3D representations into meshes. However, it is important to note that previous approaches are reconstruction-like methods that produce dense meshes, while our approach is generative, creating Artist-Created Meshes (AMs) that are significantly more complex to produce than dense meshes. Therefore, strictly speaking, our method cannot be considered the same as these reconstruction-based mesh extraction methods. The main purpose of this comparison is to use these mesh extraction methods as a reference for evaluating the quality of the meshes generated by MeshAnything in terms of shape. We compare MeshAnything with Lorensen & Cline (1987); Shen et al. (2023); Peng et al. (2021). Among these, MarchingCubes is the most popular mesh extraction method, FlexiCubes represents the state-of-the-art in mesh extraction, and Shape as Points is the leading method for extracting mesh from point cloud." + } + ] + }, + "bbox": [ + 169, + 825, + 826, + 925 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "17" + } + ] + }, + "bbox": [ + 490, + 946, + 508, + 959 + ] + } + ], + [ + { + "type": "table", + "content": { + "image_source": { + "path": "images/570664b3881998a3dd6868c6ee55bf8d42bd6333a7d525ab86e65793864941da.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 5: Quantitative evaluation with mesh extraction baselines. MC, FC, SAP refer to Marching Cubes Lorensen & Cline (1987), FlexiCubes Shen et al. (2023), and Shape As Points Peng et al. (2021), respectively. Please refer to A.1 for metrics explanation." + } + ], + "table_footnote": [], + "html": "
Method $\\mathbf{CD}\\downarrow$ $(\\times 10^{-2})$ $\\mathbf{ECD}\\downarrow$ $(\\times 10^{-2})$ $\\mathbf{NC}\\uparrow$ $\\#V\\downarrow$ $(\\times 10^{3})$ $\\#F\\downarrow$ $(\\times 10^{3})$ $\\mathbf{V\\_R}\\downarrow$ $\\mathbf{F\\_R}\\downarrow$
(a) Marching Cubes1.5326.7330.95473.22146.0440.2462.2
(b) MC+Remesh (0.005)2.1747.8130.912127.8167.9748.1534.6
(c) MC+Remesh (0.010)2.0837.5780.92939.0141.78225.4132.3
(d) MC+Remesh (0.030)2.9158.3290.8635.8484.41034.3814.05
(e) MC+Remesh (0.050)4.1798.1380.8142.2991.53813.644.920
(f) MC+Remesh (0.100)7.31210.7710.7480.6250.3593.7351.149
(g) FC1.1906.1210.96759.12121.1378.2391.1
(h) FC+Remesh (0.010)1.8616.9400.93337.9840.19205.5124.2
(i) SAP1.7717.1120.93979.12152.3481.2489.3
(j) SAP+Remesh (0.010)2.3677.8620.92539.1742.87239.1136.6
(k) MeshAnything2.2566.2450.9020.1720.3180.8880.871
", + "table_type": "simple_table", + "table_nest_level": 1 + }, + "bbox": [ + 183, + 152, + 810, + 339 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [] + }, + "bbox": [ + 169, + 375, + 823, + 445 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "We also combined these methods with the remesh technique to test whether they could significantly reduce the number of faces while maintaining shape quality. We used Blender Remesh in voxel mode Community (2018); Blender Development Team (2024), specifically using Blender version 4.1, as the remesh method. Since our evaluation dataset includes non-watertight meshes, we first extract the signed distance fields (SDF) of all ground truth meshes using Wang et al. (2022), which can handle non-watertight meshes. We then apply Marching Cubes with a resolution of 128 on these SDFs. Next, we apply Blender remesh Blender Development Team (2024) with different voxel sizes to the Marching Cubes results, as both the remesh method and our approach are capable of simplifying topology. Additionally, the Marching Cubes result is used as the shape condition input to MeshAnything to obtain our results. The settings of Shen et al. (2023) and Peng et al. (2021) follow their papers." + } + ] + }, + "bbox": [ + 169, + 450, + 826, + 604 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "As shown in Tab. 5, we found that these methods require hundreds of times more faces to achieve results comparable to our method. Comparing (a), (g), (i) and (k), our method lags in Chamfer Distance (CD) and Normal Consistency (NC), mainly due to our method’s inherent failure cases as a generative model, which makes it less robust than these reconstruction-based mesh extraction methods. When comparing with remesh methods, we observe that they incur a high cost to achieve a face count similar to ours. Comparing (f) and (k), we find that even when remesh methods achieve a comparable face count, the number of vertices is still several times higher than ours, indicating that the topology efficiency of remesh methods is far inferior to ours, as they completely ignore the shape characteristics of the 3D assets. It’s important to note that the metrics in mesh etraction can only indicate the quality of shape alignment, which do not effectively reflect the topological advantages of our method. Additionally, we surprisingly find that our method can produce results with fewer faces than the ground truth, demonstrating that MeshAnything is not overfitting to the data but instead learns an efficient topology representation, occasionally surpassing the ground truth meshes." + } + ] + }, + "bbox": [ + 169, + 611, + 826, + 805 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Ablations on Noise-Resistant Conditional Decoder. We perform ablation experiments to verify the effectiveness of the Noise-Resistant Decoder. We begin with a VQ-VAE trained without any noise or conditioning. We then perform ablation between two settings: one where the decoder remains unchanged and unaware of the shape condition, and another where the shape condition is injected into the transformer, as described in Section 4.2. Next, we randomly sample a noise from gumbel distribution and add it to codebook sampling logits during the vector quantization process to simulate the potential low-quality token sequences generated by the transformer. We control the noise level by scaling the added noise." + } + ] + }, + "bbox": [ + 169, + 811, + 826, + 925 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "18" + } + ] + }, + "bbox": [ + 490, + 948, + 508, + 959 + ] + } + ], + [ + { + "type": "table", + "content": { + "image_source": { + "path": "images/e9773db60cbbbf34982b211de9fb22c88377fbfb0429f74b9c5324bd472f3c08.jpg" + }, + "table_caption": [ + { + "type": "text", + "content": "Table 6: Experiments on the Impact of Input Point Cloud Quality on Generated Results." + } + ], + "table_footnote": [], + "html": "
Method $\\mathbf{CD}↓$ $(×10^{-2})$ $\\mathbf{ECD}↓$ $(×10^{-2})$ $\\mathbf{NC}↑$ $#V↓$ $(×10^{3})$ $#F↓$ $(×10^{3})$ $V\\_R↓$ $F\\_R↓$
(a) Noise scale 0.0052.3516.4120.8970.1750.3210.8950.880
(b) Noise scale 0.0202.9806.9700.8810.1800.3300.9010.910
(c) Noise scale 0.0504.9108.5560.7550.1620.2840.8110.802
(d) Rodin2.5526.6220.8330.1850.3420.9190.923
(e) $MeshAnything$ 2.2566.2450.9020.1720.3180.8880.871
", + "table_type": "simple_table", + "table_nest_level": 1 + }, + "bbox": [ + 196, + 125, + 799, + 229 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "After training both models for enough epochs, we test their performance to the same level of noise. As shown in Tab. 3, as the intensity of the added noise increases, the Noise-Resistant Decoder with shape condition clearly achieves better reconstruction results. This indicates that the shape condition helps the decoder identify and correct imperfections in the input token sequences." + } + ] + }, + "bbox": [ + 169, + 242, + 823, + 301 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Next, we verify whether the Noise-Resistant Decoder indeed enhances the transformer’s performance during inference. The test method used dense meshes derived from corrupted GT meshes as the condition for generating new meshes. The generated meshes were then assessed for shape alignment with the conditional shape. As shown in Tab. 4, the model with Noise-Resistant Decoder achieved better results." + } + ] + }, + "bbox": [ + 169, + 306, + 823, + 376 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Experiments on the Impact of Input Point Cloud Quality on Generated Results. MeshAnything takes point clouds as input, and its robustness to point cloud quality determines its versatility across various applications. We design two experiments to evaluate its tolerance to input point cloud quality: First, keeping the other evaluation settings unchanged, we apply Gaussian noise to the input point cloud coordinates and normals. Specifically, for each point, we randomly sample Gaussian noise from a standard distribution, scale it by a noise factor, and add it to the point’s coordinates. The same approach is applied to the normals, but normalization is applied after adding the noise. Second, we use Rodin’s generation result as the ground truth mesh, sample point clouds from this mesh as input, and evaluate the deviation between the generated result and the ground truth." + } + ] + }, + "bbox": [ + 169, + 382, + 826, + 508 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "As shown in Tab. 6, MeshAnything did not experience a significant performance drop in (a) and (b), demonstrating resilience to noise in the point cloud, with a noticeable performance decrease only in (c). It is important to note that the input point cloud is normalized to the range [-1,1], and the noise scale in (c) is already quite large. The experiment in (d) further demonstrates that MeshAnything can tolerate generated point clouds and effectively integrate with 3D generation models." + } + ] + }, + "bbox": [ + 169, + 513, + 825, + 585 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "A.3 LIMITATIONS" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 601, + 312, + 614 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Our method cannot generate meshes that exceed the maximum face count limit, so it cannot convert large scenes and particularly complex objects into meshes. Additionally, due to its generative nature, our method is not as stable as reconstruction-based mesh extraction methods like Lorensen & Cline (1987); Shen et al. (2023)." + } + ] + }, + "bbox": [ + 169, + 627, + 823, + 684 + ] + }, + { + "type": "title", + "content": { + "title_content": [ + { + "type": "text", + "content": "A.4 SOCIAL IMPACT" + } + ], + "level": 2 + }, + "bbox": [ + 171, + 700, + 331, + 714 + ] + }, + { + "type": "paragraph", + "content": { + "paragraph_content": [ + { + "type": "text", + "content": "Our method points to a promising approach for the automatically generation of Artist-Created Meshes, which has the potential to significantly reduce labor costs in the 3D industry, thereby facilitating advancements in industries such as gaming, film, and the metaverse. However, the reduced cost of obtaining 3D Artist-Created meshes could also lead to potential criminal activities." + } + ] + }, + "bbox": [ + 169, + 726, + 825, + 784 + ] + }, + { + "type": "page_number", + "content": { + "page_number_content": [ + { + "type": "text", + "content": "19" + } + ] + }, + "bbox": [ + 490, + 946, + 508, + 959 + ] + } + ] +] \ No newline at end of file diff --git a/papers/markdown/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers/hybrid_auto/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers_layout.pdf b/papers/markdown/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers/hybrid_auto/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers_layout.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c520440541812c4c85a8e740016a04ed3ab3ba80 --- /dev/null +++ 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To", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 143, + 139, + 468, + 148 + ], + "spans": [ + { + "bbox": [ + 143, + 139, + 468, + 148 + ], + "type": "text", + "content": "address these issues, we introduce MeshAnything, a model that treats mesh ex-", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 143, + 150, + 467, + 159 + ], + "spans": [ + { + "bbox": [ + 143, + 150, + 467, + 159 + ], + "type": "text", + "content": "traction as a generation problem, producing AMs aligned with specified shapes.", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 143, + 160, + 468, + 170 + ], + "spans": [ + { + "bbox": [ + 143, + 160, + 468, + 170 + ], + "type": "text", + "content": "By converting 3D assets in any 3D representation into AMs, MeshAnything can", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 143, + 171, + 468, + 181 + ], + "spans": [ + { + "bbox": [ + 143, + 171, + 468, + 181 + ], + "type": "text", + "content": "be integrated with various 3D asset production methods, thereby enhancing their", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 143, + 182, + 468, + 192 + ], + "spans": [ + { + "bbox": [ + 143, + 182, + 468, + 192 + ], + "type": "text", + "content": "application across the 3D industry. 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To", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 139, + 468, + 148 + ], + "spans": [ + { + "bbox": [ + 143, + 139, + 468, + 148 + ], + "type": "text", + "content": "address these issues, we introduce MeshAnything, a model that treats mesh ex-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 150, + 467, + 159 + ], + "spans": [ + { + "bbox": [ + 143, + 150, + 467, + 159 + ], + "type": "text", + "content": "traction as a generation problem, producing AMs aligned with specified shapes.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 160, + 468, + 170 + ], + "spans": [ + { + "bbox": [ + 143, + 160, + 468, + 170 + ], + "type": "text", + "content": "By converting 3D assets in any 3D representation into AMs, MeshAnything can", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 171, + 468, + 181 + ], + "spans": [ + { + "bbox": [ + 143, + 171, + 468, + 181 + ], + "type": "text", + "content": "be integrated with various 3D asset production methods, thereby enhancing their", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 182, + 468, + 192 + ], + "spans": [ + { + "bbox": [ + 143, + 182, + 468, + 192 + ], + "type": "text", + "content": "application across the 3D industry. 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Therefore, substantial efforts Lorensen & Cline (1987); Chernyaev (1995);", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 480, + 503, + 488 + ], + "spans": [ + { + "bbox": [ + 107, + 480, + 503, + 488 + ], + "type": "text", + "content": "Lorensen & Cline (1998); Shen et al. (2021b); Chen et al. (2022); Shen et al. (2023) are devoted", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 491, + 504, + 500 + ], + "spans": [ + { + "bbox": [ + 107, + 491, + 504, + 500 + ], + "type": "text", + "content": "to converting other 3D representations into meshes and have achieved some success. Meshes pro-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 502, + 504, + 511 + ], + "spans": [ + { + "bbox": [ + 107, + 502, + 504, + 511 + ], + "type": "text", + "content": "duced by these methods approximate the shape quality of those created by human artists, which we", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 513, + 504, + 522 + ], + "spans": [ + { + "bbox": [ + 107, + 513, + 504, + 522 + ], + "type": "text", + "content": "refer to as Artist-Created Meshes (AMs), but they still fall short in addressing the aforementioned", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 523, + 135, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 523, + 135, + 533 + ], + "type": "text", + "content": "issues.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 539, + 504, + 661 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 540, + 504, + 550 + ], + "spans": [ + { + "bbox": [ + 107, + 540, + 504, + 550 + ], + "type": "text", + "content": "This is because all meshes produced by these methods Lorensen & Cline (1987); Chernyaev (1995);", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 551, + 503, + 560 + ], + "spans": [ + { + "bbox": [ + 107, + 551, + 503, + 560 + ], + "type": "text", + "content": "Lorensen & Cline (1998); Shen et al. 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The success", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 396, + 503, + 407 + ], + "spans": [ + { + "bbox": [ + 106, + 396, + 503, + 407 + ], + "type": "text", + "content": "of these methods reveals the potential to replace manually created 3D models with automatically", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 408, + 503, + 418 + ], + "spans": [ + { + "bbox": [ + 107, + 408, + 503, + 418 + ], + "type": "text", + "content": "produced ones in the 3D industry, including applications in games, movies, and the metaverse, sig-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 420, + 266, + 427 + ], + "spans": [ + { + "bbox": [ + 107, + 420, + 266, + 427 + ], + "type": "text", + "content": "nificantly reducing time and labor costs.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 434, + 504, + 533 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 436, + 503, + 445 + ], + "spans": [ + { + "bbox": [ + 107, + 436, + 503, + 445 + ], + "type": "text", + "content": "However, this potential remains largely unrealized because the current 3D industry predominantly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 447, + 503, + 456 + ], + "spans": [ + { + "bbox": [ + 107, + 447, + 503, + 456 + ], + "type": "text", + "content": "relies on mesh-based pipelines for their superior efficiency and controllability, while methods for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 458, + 504, + 467 + ], + "spans": [ + { + "bbox": [ + 107, + 458, + 504, + 467 + ], + "type": "text", + "content": "producing 3D assets typically use alternative 3D representations to achieve optimal results across", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 468, + 504, + 478 + ], + "spans": [ + { + "bbox": [ + 107, + 468, + 504, + 478 + ], + "type": "text", + "content": "various scenarios. Therefore, substantial efforts Lorensen & Cline (1987); Chernyaev (1995);", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 480, + 503, + 488 + ], + "spans": [ + { + "bbox": [ + 107, + 480, + 503, + 488 + ], + "type": "text", + "content": "Lorensen & Cline (1998); Shen et al. (2021b); Chen et al. (2022); Shen et al. (2023) are devoted", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 491, + 504, + 500 + ], + "spans": [ + { + "bbox": [ + 107, + 491, + 504, + 500 + ], + "type": "text", + "content": "to converting other 3D representations into meshes and have achieved some success. Meshes pro-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 502, + 504, + 511 + ], + "spans": [ + { + "bbox": [ + 107, + 502, + 504, + 511 + ], + "type": "text", + "content": "duced by these methods approximate the shape quality of those created by human artists, which we", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 513, + 504, + 522 + ], + "spans": [ + { + "bbox": [ + 107, + 513, + 504, + 522 + ], + "type": "text", + "content": "refer to as Artist-Created Meshes (AMs), but they still fall short in addressing the aforementioned", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 523, + 135, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 523, + 135, + 533 + ], + "type": "text", + "content": "issues.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 539, + 504, + 661 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 540, + 504, + 550 + ], + "spans": [ + { + "bbox": [ + 107, + 540, + 504, + 550 + ], + "type": "text", + "content": "This is because all meshes produced by these methods Lorensen & Cline (1987); Chernyaev (1995);", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 551, + 503, + 560 + ], + "spans": [ + { + "bbox": [ + 107, + 551, + 503, + 560 + ], + "type": "text", + "content": "Lorensen & Cline (1998); Shen et al. (2021b); Chen et al. (2022); Shen et al. (2023) exhibit signifi-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 562, + 504, + 572 + ], + "spans": [ + { + "bbox": [ + 106, + 562, + 504, + 572 + ], + "type": "text", + "content": "cantly poorer topology quality compared to AMs. As shown in Fig. 2, these methods rely on dense", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 572, + 504, + 583 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 504, + 583 + ], + "type": "text", + "content": "faces to reconstruct 3D shapes, completely ignoring geometric characteristics. Using these meshes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 585, + 504, + 594 + ], + "spans": [ + { + "bbox": [ + 107, + 585, + 504, + 594 + ], + "type": "text", + "content": "in the 3D industry leads to three significant problems: First, converted meshes typically contain", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 595, + 504, + 605 + ], + "spans": [ + { + "bbox": [ + 106, + 595, + 504, + 605 + ], + "type": "text", + "content": "several orders of magnitude more faces compared to AMs, leading to significant inefficiencies in", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 606, + 504, + 616 + ], + "spans": [ + { + "bbox": [ + 107, + 606, + 504, + 616 + ], + "type": "text", + "content": "storage, rendering, and simulation. Moreover, the converted meshes complicate post-processing and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 617, + 504, + 628 + ], + "spans": [ + { + "bbox": [ + 107, + 617, + 504, + 628 + ], + "type": "text", + "content": "downstream tasks in the 3D pipeline. They significantly increase the challenge for human artists in", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 628, + 503, + 637 + ], + "spans": [ + { + "bbox": [ + 107, + 628, + 503, + 637 + ], + "type": "text", + "content": "optimizing these meshes due to their chaotic and inefficient topologies. Finally, previous methods", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 639, + 503, + 648 + ], + "spans": [ + { + "bbox": [ + 107, + 639, + 503, + 648 + ], + "type": "text", + "content": "struggle to represent sharp edges and flat surfaces, resulting in oversmoothing and bumpy artifacts", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 650, + 182, + 659 + ], + "spans": [ + { + "bbox": [ + 107, + 650, + 182, + 659 + ], + "type": "text", + "content": "as shown in Fig. 2.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 666, + 504, + 733 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 667, + 503, + 676 + ], + "spans": [ + { + "bbox": [ + 107, + 667, + 503, + 676 + ], + "type": "text", + "content": "In this work, we aim to solve the aforementioned issues to facilitate the application of automatically", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 678, + 504, + 687 + ], + "spans": [ + { + "bbox": [ + 107, + 678, + 504, + 687 + ], + "type": "text", + "content": "generated 3D assets in the 3D industry. As mentioned earlier, all previous methods Lorensen & Cline", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 689, + 504, + 699 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 504, + 699 + ], + "type": "text", + "content": "(1987); Chernyaev (1995); Lorensen & Cline (1998); Shen et al. (2021b); Chen et al. (2022); Shen", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 503, + 709 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 503, + 709 + ], + "type": "text", + "content": "et al. (2023) extract 3D meshes with excessively dense faces in a reconstruction manner, which in-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 712, + 504, + 720 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 504, + 720 + ], + "type": "text", + "content": "herently cannot solve these issues. Therefore, we diverge from previous approaches by formulating", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 722, + 503, + 731 + ], + "spans": [ + { + "bbox": [ + 107, + 722, + 503, + 731 + ], + "type": "text", + "content": "mesh extraction as a generation problem for the first time: we teach models to generate Artist-", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 108, + 79, + 504, + 340 + ], + "blocks": [ + { + "bbox": [ + 108, + 79, + 504, + 340 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 79, + 504, + 340 + ], + "spans": [ + { + "bbox": [ + 108, + 79, + 504, + 340 + ], + "type": "image", + "content": "Faces: 90k\nVertices: 45k\nMarching Cubes\nFaces: 33k\nVertices: 53k\nRemesh-0.01\nFaces: 3.5k\nVertices: 6.7k\nRemesh-0.03\nFaces: 1.1k\nVertices: 2.2k\nRemesh-0.05\nFaces: 0.28k\nVertices: 0.57k\nRemesh-0.10\nFaces: 0.64k\nVertices: 0.31k\nMeshAnything\nFaces: 200k\nVertices: 100k\nMarching Cubes\nFaces: 84k\nVertices: 132k\nRemesh-0.01\nFaces: 7.4k\nVertices: 13k\nRemesh-0.03\nFaces: 2k\nVertices: 3.9k\nRemesh-0.05\nFaces: 0.46k\nVertices: 0.92k\nRemesh-0.10\nFaces: 0.80k\nVertices: 0.47k\nMeshAnything", + "image_path": "9fa5b06a364431abe5830c26121adaca68b8bb5f0c40aa46d34f732c3aea7e4c.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 350, + 504, + 417 + ], + "type": "image_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 352, + 504, + 361 + ], + "spans": [ + { + "bbox": [ + 107, + 352, + 504, + 361 + ], + "type": "text", + "content": "Figure 2: Comparison with Marching Cubes Lorensen & Cline (1987) and Remesh Blender", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 362, + 504, + 373 + ], + "spans": [ + { + "bbox": [ + 107, + 362, + 504, + 373 + ], + "type": "text", + "content": "Development Team (2024). We apply Marching Cubes and MeshAnything to ground truth shapes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 374, + 503, + 383 + ], + "spans": [ + { + "bbox": [ + 107, + 374, + 503, + 383 + ], + "type": "text", + "content": "and then apply remeshing to the Marching Cubes results with different voxel sizes. Existing meth-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 384, + 504, + 394 + ], + "spans": [ + { + "bbox": [ + 107, + 384, + 504, + 394 + ], + "type": "text", + "content": "ods extract meshes in a reconstruction manner, ignoring the geometric features of the object and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 396, + 503, + 406 + ], + "spans": [ + { + "bbox": [ + 107, + 396, + 503, + 406 + ], + "type": "text", + "content": "producing dense meshes with poor topology. These methods fundamentally fail to capture sharp", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 407, + 337, + 416 + ], + "spans": [ + { + "bbox": [ + 107, + 407, + 337, + 416 + ], + "type": "text", + "content": "edges and flat surfaces, as shown in the zoomed-in figure.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_type": "text_image" + }, + { + "bbox": [ + 104, + 439, + 504, + 485 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 441, + 504, + 451 + ], + "spans": [ + { + "bbox": [ + 107, + 441, + 504, + 451 + ], + "type": "text", + "content": "Created Meshes (AMs) that are aligned with the given 3D assets. The meshes generated by our", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 452, + 504, + 461 + ], + "spans": [ + { + "bbox": [ + 107, + 452, + 504, + 461 + ], + "type": "text", + "content": "methods mimic the shape and topology quality of those created by human artists. Consequently, our", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 463, + 504, + 472 + ], + "spans": [ + { + "bbox": [ + 107, + 463, + 504, + 472 + ], + "type": "text", + "content": "setting, namely Shape-Conditioned AM Generation, is fundamentally free from all previous issues,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 474, + 440, + 483 + ], + "spans": [ + { + "bbox": [ + 107, + 474, + 440, + 483 + ], + "type": "text", + "content": "enabling seamless integration of the generated results into the 3D industry pipeline.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 489, + 504, + 578 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 106, + 490, + 504, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 490, + 504, + 500 + ], + "type": "text", + "content": "However, training such a model presents significant challenges. The first challenge is constructing", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 502, + 503, + 510 + ], + "spans": [ + { + "bbox": [ + 107, + 502, + 503, + 510 + ], + "type": "text", + "content": "the dataset, as we need paired shape conditions and Artist-Created Meshes (AMs) for model train-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 512, + 504, + 522 + ], + "spans": [ + { + "bbox": [ + 106, + 512, + 504, + 522 + ], + "type": "text", + "content": "ing. The shape condition must be efficiently derived from as many diverse 3D representations as", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 524, + 504, + 533 + ], + "spans": [ + { + "bbox": [ + 107, + 524, + 504, + 533 + ], + "type": "text", + "content": "possible to serve as a condition during inference. Additionally, it must have sufficient precision to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 535, + 503, + 544 + ], + "spans": [ + { + "bbox": [ + 107, + 535, + 503, + 544 + ], + "type": "text", + "content": "accurately represent 3D shapes and be efficiently processed into features that can be injected into", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 545, + 504, + 555 + ], + "spans": [ + { + "bbox": [ + 106, + 545, + 504, + 555 + ], + "type": "text", + "content": "the model. After weighing the trade-offs, we chose point clouds due to their explicit and continuous", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 557, + 504, + 566 + ], + "spans": [ + { + "bbox": [ + 107, + 557, + 504, + 566 + ], + "type": "text", + "content": "representation, ease of derivation from most 3D representations, and the availability of mature point", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 567, + 321, + 576 + ], + "spans": [ + { + "bbox": [ + 107, + 567, + 321, + 576 + ], + "type": "text", + "content": "cloud encoders Qi et al. (2017a;b); Zhao et al. (2024).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 582, + 504, + 683 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 584, + 503, + 594 + ], + "spans": [ + { + "bbox": [ + 107, + 584, + 503, + 594 + ], + "type": "text", + "content": "We filter out high-quality AMs from Objaverse Deitke et al. (2023b;a) and ShapeNet Chang et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 595, + 503, + 605 + ], + "spans": [ + { + "bbox": [ + 107, + 595, + 503, + 605 + ], + "type": "text", + "content": "(2015). When obtaining paired shape conditions, a naive approach would be to sample point clouds", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 606, + 504, + 616 + ], + "spans": [ + { + "bbox": [ + 107, + 606, + 504, + 616 + ], + "type": "text", + "content": "directly from AMs. However, this leads to poor results during inference because the sampled", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "spans": [ + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "type": "text", + "content": "point clouds have excessive precision, while automatically produced 3D assets cannot provide point", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 628, + 504, + 638 + ], + "spans": [ + { + "bbox": [ + 107, + 628, + 504, + 638 + ], + "type": "text", + "content": "clouds of similar quality, causing a domain gap between training and inference. To address this", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 639, + 504, + 649 + ], + "spans": [ + { + "bbox": [ + 107, + 639, + 504, + 649 + ], + "type": "text", + "content": "issue, we intentionally corrupt the shape quality of AMs. We first extract the signed distance func-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 650, + 503, + 660 + ], + "spans": [ + { + "bbox": [ + 107, + 650, + 503, + 660 + ], + "type": "text", + "content": "tion from AMs Wang et al. (2022), convert it into a coarser mesh using Lorensen & Cline (1987),", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 662, + 503, + 670 + ], + "spans": [ + { + "bbox": [ + 107, + 662, + 503, + 670 + ], + "type": "text", + "content": "and then sample point clouds from this coarse mesh to narrow the domain gap in shape conditions", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 671, + 233, + 681 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 233, + 681 + ], + "type": "text", + "content": "between inference and training.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 687, + 504, + 733 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 689, + 503, + 698 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 503, + 698 + ], + "type": "text", + "content": "Following Siddiqui et al. (2023), we use a VQ-VAE Van Den Oord et al. (2017) to learn a mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 504, + 710 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 504, + 710 + ], + "type": "text", + "content": "vocabulary and train a decoder-only transformer Vaswani et al. (2017) on this vocabulary for mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 711, + 503, + 720 + ], + "spans": [ + { + "bbox": [ + 107, + 711, + 503, + 720 + ], + "type": "text", + "content": "generation. To inject shape condition, we draw inspiration from the recent success of multimodal", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 721, + 504, + 731 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 504, + 731 + ], + "type": "text", + "content": "large language models (MLLM) Wu et al. (2023); Liu et al. (2024a), where image features encoded", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 751, + 308, + 760 + ], + "type": "page_number", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 761 + ], + "type": "text", + "content": "3", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2, + "para_blocks": [ + { + "type": "image", + "bbox": [ + 108, + 79, + 504, + 340 + ], + "blocks": [ + { + "bbox": [ + 108, + 79, + 504, + 340 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 79, + 504, + 340 + ], + "spans": [ + { + "bbox": [ + 108, + 79, + 504, + 340 + ], + "type": "image", + "content": "Faces: 90k\nVertices: 45k\nMarching Cubes\nFaces: 33k\nVertices: 53k\nRemesh-0.01\nFaces: 3.5k\nVertices: 6.7k\nRemesh-0.03\nFaces: 1.1k\nVertices: 2.2k\nRemesh-0.05\nFaces: 0.28k\nVertices: 0.57k\nRemesh-0.10\nFaces: 0.64k\nVertices: 0.31k\nMeshAnything\nFaces: 200k\nVertices: 100k\nMarching Cubes\nFaces: 84k\nVertices: 132k\nRemesh-0.01\nFaces: 7.4k\nVertices: 13k\nRemesh-0.03\nFaces: 2k\nVertices: 3.9k\nRemesh-0.05\nFaces: 0.46k\nVertices: 0.92k\nRemesh-0.10\nFaces: 0.80k\nVertices: 0.47k\nMeshAnything", + "image_path": "9fa5b06a364431abe5830c26121adaca68b8bb5f0c40aa46d34f732c3aea7e4c.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 350, + 504, + 417 + ], + "type": "image_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 352, + 504, + 361 + ], + "spans": [ + { + "bbox": [ + 107, + 352, + 504, + 361 + ], + "type": "text", + "content": "Figure 2: Comparison with Marching Cubes Lorensen & Cline (1987) and Remesh Blender", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 362, + 504, + 373 + ], + "spans": [ + { + "bbox": [ + 107, + 362, + 504, + 373 + ], + "type": "text", + "content": "Development Team (2024). We apply Marching Cubes and MeshAnything to ground truth shapes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 374, + 503, + 383 + ], + "spans": [ + { + "bbox": [ + 107, + 374, + 503, + 383 + ], + "type": "text", + "content": "and then apply remeshing to the Marching Cubes results with different voxel sizes. Existing meth-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 384, + 504, + 394 + ], + "spans": [ + { + "bbox": [ + 107, + 384, + 504, + 394 + ], + "type": "text", + "content": "ods extract meshes in a reconstruction manner, ignoring the geometric features of the object and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 396, + 503, + 406 + ], + "spans": [ + { + "bbox": [ + 107, + 396, + 503, + 406 + ], + "type": "text", + "content": "producing dense meshes with poor topology. These methods fundamentally fail to capture sharp", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 407, + 337, + 416 + ], + "spans": [ + { + "bbox": [ + 107, + 407, + 337, + 416 + ], + "type": "text", + "content": "edges and flat surfaces, as shown in the zoomed-in figure.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_type": "text_image" + }, + { + "bbox": [ + 104, + 439, + 504, + 485 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 441, + 504, + 451 + ], + "spans": [ + { + "bbox": [ + 107, + 441, + 504, + 451 + ], + "type": "text", + "content": "Created Meshes (AMs) that are aligned with the given 3D assets. The meshes generated by our", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 452, + 504, + 461 + ], + "spans": [ + { + "bbox": [ + 107, + 452, + 504, + 461 + ], + "type": "text", + "content": "methods mimic the shape and topology quality of those created by human artists. Consequently, our", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 463, + 504, + 472 + ], + "spans": [ + { + "bbox": [ + 107, + 463, + 504, + 472 + ], + "type": "text", + "content": "setting, namely Shape-Conditioned AM Generation, is fundamentally free from all previous issues,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 474, + 440, + 483 + ], + "spans": [ + { + "bbox": [ + 107, + 474, + 440, + 483 + ], + "type": "text", + "content": "enabling seamless integration of the generated results into the 3D industry pipeline.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 489, + 504, + 578 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 106, + 490, + 504, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 490, + 504, + 500 + ], + "type": "text", + "content": "However, training such a model presents significant challenges. The first challenge is constructing", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 502, + 503, + 510 + ], + "spans": [ + { + "bbox": [ + 107, + 502, + 503, + 510 + ], + "type": "text", + "content": "the dataset, as we need paired shape conditions and Artist-Created Meshes (AMs) for model train-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 512, + 504, + 522 + ], + "spans": [ + { + "bbox": [ + 106, + 512, + 504, + 522 + ], + "type": "text", + "content": "ing. The shape condition must be efficiently derived from as many diverse 3D representations as", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 524, + 504, + 533 + ], + "spans": [ + { + "bbox": [ + 107, + 524, + 504, + 533 + ], + "type": "text", + "content": "possible to serve as a condition during inference. Additionally, it must have sufficient precision to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 535, + 503, + 544 + ], + "spans": [ + { + "bbox": [ + 107, + 535, + 503, + 544 + ], + "type": "text", + "content": "accurately represent 3D shapes and be efficiently processed into features that can be injected into", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 545, + 504, + 555 + ], + "spans": [ + { + "bbox": [ + 106, + 545, + 504, + 555 + ], + "type": "text", + "content": "the model. After weighing the trade-offs, we chose point clouds due to their explicit and continuous", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 557, + 504, + 566 + ], + "spans": [ + { + "bbox": [ + 107, + 557, + 504, + 566 + ], + "type": "text", + "content": "representation, ease of derivation from most 3D representations, and the availability of mature point", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 567, + 321, + 576 + ], + "spans": [ + { + "bbox": [ + 107, + 567, + 321, + 576 + ], + "type": "text", + "content": "cloud encoders Qi et al. (2017a;b); Zhao et al. (2024).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 582, + 504, + 683 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 584, + 503, + 594 + ], + "spans": [ + { + "bbox": [ + 107, + 584, + 503, + 594 + ], + "type": "text", + "content": "We filter out high-quality AMs from Objaverse Deitke et al. (2023b;a) and ShapeNet Chang et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 595, + 503, + 605 + ], + "spans": [ + { + "bbox": [ + 107, + 595, + 503, + 605 + ], + "type": "text", + "content": "(2015). When obtaining paired shape conditions, a naive approach would be to sample point clouds", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 606, + 504, + 616 + ], + "spans": [ + { + "bbox": [ + 107, + 606, + 504, + 616 + ], + "type": "text", + "content": "directly from AMs. However, this leads to poor results during inference because the sampled", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "spans": [ + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "type": "text", + "content": "point clouds have excessive precision, while automatically produced 3D assets cannot provide point", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 628, + 504, + 638 + ], + "spans": [ + { + "bbox": [ + 107, + 628, + 504, + 638 + ], + "type": "text", + "content": "clouds of similar quality, causing a domain gap between training and inference. To address this", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 639, + 504, + 649 + ], + "spans": [ + { + "bbox": [ + 107, + 639, + 504, + 649 + ], + "type": "text", + "content": "issue, we intentionally corrupt the shape quality of AMs. We first extract the signed distance func-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 650, + 503, + 660 + ], + "spans": [ + { + "bbox": [ + 107, + 650, + 503, + 660 + ], + "type": "text", + "content": "tion from AMs Wang et al. (2022), convert it into a coarser mesh using Lorensen & Cline (1987),", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 662, + 503, + 670 + ], + "spans": [ + { + "bbox": [ + 107, + 662, + 503, + 670 + ], + "type": "text", + "content": "and then sample point clouds from this coarse mesh to narrow the domain gap in shape conditions", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 671, + 233, + 681 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 233, + 681 + ], + "type": "text", + "content": "between inference and training.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 687, + 504, + 733 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 689, + 503, + 698 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 503, + 698 + ], + "type": "text", + "content": "Following Siddiqui et al. (2023), we use a VQ-VAE Van Den Oord et al. (2017) to learn a mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 504, + 710 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 504, + 710 + ], + "type": "text", + "content": "vocabulary and train a decoder-only transformer Vaswani et al. (2017) on this vocabulary for mesh", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 711, + 503, + 720 + ], + "spans": [ + { + "bbox": [ + 107, + 711, + 503, + 720 + ], + "type": "text", + "content": "generation. To inject shape condition, we draw inspiration from the recent success of multimodal", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 721, + 504, + 731 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 504, + 731 + ], + "type": "text", + "content": "large language models (MLLM) Wu et al. (2023); Liu et al. (2024a), where image features encoded", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 84, + 503, + 93 + ], + "spans": [ + { + "bbox": [ + 107, + 84, + 503, + 93 + ], + "type": "text", + "content": "by pre-trained image encoders are projected into the token space of the large language models for", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 95, + 504, + 104 + ], + "spans": [ + { + "bbox": [ + 107, + 95, + 504, + 104 + ], + "type": "text", + "content": "efficient multimodal understanding. Similarly, we treat the mesh tokens obtained from the trained", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 106, + 503, + 114 + ], + "spans": [ + { + "bbox": [ + 107, + 106, + 503, + 114 + ], + "type": "text", + "content": "VQ-VAE as the language token in LLMs and use a pre-trained encoder Zhao et al. (2024) to encode", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 117, + 504, + 126 + ], + "spans": [ + { + "bbox": [ + 107, + 117, + 504, + 126 + ], + "type": "text", + "content": "the point clouds into shape features, which is later projected into the mesh token space. These shape", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 128, + 503, + 137 + ], + "spans": [ + { + "bbox": [ + 107, + 128, + 503, + 137 + ], + "type": "text", + "content": "tokens are placed at the beginning of the mesh token sequences, effectively serving as the shape", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 138, + 504, + 148 + ], + "spans": [ + { + "bbox": [ + 107, + 138, + 504, + 148 + ], + "type": "text", + "content": "conditions for next-token predictions. After predictions, these predicted mesh tokens are decoded", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 150, + 365, + 159 + ], + "spans": [ + { + "bbox": [ + 107, + 150, + 365, + 159 + ], + "type": "text", + "content": "back to meshes with the VQ-VAE decoder Siddiqui et al. (2023).", + "score": 1.0, + "cross_page": true + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "bbox": [ + 104, + 83, + 504, + 160 + ], + "type": "text", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 107, + 84, + 503, + 93 + ], + "spans": [ + { + "bbox": [ + 107, + 84, + 503, + 93 + ], + "type": "text", + "content": "by pre-trained image encoders are projected into the token space of the large language models for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 95, + 504, + 104 + ], + "spans": [ + { + "bbox": [ + 107, + 95, + 504, + 104 + ], + "type": "text", + "content": "efficient multimodal understanding. Similarly, we treat the mesh tokens obtained from the trained", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 106, + 503, + 114 + ], + "spans": [ + { + "bbox": [ + 107, + 106, + 503, + 114 + ], + "type": "text", + "content": "VQ-VAE as the language token in LLMs and use a pre-trained encoder Zhao et al. (2024) to encode", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 117, + 504, + 126 + ], + "spans": [ + { + "bbox": [ + 107, + 117, + 504, + 126 + ], + "type": "text", + "content": "the point clouds into shape features, which is later projected into the mesh token space. These shape", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 128, + 503, + 137 + ], + "spans": [ + { + "bbox": [ + 107, + 128, + 503, + 137 + ], + "type": "text", + "content": "tokens are placed at the beginning of the mesh token sequences, effectively serving as the shape", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 138, + 504, + 148 + ], + "spans": [ + { + "bbox": [ + 107, + 138, + 504, + 148 + ], + "type": "text", + "content": "conditions for next-token predictions. After predictions, these predicted mesh tokens are decoded", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 150, + 365, + 159 + ], + "spans": [ + { + "bbox": [ + 107, + 150, + 365, + 159 + ], + "type": "text", + "content": "back to meshes with the VQ-VAE decoder Siddiqui et al. (2023).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 165, + 506, + 255 + ], + "type": "text", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 167, + 504, + 175 + ], + "spans": [ + { + "bbox": [ + 107, + 167, + 504, + 175 + ], + "type": "text", + "content": "To further enhance the quality of mesh generation, we develop a novel noise-resistant decoder for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 178, + 503, + 186 + ], + "spans": [ + { + "bbox": [ + 107, + 178, + 503, + 186 + ], + "type": "text", + "content": "robust mesh decoding. Our observation is that as the decoder in the VQ-VAE Van Den Oord et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 188, + 504, + 198 + ], + "spans": [ + { + "bbox": [ + 107, + 188, + 504, + 198 + ], + "type": "text", + "content": "(2017) is only trained with ground truth token sequences from the encoder, it could potentially lead", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 199, + 504, + 209 + ], + "spans": [ + { + "bbox": [ + 107, + 199, + 504, + 209 + ], + "type": "text", + "content": "to a domain gap when decoding the generated token sequences. To mitigate this problem, we inject", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 210, + 503, + 219 + ], + "spans": [ + { + "bbox": [ + 107, + 210, + 503, + 219 + ], + "type": "text", + "content": "the shape condition into the VQ-VAE decoder as auxiliary information for robust decoding and fine-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 221, + 503, + 230 + ], + "spans": [ + { + "bbox": [ + 107, + 221, + 503, + 230 + ], + "type": "text", + "content": "tune it after the VQ-VAE training. This fine-tuning process involves adding noise to the mesh token", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 233, + 503, + 241 + ], + "spans": [ + { + "bbox": [ + 107, + 233, + 503, + 241 + ], + "type": "text", + "content": "sequences to simulate possible poor-quality token sequences from the decoder-only transformer,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 243, + 360, + 253 + ], + "spans": [ + { + "bbox": [ + 107, + 243, + 360, + 253 + ], + "type": "text", + "content": "thus making the decoder robust to such poor-quality sequences.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 258, + 504, + 315 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 260, + 503, + 270 + ], + "spans": [ + { + "bbox": [ + 107, + 260, + 503, + 270 + ], + "type": "text", + "content": "Finally, we introduce our model, MeshAnything, trained based on the aforementioned techniques.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 272, + 503, + 280 + ], + "spans": [ + { + "bbox": [ + 107, + 272, + 503, + 280 + ], + "type": "text", + "content": "As shown in Fig. 1, MeshAnything can convert 3D assets across various 3D representations into", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 282, + 504, + 292 + ], + "spans": [ + { + "bbox": [ + 107, + 282, + 504, + 292 + ], + "type": "text", + "content": "AMs, thereby significantly facilitating their application. Furthermore, our extensive experiments", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 293, + 503, + 302 + ], + "spans": [ + { + "bbox": [ + 107, + 293, + 503, + 302 + ], + "type": "text", + "content": "demonstrate that our method generates AMs with significantly fewer faces and more refined topol-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 304, + 481, + 314 + ], + "spans": [ + { + "bbox": [ + 107, + 304, + 481, + 314 + ], + "type": "text", + "content": "ogy, while achieving precision metrics that are close to or comparable with previous methods.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 319, + 289, + 331 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 321, + 288, + 331 + ], + "spans": [ + { + "bbox": [ + 107, + 321, + 288, + 331 + ], + "type": "text", + "content": "In summary, our contributions are as follows:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 132, + 342, + 504, + 526 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 132, + 342, + 504, + 397 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 135, + 343, + 504, + 353 + ], + "spans": [ + { + "bbox": [ + 135, + 343, + 504, + 353 + ], + "type": "text", + "content": "• We highlight one important reason why current automatically produced 3D assets can-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 354, + 504, + 364 + ], + "spans": [ + { + "bbox": [ + 142, + 354, + 504, + 364 + ], + "type": "text", + "content": "not replace those created by human artists: current methods cannot convert these 3D as-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 365, + 504, + 375 + ], + "spans": [ + { + "bbox": [ + 142, + 365, + 504, + 375 + ], + "type": "text", + "content": "sets into Artist-Created Meshes (AMs). To solve this issue, we propose a novel solution", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 376, + 504, + 385 + ], + "spans": [ + { + "bbox": [ + 143, + 376, + 504, + 385 + ], + "type": "text", + "content": "called Shape-Conditioned AM Generation, which aims to generate AMs aligned with given", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 141, + 387, + 173, + 398 + ], + "spans": [ + { + "bbox": [ + 141, + 387, + 173, + 398 + ], + "type": "text", + "content": "shapes.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 132, + 403, + 504, + 437 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 133, + 403, + 504, + 415 + ], + "spans": [ + { + "bbox": [ + 133, + 403, + 504, + 415 + ], + "type": "text", + "content": "• We introduce MeshAnything for Shape-Conditioned AM Generation. MeshAnything can", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 415, + 504, + 425 + ], + "spans": [ + { + "bbox": [ + 142, + 415, + 504, + 425 + ], + "type": "text", + "content": "be integrated with various 3D asset production methods, converting their results into AMs", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 426, + 332, + 437 + ], + "spans": [ + { + "bbox": [ + 142, + 426, + 332, + 437 + ], + "type": "text", + "content": "to facilitate their application in the 3D industry.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 132, + 443, + 504, + 486 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 134, + 443, + 503, + 453 + ], + "spans": [ + { + "bbox": [ + 134, + 443, + 503, + 453 + ], + "type": "text", + "content": "• We develop a novel noise-resistant decoder to enhance mesh generation quality. We in-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 141, + 455, + 504, + 464 + ], + "spans": [ + { + "bbox": [ + 141, + 455, + 504, + 464 + ], + "type": "text", + "content": "ject the shape condition into the decoder as auxiliary information for robust decoding and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 467, + 504, + 475 + ], + "spans": [ + { + "bbox": [ + 142, + 467, + 504, + 475 + ], + "type": "text", + "content": "fine-tune it using noised token sequences to narrow the domain gap between training and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 141, + 476, + 184, + 487 + ], + "spans": [ + { + "bbox": [ + 141, + 476, + 184, + 487 + ], + "type": "text", + "content": "inference.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 132, + 493, + 504, + 526 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 134, + 495, + 504, + 504 + ], + "spans": [ + { + "bbox": [ + 134, + 495, + 504, + 504 + ], + "type": "text", + "content": "• Extensive experiments demonstrate that Shape-Conditioned Mesh Generation is a more", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 505, + 504, + 515 + ], + "spans": [ + { + "bbox": [ + 142, + 505, + 504, + 515 + ], + "type": "text", + "content": "suitable setting for mesh generation, and MeshAnything significantly surpasses previous", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 517, + 247, + 525 + ], + "spans": [ + { + "bbox": [ + 143, + 517, + 247, + 525 + ], + "type": "text", + "content": "mesh generation methods.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 105, + 545, + 217, + 558 + ], + "type": "title", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 106, + 546, + 216, + 557 + ], + "spans": [ + { + "bbox": [ + 106, + 546, + 216, + 557 + ], + "type": "text", + "content": "2 RELATED WORKS", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 105, + 572, + 217, + 583 + ], + "type": "title", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 573, + 216, + 583 + ], + "spans": [ + { + "bbox": [ + 107, + 573, + 216, + 583 + ], + "type": "text", + "content": "2.1 MESH EXTRACTION", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 594, + 504, + 661 + ], + "type": "text", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 107, + 595, + 504, + 604 + ], + "spans": [ + { + "bbox": [ + 107, + 595, + 504, + 604 + ], + "type": "text", + "content": "Methods for extracting meshes from 3D models are numerous and have been a subject of research for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 605, + 504, + 616 + ], + "spans": [ + { + "bbox": [ + 107, + 605, + 504, + 616 + ], + "type": "text", + "content": "decades. Following Shen et al. (2023), we categorize these methods into two main types: Isosurface", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 105, + 616, + 504, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 504, + 628 + ], + "type": "text", + "content": "Extraction Lorensen & Cline (1987); Bloomenthal (1988); Chernyaev (1995); Bloomenthal & Bajaj", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 628, + 504, + 637 + ], + "spans": [ + { + "bbox": [ + 107, + 628, + 504, + 637 + ], + "type": "text", + "content": "(1997); Lorensen & Cline (1998); Chen et al. (2022) and Gradient-Based Mesh Optimization Chen", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 639, + 503, + 648 + ], + "spans": [ + { + "bbox": [ + 107, + 639, + 503, + 648 + ], + "type": "text", + "content": "et al. (2019); Gao et al. (2020); Hanocka et al. (2020); Kato et al. (2018); Shen et al. (2021a); Liao", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 650, + 235, + 659 + ], + "spans": [ + { + "bbox": [ + 107, + 650, + 235, + 659 + ], + "type": "text", + "content": "et al. (2018); Shen et al. (2023).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 665, + 506, + 733 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 107, + 666, + 503, + 676 + ], + "spans": [ + { + "bbox": [ + 107, + 666, + 503, + 676 + ], + "type": "text", + "content": "Traditional isosurface extraction methods Lorensen & Cline (1987; 1998); Chernyaev (1995); Doi", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 677, + 503, + 687 + ], + "spans": [ + { + "bbox": [ + 107, + 677, + 503, + 687 + ], + "type": "text", + "content": "& Koide (1991); Ju et al. (2002); Schaefer et al. (2007); Chen & Zhang (2021); Chen et al. (2022)", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 689, + 504, + 698 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 504, + 698 + ], + "type": "text", + "content": "focus on extracting a polygonal mesh that represents the level set of a scalar function, an area that", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 504, + 709 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 504, + 709 + ], + "type": "text", + "content": "has seen extensive study in various fields. The most popular method among them is Marching", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 711, + 504, + 720 + ], + "spans": [ + { + "bbox": [ + 107, + 711, + 504, + 720 + ], + "type": "text", + "content": "Cubes Lorensen & Cline (1987). It divides the space into cells, within which polygons are created", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 721, + 503, + 731 + ], + "spans": [ + { + "bbox": [ + 107, + 721, + 503, + 731 + ], + "type": "text", + "content": "to approximate the surface. Marching Cubes has been widely used for mesh extraction its robust-", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 751, + 309, + 760 + ], + "type": "page_number", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 302, + 752, + 309, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 752, + 309, + 761 + ], + "type": "text", + "content": "4", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3, + "para_blocks": [ + { + "bbox": [ + 104, + 83, + 504, + 160 + ], + "type": "text", + "angle": 0, + "index": 0, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 104, + 165, + 506, + 255 + ], + "type": "text", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 167, + 504, + 175 + ], + "spans": [ + { + "bbox": [ + 107, + 167, + 504, + 175 + ], + "type": "text", + "content": "To further enhance the quality of mesh generation, we develop a novel noise-resistant decoder for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 178, + 503, + 186 + ], + "spans": [ + { + "bbox": [ + 107, + 178, + 503, + 186 + ], + "type": "text", + "content": "robust mesh decoding. Our observation is that as the decoder in the VQ-VAE Van Den Oord et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 188, + 504, + 198 + ], + "spans": [ + { + "bbox": [ + 107, + 188, + 504, + 198 + ], + "type": "text", + "content": "(2017) is only trained with ground truth token sequences from the encoder, it could potentially lead", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 199, + 504, + 209 + ], + "spans": [ + { + "bbox": [ + 107, + 199, + 504, + 209 + ], + "type": "text", + "content": "to a domain gap when decoding the generated token sequences. To mitigate this problem, we inject", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 210, + 503, + 219 + ], + "spans": [ + { + "bbox": [ + 107, + 210, + 503, + 219 + ], + "type": "text", + "content": "the shape condition into the VQ-VAE decoder as auxiliary information for robust decoding and fine-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 221, + 503, + 230 + ], + "spans": [ + { + "bbox": [ + 107, + 221, + 503, + 230 + ], + "type": "text", + "content": "tune it after the VQ-VAE training. This fine-tuning process involves adding noise to the mesh token", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 233, + 503, + 241 + ], + "spans": [ + { + "bbox": [ + 107, + 233, + 503, + 241 + ], + "type": "text", + "content": "sequences to simulate possible poor-quality token sequences from the decoder-only transformer,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 243, + 360, + 253 + ], + "spans": [ + { + "bbox": [ + 107, + 243, + 360, + 253 + ], + "type": "text", + "content": "thus making the decoder robust to such poor-quality sequences.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 258, + 504, + 315 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 260, + 503, + 270 + ], + "spans": [ + { + "bbox": [ + 107, + 260, + 503, + 270 + ], + "type": "text", + "content": "Finally, we introduce our model, MeshAnything, trained based on the aforementioned techniques.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 272, + 503, + 280 + ], + "spans": [ + { + "bbox": [ + 107, + 272, + 503, + 280 + ], + "type": "text", + "content": "As shown in Fig. 1, MeshAnything can convert 3D assets across various 3D representations into", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 282, + 504, + 292 + ], + "spans": [ + { + "bbox": [ + 107, + 282, + 504, + 292 + ], + "type": "text", + "content": "AMs, thereby significantly facilitating their application. Furthermore, our extensive experiments", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 293, + 503, + 302 + ], + "spans": [ + { + "bbox": [ + 107, + 293, + 503, + 302 + ], + "type": "text", + "content": "demonstrate that our method generates AMs with significantly fewer faces and more refined topol-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 304, + 481, + 314 + ], + "spans": [ + { + "bbox": [ + 107, + 304, + 481, + 314 + ], + "type": "text", + "content": "ogy, while achieving precision metrics that are close to or comparable with previous methods.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 319, + 289, + 331 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 321, + 288, + 331 + ], + "spans": [ + { + "bbox": [ + 107, + 321, + 288, + 331 + ], + "type": "text", + "content": "In summary, our contributions are as follows:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 132, + 342, + 504, + 526 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 132, + 342, + 504, + 397 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 135, + 343, + 504, + 353 + ], + "spans": [ + { + "bbox": [ + 135, + 343, + 504, + 353 + ], + "type": "text", + "content": "• We highlight one important reason why current automatically produced 3D assets can-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 354, + 504, + 364 + ], + "spans": [ + { + "bbox": [ + 142, + 354, + 504, + 364 + ], + "type": "text", + "content": "not replace those created by human artists: current methods cannot convert these 3D as-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 365, + 504, + 375 + ], + "spans": [ + { + "bbox": [ + 142, + 365, + 504, + 375 + ], + "type": "text", + "content": "sets into Artist-Created Meshes (AMs). To solve this issue, we propose a novel solution", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 376, + 504, + 385 + ], + "spans": [ + { + "bbox": [ + 143, + 376, + 504, + 385 + ], + "type": "text", + "content": "called Shape-Conditioned AM Generation, which aims to generate AMs aligned with given", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 141, + 387, + 173, + 398 + ], + "spans": [ + { + "bbox": [ + 141, + 387, + 173, + 398 + ], + "type": "text", + "content": "shapes.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 132, + 403, + 504, + 437 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 133, + 403, + 504, + 415 + ], + "spans": [ + { + "bbox": [ + 133, + 403, + 504, + 415 + ], + "type": "text", + "content": "• We introduce MeshAnything for Shape-Conditioned AM Generation. MeshAnything can", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 415, + 504, + 425 + ], + "spans": [ + { + "bbox": [ + 142, + 415, + 504, + 425 + ], + "type": "text", + "content": "be integrated with various 3D asset production methods, converting their results into AMs", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 426, + 332, + 437 + ], + "spans": [ + { + "bbox": [ + 142, + 426, + 332, + 437 + ], + "type": "text", + "content": "to facilitate their application in the 3D industry.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 132, + 443, + 504, + 486 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 134, + 443, + 503, + 453 + ], + "spans": [ + { + "bbox": [ + 134, + 443, + 503, + 453 + ], + "type": "text", + "content": "• We develop a novel noise-resistant decoder to enhance mesh generation quality. We in-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 141, + 455, + 504, + 464 + ], + "spans": [ + { + "bbox": [ + 141, + 455, + 504, + 464 + ], + "type": "text", + "content": "ject the shape condition into the decoder as auxiliary information for robust decoding and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 467, + 504, + 475 + ], + "spans": [ + { + "bbox": [ + 142, + 467, + 504, + 475 + ], + "type": "text", + "content": "fine-tune it using noised token sequences to narrow the domain gap between training and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 141, + 476, + 184, + 487 + ], + "spans": [ + { + "bbox": [ + 141, + 476, + 184, + 487 + ], + "type": "text", + "content": "inference.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 132, + 493, + 504, + 526 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 134, + 495, + 504, + 504 + ], + "spans": [ + { + "bbox": [ + 134, + 495, + 504, + 504 + ], + "type": "text", + "content": "• Extensive experiments demonstrate that Shape-Conditioned Mesh Generation is a more", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 505, + 504, + 515 + ], + "spans": [ + { + "bbox": [ + 142, + 505, + 504, + 515 + ], + "type": "text", + "content": "suitable setting for mesh generation, and MeshAnything significantly surpasses previous", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 517, + 247, + 525 + ], + "spans": [ + { + "bbox": [ + 143, + 517, + 247, + 525 + ], + "type": "text", + "content": "mesh generation methods.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 105, + 545, + 217, + 558 + ], + "type": "title", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 106, + 546, + 216, + 557 + ], + "spans": [ + { + "bbox": [ + 106, + 546, + 216, + 557 + ], + "type": "text", + "content": "2 RELATED WORKS", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 105, + 572, + 217, + 583 + ], + "type": "title", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 573, + 216, + 583 + ], + "spans": [ + { + "bbox": [ + 107, + 573, + 216, + 583 + ], + "type": "text", + "content": "2.1 MESH EXTRACTION", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 594, + 504, + 661 + ], + "type": "text", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 107, + 595, + 504, + 604 + ], + "spans": [ + { + "bbox": [ + 107, + 595, + 504, + 604 + ], + "type": "text", + "content": "Methods for extracting meshes from 3D models are numerous and have been a subject of research for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 605, + 504, + 616 + ], + "spans": [ + { + "bbox": [ + 107, + 605, + 504, + 616 + ], + "type": "text", + "content": "decades. Following Shen et al. (2023), we categorize these methods into two main types: Isosurface", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 105, + 616, + 504, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 504, + 628 + ], + "type": "text", + "content": "Extraction Lorensen & Cline (1987); Bloomenthal (1988); Chernyaev (1995); Bloomenthal & Bajaj", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 628, + 504, + 637 + ], + "spans": [ + { + "bbox": [ + 107, + 628, + 504, + 637 + ], + "type": "text", + "content": "(1997); Lorensen & Cline (1998); Chen et al. (2022) and Gradient-Based Mesh Optimization Chen", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 639, + 503, + 648 + ], + "spans": [ + { + "bbox": [ + 107, + 639, + 503, + 648 + ], + "type": "text", + "content": "et al. (2019); Gao et al. (2020); Hanocka et al. (2020); Kato et al. (2018); Shen et al. (2021a); Liao", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 650, + 235, + 659 + ], + "spans": [ + { + "bbox": [ + 107, + 650, + 235, + 659 + ], + "type": "text", + "content": "et al. (2018); Shen et al. (2023).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 665, + 506, + 733 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 107, + 666, + 503, + 676 + ], + "spans": [ + { + "bbox": [ + 107, + 666, + 503, + 676 + ], + "type": "text", + "content": "Traditional isosurface extraction methods Lorensen & Cline (1987; 1998); Chernyaev (1995); Doi", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 677, + 503, + 687 + ], + "spans": [ + { + "bbox": [ + 107, + 677, + 503, + 687 + ], + "type": "text", + "content": "& Koide (1991); Ju et al. (2002); Schaefer et al. (2007); Chen & Zhang (2021); Chen et al. (2022)", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 689, + 504, + 698 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 504, + 698 + ], + "type": "text", + "content": "focus on extracting a polygonal mesh that represents the level set of a scalar function, an area that", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 504, + 709 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 504, + 709 + ], + "type": "text", + "content": "has seen extensive study in various fields. The most popular method among them is Marching", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 711, + 504, + 720 + ], + "spans": [ + { + "bbox": [ + 107, + 711, + 504, + 720 + ], + "type": "text", + "content": "Cubes Lorensen & Cline (1987). 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They ignore the characteristics of the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 205, + 503, + 214 + ], + "spans": [ + { + "bbox": [ + 107, + 205, + 503, + 214 + ], + "type": "text", + "content": "shape and inherently cannot produce meshes with efficient topology. 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Methods such as Gao et al. (2022);", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 327, + 504, + 337 + ], + "spans": [ + { + "bbox": [ + 107, + 327, + 504, + 337 + ], + "type": "text", + "content": "Wei et al. (2024); Xu et al. (2024) directly generate meshes in a feed-forward manner, but because", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 338, + 504, + 348 + ], + "spans": [ + { + "bbox": [ + 107, + 338, + 504, + 348 + ], + "type": "text", + "content": "they produce dense meshes with low-quality topology similar to previous mesh extraction methods,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 350, + 380, + 359 + ], + "spans": [ + { + "bbox": [ + 107, + 350, + 380, + 359 + ], + "type": "text", + "content": "they still encounter the same issues when applied in the 3D industry.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 365, + 505, + 443 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 367, + 503, + 376 + ], + "spans": [ + { + "bbox": [ + 107, + 367, + 503, + 376 + ], + "type": "text", + "content": "Notably, numerous 3D generation methods Poole et al. (2023); Tang et al. (2023b); Wang et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 377, + 504, + 388 + ], + "spans": [ + { + "bbox": [ + 107, + 377, + 504, + 388 + ], + "type": "text", + "content": "(2023); Chen et al. (2024b); Tang et al. (2023a); Yang et al. (2023); Hong et al. (2023); Fang et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 388, + 504, + 397 + ], + "spans": [ + { + "bbox": [ + 107, + 388, + 504, + 397 + ], + "type": "text", + "content": "(2023); Chen et al. (2023a); Liu et al. (2024b); Shi et al. (2023); Li et al. (2023); Chen et al. (2023b;", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 399, + 503, + 408 + ], + "spans": [ + { + "bbox": [ + 107, + 399, + 503, + 408 + ], + "type": "text", + "content": "2024c); Tang et al. (2024); Wang et al. (2024); Tochilkin et al. (2024) can also produce meshes.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 410, + 504, + 420 + ], + "spans": [ + { + "bbox": [ + 106, + 410, + 504, + 420 + ], + "type": "text", + "content": "These methods first generate 3D assets and then convert them to dense meshes using mesh extraction", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 421, + 504, + 431 + ], + "spans": [ + { + "bbox": [ + 106, + 421, + 504, + 431 + ], + "type": "text", + "content": "methods like Lorensen & Cline (1987). 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(2024a).", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 471, + 503, + 480 + ], + "spans": [ + { + "bbox": [ + 107, + 471, + 503, + 480 + ], + "type": "text", + "content": "Although our approach also focuses on AM generation, it fundamentally differs from these meth-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 483, + 503, + 491 + ], + "spans": [ + { + "bbox": [ + 107, + 483, + 503, + 491 + ], + "type": "text", + "content": "ods. Since they lack shape conditioning, these methods must simultaneously learn the complex 3D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 493, + 503, + 502 + ], + "spans": [ + { + "bbox": [ + 107, + 493, + 503, + 502 + ], + "type": "text", + "content": "shape distribution—which typically alone requires extensive training Hong et al. 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This not only significantly reduces training costs but", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 537, + 283, + 547 + ], + "spans": [ + { + "bbox": [ + 107, + 537, + 283, + 547 + ], + "type": "text", + "content": "also enhances the model’s application value.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 552, + 505, + 641 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 554, + 503, + 563 + ], + "spans": [ + { + "bbox": [ + 107, + 554, + 503, + 563 + ], + "type": "text", + "content": "Among these methods, the most relevant to ours is MeshGPT Siddiqui et al. (2023), as we follow", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 565, + 503, + 574 + ], + "spans": [ + { + "bbox": [ + 107, + 565, + 503, + 574 + ], + "type": "text", + "content": "its architecture. Siddiqui et al. (2023) introduced a combination of a VQ-VAE Van Den Oord et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 576, + 503, + 585 + ], + "spans": [ + { + "bbox": [ + 107, + 576, + 503, + 585 + ], + "type": "text", + "content": "(2017) and an autoregressive transformer architecture. It first learns a mesh vocabulary with the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 587, + 504, + 596 + ], + "spans": [ + { + "bbox": [ + 107, + 587, + 504, + 596 + ], + "type": "text", + "content": "VQ-VAE and then trains the transformer on the learned vocabulary for mesh generation. However,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 105, + 597, + 504, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 597, + 504, + 608 + ], + "type": "text", + "content": "MeshGPT’s results are limited to several categories in ShapeNet. MeshGPT requires a training GPU", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 609, + 504, + 618 + ], + "spans": [ + { + "bbox": [ + 107, + 609, + 504, + 618 + ], + "type": "text", + "content": "hours similar to ours, but our method can generalize to unlimited categories in Objaverse. As shown", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 620, + 503, + 629 + ], + "spans": [ + { + "bbox": [ + 107, + 620, + 503, + 629 + ], + "type": "text", + "content": "in Fig. 3, this is largely due to the difference in target complexity caused by MeshGPT needing to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 630, + 320, + 640 + ], + "spans": [ + { + "bbox": [ + 107, + 630, + 320, + 640 + ], + "type": "text", + "content": "additionally learn the complex 3D shape distribution.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 660, + 335, + 673 + ], + "type": "title", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 105, + 661, + 334, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 661, + 334, + 673 + ], + "type": "text", + "content": "3 SHAPE-CONDITIONED AM GENERATION", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 687, + 504, + 733 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 689, + 504, + 698 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 504, + 698 + ], + "type": "text", + "content": "In this section, we first introduce the formal formulation for Shape-Conditioned AM Generation and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 504, + 710 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 504, + 710 + ], + "type": "text", + "content": "compare it with previous mesh generation settings Nash et al. 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We show that it can achieve better performance and a broader range of applications", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 722, + 503, + 732 + ], + "spans": [ + { + "bbox": [ + 107, + 722, + 503, + 732 + ], + "type": "text", + "content": "compared to the settings in previous mesh generation methods, with significantly less training effort.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 751, + 309, + 760 + ], + "type": "page_number", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 761 + ], + "type": "text", + "content": "5", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4, + "para_blocks": [ + { + "bbox": [ + 104, + 82, + 504, + 106 + ], + "type": "text", + "angle": 0, + "index": 0, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 104, + 110, + 506, + 189 + ], + "type": "text", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 112, + 503, + 121 + ], + "spans": [ + { + "bbox": [ + 107, + 112, + 503, + 121 + ], + "type": "text", + "content": "Transitioning to more recent developments, the advent of machine learning has ushered in new tech-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 122, + 503, + 131 + ], + "spans": [ + { + "bbox": [ + 107, + 122, + 503, + 131 + ], + "type": "text", + "content": "niques for generating 3D meshes Chen et al. 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They ignore the characteristics of the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 205, + 503, + 214 + ], + "spans": [ + { + "bbox": [ + 107, + 205, + 503, + 214 + ], + "type": "text", + "content": "shape and inherently cannot produce meshes with efficient topology. In contrast, MeshAnything", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 217, + 504, + 226 + ], + "spans": [ + { + "bbox": [ + 107, + 217, + 504, + 226 + ], + "type": "text", + "content": "formulates mesh extraction as a generation problem for the first time, aiming to mimic human artists", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 228, + 504, + 237 + ], + "spans": [ + { + "bbox": [ + 107, + 228, + 504, + 237 + ], + "type": "text", + "content": "in mesh extraction and thereby generating Artist-Created Meshes (AMs) with hundreds of times", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 238, + 156, + 247 + ], + "spans": [ + { + "bbox": [ + 106, + 238, + 156, + 247 + ], + "type": "text", + "content": "fewer faces.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 265, + 239, + 277 + ], + "type": "title", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 266, + 237, + 276 + ], + "spans": [ + { + "bbox": [ + 107, + 266, + 237, + 276 + ], + "type": "text", + "content": "2.2 3D MESH GENERATIONS", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 288, + 504, + 311 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 289, + 504, + 298 + ], + "spans": [ + { + "bbox": [ + 107, + 289, + 504, + 298 + ], + "type": "text", + "content": "3D mesh generation can be mainly divided into two categories: generating dense meshes similar to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 300, + 503, + 309 + ], + "spans": [ + { + "bbox": [ + 107, + 300, + 503, + 309 + ], + "type": "text", + "content": "those produced by previous mesh extraction methods, and generating Artist-Created Meshes (AMs).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 316, + 504, + 361 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 316, + 503, + 326 + ], + "spans": [ + { + "bbox": [ + 107, + 316, + 503, + 326 + ], + "type": "text", + "content": "The former category is currently the mainstream research focus. Methods such as Gao et al. (2022);", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 327, + 504, + 337 + ], + "spans": [ + { + "bbox": [ + 107, + 327, + 504, + 337 + ], + "type": "text", + "content": "Wei et al. (2024); Xu et al. (2024) directly generate meshes in a feed-forward manner, but because", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 338, + 504, + 348 + ], + "spans": [ + { + "bbox": [ + 107, + 338, + 504, + 348 + ], + "type": "text", + "content": "they produce dense meshes with low-quality topology similar to previous mesh extraction methods,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 350, + 380, + 359 + ], + "spans": [ + { + "bbox": [ + 107, + 350, + 380, + 359 + ], + "type": "text", + "content": "they still encounter the same issues when applied in the 3D industry.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 365, + 505, + 443 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 367, + 503, + 376 + ], + "spans": [ + { + "bbox": [ + 107, + 367, + 503, + 376 + ], + "type": "text", + "content": "Notably, numerous 3D generation methods Poole et al. (2023); Tang et al. (2023b); Wang et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 377, + 504, + 388 + ], + "spans": [ + { + "bbox": [ + 107, + 377, + 504, + 388 + ], + "type": "text", + "content": "(2023); Chen et al. (2024b); Tang et al. (2023a); Yang et al. (2023); Hong et al. (2023); Fang et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 388, + 504, + 397 + ], + "spans": [ + { + "bbox": [ + 107, + 388, + 504, + 397 + ], + "type": "text", + "content": "(2023); Chen et al. (2023a); Liu et al. (2024b); Shi et al. (2023); Li et al. (2023); Chen et al. (2023b;", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 399, + 503, + 408 + ], + "spans": [ + { + "bbox": [ + 107, + 399, + 503, + 408 + ], + "type": "text", + "content": "2024c); Tang et al. (2024); Wang et al. (2024); Tochilkin et al. (2024) can also produce meshes.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 410, + 504, + 420 + ], + "spans": [ + { + "bbox": [ + 106, + 410, + 504, + 420 + ], + "type": "text", + "content": "These methods first generate 3D assets and then convert them to dense meshes using mesh extraction", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 421, + 504, + 431 + ], + "spans": [ + { + "bbox": [ + 106, + 421, + 504, + 431 + ], + "type": "text", + "content": "methods like Lorensen & Cline (1987). Consequently, they face challenges when applied to the 3D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 432, + 270, + 442 + ], + "spans": [ + { + "bbox": [ + 107, + 432, + 270, + 442 + ], + "type": "text", + "content": "industry due to their inefficient topology.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 448, + 506, + 548 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 107, + 448, + 504, + 459 + ], + "spans": [ + { + "bbox": [ + 107, + 448, + 504, + 459 + ], + "type": "text", + "content": "Recently, several works have focused on the second category: generating Artist-Created", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 460, + 503, + 470 + ], + "spans": [ + { + "bbox": [ + 107, + 460, + 503, + 470 + ], + "type": "text", + "content": "Meshes(AMs) Nash et al. (2020); Alliegro et al. (2023); Siddiqui et al. (2023); Chen et al. (2024a).", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 471, + 503, + 480 + ], + "spans": [ + { + "bbox": [ + 107, + 471, + 503, + 480 + ], + "type": "text", + "content": "Although our approach also focuses on AM generation, it fundamentally differs from these meth-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 483, + 503, + 491 + ], + "spans": [ + { + "bbox": [ + 107, + 483, + 503, + 491 + ], + "type": "text", + "content": "ods. Since they lack shape conditioning, these methods must simultaneously learn the complex 3D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 493, + 503, + 502 + ], + "spans": [ + { + "bbox": [ + 107, + 493, + 503, + 502 + ], + "type": "text", + "content": "shape distribution—which typically alone requires extensive training Hong et al. (2023); Tang et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 503, + 504, + 514 + ], + "spans": [ + { + "bbox": [ + 107, + 503, + 504, + 514 + ], + "type": "text", + "content": "(2024)—and the topology distribution of AMs, leading to very challenging training processes. In", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 514, + 503, + 524 + ], + "spans": [ + { + "bbox": [ + 107, + 514, + 503, + 524 + ], + "type": "text", + "content": "contrast, our methods eliminate the challenge of learning the shape distribution, allowing the model", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 526, + 504, + 535 + ], + "spans": [ + { + "bbox": [ + 107, + 526, + 504, + 535 + ], + "type": "text", + "content": "to focus on learning the topology distribution. This not only significantly reduces training costs but", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 537, + 283, + 547 + ], + "spans": [ + { + "bbox": [ + 107, + 537, + 283, + 547 + ], + "type": "text", + "content": "also enhances the model’s application value.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 552, + 505, + 641 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 554, + 503, + 563 + ], + "spans": [ + { + "bbox": [ + 107, + 554, + 503, + 563 + ], + "type": "text", + "content": "Among these methods, the most relevant to ours is MeshGPT Siddiqui et al. (2023), as we follow", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 565, + 503, + 574 + ], + "spans": [ + { + "bbox": [ + 107, + 565, + 503, + 574 + ], + "type": "text", + "content": "its architecture. Siddiqui et al. (2023) introduced a combination of a VQ-VAE Van Den Oord et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 576, + 503, + 585 + ], + "spans": [ + { + "bbox": [ + 107, + 576, + 503, + 585 + ], + "type": "text", + "content": "(2017) and an autoregressive transformer architecture. It first learns a mesh vocabulary with the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 587, + 504, + 596 + ], + "spans": [ + { + "bbox": [ + 107, + 587, + 504, + 596 + ], + "type": "text", + "content": "VQ-VAE and then trains the transformer on the learned vocabulary for mesh generation. However,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 105, + 597, + 504, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 597, + 504, + 608 + ], + "type": "text", + "content": "MeshGPT’s results are limited to several categories in ShapeNet. MeshGPT requires a training GPU", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 609, + 504, + 618 + ], + "spans": [ + { + "bbox": [ + 107, + 609, + 504, + 618 + ], + "type": "text", + "content": "hours similar to ours, but our method can generalize to unlimited categories in Objaverse. As shown", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 620, + 503, + 629 + ], + "spans": [ + { + "bbox": [ + 107, + 620, + 503, + 629 + ], + "type": "text", + "content": "in Fig. 3, this is largely due to the difference in target complexity caused by MeshGPT needing to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 630, + 320, + 640 + ], + "spans": [ + { + "bbox": [ + 107, + 630, + 320, + 640 + ], + "type": "text", + "content": "additionally learn the complex 3D shape distribution.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 660, + 335, + 673 + ], + "type": "title", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 105, + 661, + 334, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 661, + 334, + 673 + ], + "type": "text", + "content": "3 SHAPE-CONDITIONED AM GENERATION", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 687, + 504, + 733 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 689, + 504, + 698 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 504, + 698 + ], + "type": "text", + "content": "In this section, we first introduce the formal formulation for Shape-Conditioned AM Generation and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 504, + 710 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 504, + 710 + ], + "type": "text", + "content": "compare it with previous mesh generation settings Nash et al. (2020); Siddiqui et al. (2023); Alliegro", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 711, + 503, + 720 + ], + "spans": [ + { + "bbox": [ + 107, + 711, + 503, + 720 + ], + "type": "text", + "content": "et al. (2023). We show that it can achieve better performance and a broader range of applications", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 722, + 503, + 732 + ], + "spans": [ + { + "bbox": [ + 107, + 722, + 503, + 732 + ], + "type": "text", + "content": "compared to the settings in previous mesh generation methods, with significantly less training effort.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "type": "chart", + "bbox": [ + 113, + 88, + 271, + 213 + ], + "blocks": [ + { + "bbox": [ + 113, + 88, + 271, + 213 + ], + "type": "chart_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 88, + 271, + 213 + ], + "spans": [ + { + "bbox": [ + 113, + 88, + 271, + 213 + ], + "type": "chart", + "content": "| Training iterations | Shape-Conditioned | Image-Conditioned | Unconditional |\n| --- | --- | --- | --- |\n| 60k | ~2.0 | — | — |\n| 80k | ~1.67 | ~1.98 | ~1.99 |\n| 100k | ~1.56 | ~1.83 | ~1.86 |\n| 120k | ~1.49 | ~1.74 | ~1.78 |\n| 140k | ~1.46 | ~1.71 | ~1.75 |\n| 160k | ~1.44 | ~1.70 | ~1.75 |\n| 180k | ~1.43 | ~1.70 | ~1.75 |\n| 200k | ~1.43 | ~1.69 | ~1.72 |\n| 220k | ~1.42 | ~1.69 | ~1.73 |", + "image_path": "aecc35c40ee63cf700f8e266846c83e8dfb32ed3aab02b0e0271258e64dac101.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 136, + 224, + 256, + 236 + ], + "type": "chart_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 138, + 225, + 254, + 236 + ], + "spans": [ + { + "bbox": [ + 138, + 225, + 254, + 236 + ], + "type": "text", + "content": "(a) Training Perplexity (PPL)", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_type": "line" + }, + { + "type": "chart", + "bbox": [ + 331, + 89, + 488, + 213 + ], + "blocks": [ + { + "bbox": [ + 331, + 89, + 488, + 213 + ], + "type": "chart_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 89, + 488, + 213 + ], + "spans": [ + { + "bbox": [ + 331, + 89, + 488, + 213 + ], + "type": "chart", + "content": "| Training iterations | Shape-Conditioned (Validation PPL) | Image-Conditioned (Validation PPL) | Unconditional (Validation PPL) |\n| --- | --- | --- | --- |\n| 60k | ~2.0 | ~2.0 | ~2.0 |\n| 80k | ~1.52 | ~1.75 | ~1.8 |\n| 100k | ~1.44 | ~1.67 | ~1.72 |\n| 120k | ~1.41 | ~1.63 | ~1.68 |\n| 140k | ~1.39 | ~1.6 | ~1.65 |\n| 160k | ~1.37 | ~1.59 | ~1.63 |\n| 180k | ~1.36 | ~1.58 | ~1.61 |\n| 200k | ~1.35 | ~1.57 | ~1.6 |\n| 220k | ~1.34 | ~1.56 | ~1.59 |", + "image_path": "82c80d138141f010fa79e32343b04995c61f9dcd45f48b620653763fb4af129e.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 350, + 224, + 477, + 236 + ], + "type": "chart_caption", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 351, + 225, + 476, + 236 + ], + "spans": [ + { + "bbox": [ + 351, + 225, + 476, + 236 + ], + "type": "text", + "content": "(b) Validation Perplexity (PPL)", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 104, + 244, + 504, + 312 + ], + "type": "chart_caption", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 246, + 503, + 255 + ], + "spans": [ + { + "bbox": [ + 107, + 246, + 503, + 255 + ], + "type": "text", + "content": "Figure 3: Training and validation perplexity (PPL) for the mesh generation model under dif-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 257, + 503, + 266 + ], + "spans": [ + { + "bbox": [ + 107, + 257, + 503, + 266 + ], + "type": "text", + "content": "ferent input conditions. All models are trained with the same settings as detailed in Section 5.2.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 268, + 504, + 277 + ], + "spans": [ + { + "bbox": [ + 107, + 268, + 504, + 277 + ], + "type": "text", + "content": "The training and validation PPL of shape-conditioned mesh generation is significantly lower than", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 279, + 503, + 289 + ], + "spans": [ + { + "bbox": [ + 107, + 279, + 503, + 289 + ], + "type": "text", + "content": "that of unconditional and image-conditioned mesh generation. This indicates that the training bur-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 291, + 503, + 299 + ], + "spans": [ + { + "bbox": [ + 107, + 291, + 503, + 299 + ], + "type": "text", + "content": "den of shape-conditioned mesh generation is much lower since it avoids learning the complex 3D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 300, + 181, + 310 + ], + "spans": [ + { + "bbox": [ + 107, + 300, + 181, + 310 + ], + "type": "text", + "content": "shape distribution.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 2, + "sub_type": "line" + }, + { + "bbox": [ + 104, + 332, + 504, + 411 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 333, + 504, + 344 + ], + "spans": [ + { + "bbox": [ + 107, + 335, + 433, + 343 + ], + "type": "text", + "content": "Shape-Conditioned AM Generation targets to estimate a conditional distribution", + "score": 1.0 + }, + { + "bbox": [ + 434, + 333, + 469, + 344 + ], + "type": "inline_equation", + "content": "p ( \\mathcal { M } | S )", + "score": 0.722 + }, + { + "bbox": [ + 470, + 334, + 504, + 343 + ], + "type": "text", + "content": ". In this", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 345, + 504, + 355 + ], + "spans": [ + { + "bbox": [ + 107, + 345, + 504, + 355 + ], + "type": "text", + "content": "formula, M refers to the Artist-Created Mesh (AM), i.e., the mesh manually modeled by human", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 357, + 503, + 365 + ], + "spans": [ + { + "bbox": [ + 107, + 357, + 503, + 365 + ], + "type": "text", + "content": "artists. S refers to the 3D shape information that indicates the 3D shape to which M should align.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 368, + 503, + 376 + ], + "spans": [ + { + "bbox": [ + 107, + 368, + 503, + 376 + ], + "type": "text", + "content": "The input form of S can be diverse, such as voxels or point clouds. Therefore, this versatility", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 378, + 503, + 388 + ], + "spans": [ + { + "bbox": [ + 107, + 378, + 503, + 388 + ], + "type": "text", + "content": "allows our method to be integrated with any 3D pipeline that outputs S, such as 3D reconstruc-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 389, + 503, + 398 + ], + "spans": [ + { + "bbox": [ + 107, + 389, + 503, + 398 + ], + "type": "text", + "content": "tion Mildenhall et al. (2020); Kerbl et al. (2023b), generation Poole et al. (2023); Hong et al. (2023),", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 400, + 392, + 410 + ], + "spans": [ + { + "bbox": [ + 107, + 400, + 392, + 410 + ], + "type": "text", + "content": "and scanning, making these methods more efficient for the 3D industry.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 415, + 504, + 460 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 416, + 504, + 427 + ], + "spans": [ + { + "bbox": [ + 107, + 418, + 437, + 426 + ], + "type": "text", + "content": "Compared to existing AM generation work, they directly estimate the distribution", + "score": 1.0 + }, + { + "bbox": [ + 439, + 416, + 474, + 427 + ], + "type": "inline_equation", + "content": "p ( \\mathcal { M } | \\mathcal { C } )", + "score": 0.7474 + }, + { + "bbox": [ + 474, + 417, + 504, + 426 + ], + "type": "text", + "content": ", where", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 105, + 427, + 504, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 504, + 438 + ], + "type": "text", + "content": "C denotes conditions such as images, text or empty sets for unconditional generation. However,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 437, + 504, + 449 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 150, + 449 + ], + "type": "text", + "content": "estimating", + "score": 1.0 + }, + { + "bbox": [ + 150, + 437, + 186, + 449 + ], + "type": "inline_equation", + "content": "p ( \\mathcal { M } | \\mathcal { C } )", + "score": 0.7211 + }, + { + "bbox": [ + 187, + 439, + 504, + 449 + ], + "type": "text", + "content": "requires an understanding of both the underlying shape, i.e., S, and complex", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 450, + 414, + 460 + ], + "spans": [ + { + "bbox": [ + 107, + 450, + 414, + 460 + ], + "type": "text", + "content": "topological structures M. 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This", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 709, + 504, + 721 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 361, + 720 + ], + "type": "text", + "content": "integration allows for a more resource-efficient way to estimate", + "score": 1.0 + }, + { + "bbox": [ + 362, + 709, + 396, + 721 + ], + "type": "inline_equation", + "content": "p ( \\mathcal { M } | \\mathcal { C } )", + "score": 0.7845 + }, + { + "bbox": [ + 396, + 712, + 504, + 720 + ], + "type": "text", + "content": ", significantly reducing the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 722, + 371, + 732 + ], + "spans": [ + { + "bbox": [ + 107, + 722, + 371, + 732 + ], + "type": "text", + "content": "complexity and resources required compared to previous methods.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 751, + 308, + 760 + ], + "type": "page_number", + "angle": 0, + "index": 16, + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "type": "text", + "content": "6", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5, + "para_blocks": [ + { + "type": "chart", + "bbox": [ + 113, + 88, + 271, + 213 + ], + "blocks": [ + { + "bbox": [ + 113, + 88, + 271, + 213 + ], + "type": "chart_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 88, + 271, + 213 + ], + "spans": [ + { + "bbox": [ + 113, + 88, + 271, + 213 + ], + "type": "chart", + "content": "| Training iterations | Shape-Conditioned | Image-Conditioned | Unconditional |\n| --- | --- | --- | --- |\n| 60k | ~2.0 | — | — |\n| 80k | ~1.67 | ~1.98 | ~1.99 |\n| 100k | ~1.56 | ~1.83 | ~1.86 |\n| 120k | ~1.49 | ~1.74 | ~1.78 |\n| 140k | ~1.46 | ~1.71 | ~1.75 |\n| 160k | ~1.44 | ~1.70 | ~1.75 |\n| 180k | ~1.43 | ~1.70 | ~1.75 |\n| 200k | ~1.43 | ~1.69 | ~1.72 |\n| 220k | ~1.42 | ~1.69 | ~1.73 |", + "image_path": "aecc35c40ee63cf700f8e266846c83e8dfb32ed3aab02b0e0271258e64dac101.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 136, + 224, + 256, + 236 + ], + "type": "chart_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 138, + 225, + 254, + 236 + ], + "spans": [ + { + "bbox": [ + 138, + 225, + 254, + 236 + ], + "type": "text", + "content": "(a) Training Perplexity (PPL)", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_type": "line" + }, + { + "type": "chart", + "bbox": [ + 331, + 89, + 488, + 213 + ], + "blocks": [ + { + "bbox": [ + 331, + 89, + 488, + 213 + ], + "type": "chart_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 89, + 488, + 213 + ], + "spans": [ + { + "bbox": [ + 331, + 89, + 488, + 213 + ], + "type": "chart", + "content": "| Training iterations | Shape-Conditioned (Validation PPL) | Image-Conditioned (Validation PPL) | Unconditional (Validation PPL) |\n| --- | --- | --- | --- |\n| 60k | ~2.0 | ~2.0 | ~2.0 |\n| 80k | ~1.52 | ~1.75 | ~1.8 |\n| 100k | ~1.44 | ~1.67 | ~1.72 |\n| 120k | ~1.41 | ~1.63 | ~1.68 |\n| 140k | ~1.39 | ~1.6 | ~1.65 |\n| 160k | ~1.37 | ~1.59 | ~1.63 |\n| 180k | ~1.36 | ~1.58 | ~1.61 |\n| 200k | ~1.35 | ~1.57 | ~1.6 |\n| 220k | ~1.34 | ~1.56 | ~1.59 |", + "image_path": "82c80d138141f010fa79e32343b04995c61f9dcd45f48b620653763fb4af129e.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 350, + 224, + 477, + 236 + ], + "type": "chart_caption", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 351, + 225, + 476, + 236 + ], + "spans": [ + { + "bbox": [ + 351, + 225, + 476, + 236 + ], + "type": "text", + "content": "(b) Validation Perplexity (PPL)", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 104, + 244, + 504, + 312 + ], + "type": "chart_caption", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 246, + 503, + 255 + ], + "spans": [ + { + "bbox": [ + 107, + 246, + 503, + 255 + ], + "type": "text", + "content": "Figure 3: Training and validation perplexity (PPL) for the mesh generation model under dif-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 257, + 503, + 266 + ], + "spans": [ + { + "bbox": [ + 107, + 257, + 503, + 266 + ], + "type": "text", + "content": "ferent input conditions. All models are trained with the same settings as detailed in Section 5.2.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 268, + 504, + 277 + ], + "spans": [ + { + "bbox": [ + 107, + 268, + 504, + 277 + ], + "type": "text", + "content": "The training and validation PPL of shape-conditioned mesh generation is significantly lower than", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 279, + 503, + 289 + ], + "spans": [ + { + "bbox": [ + 107, + 279, + 503, + 289 + ], + "type": "text", + "content": "that of unconditional and image-conditioned mesh generation. This indicates that the training bur-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 291, + 503, + 299 + ], + "spans": [ + { + "bbox": [ + 107, + 291, + 503, + 299 + ], + "type": "text", + "content": "den of shape-conditioned mesh generation is much lower since it avoids learning the complex 3D", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 300, + 181, + 310 + ], + "spans": [ + { + "bbox": [ + 107, + 300, + 181, + 310 + ], + "type": "text", + "content": "shape distribution.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 2, + "sub_type": "line" + }, + { + "bbox": [ + 104, + 332, + 504, + 411 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 333, + 504, + 344 + ], + "spans": [ + { + "bbox": [ + 107, + 335, + 433, + 343 + ], + "type": "text", + "content": "Shape-Conditioned AM Generation targets to estimate a conditional distribution", + "score": 1.0 + }, + { + "bbox": [ + 434, + 333, + 469, + 344 + ], + "type": "inline_equation", + "content": "p ( \\mathcal { M } | S )", + "score": 0.722 + }, + { + "bbox": [ + 470, + 334, + 504, + 343 + ], + "type": "text", + "content": ". In this", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 345, + 504, + 355 + ], + "spans": [ + { + "bbox": [ + 107, + 345, + 504, + 355 + ], + "type": "text", + "content": "formula, M refers to the Artist-Created Mesh (AM), i.e., the mesh manually modeled by human", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 357, + 503, + 365 + ], + "spans": [ + { + "bbox": [ + 107, + 357, + 503, + 365 + ], + "type": "text", + "content": "artists. S refers to the 3D shape information that indicates the 3D shape to which M should align.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 368, + 503, + 376 + ], + "spans": [ + { + "bbox": [ + 107, + 368, + 503, + 376 + ], + "type": "text", + "content": "The input form of S can be diverse, such as voxels or point clouds. Therefore, this versatility", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 378, + 503, + 388 + ], + "spans": [ + { + "bbox": [ + 107, + 378, + 503, + 388 + ], + "type": "text", + "content": "allows our method to be integrated with any 3D pipeline that outputs S, such as 3D reconstruc-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 389, + 503, + 398 + ], + "spans": [ + { + "bbox": [ + 107, + 389, + 503, + 398 + ], + "type": "text", + "content": "tion Mildenhall et al. (2020); Kerbl et al. (2023b), generation Poole et al. (2023); Hong et al. (2023),", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 400, + 392, + 410 + ], + "spans": [ + { + "bbox": [ + 107, + 400, + 392, + 410 + ], + "type": "text", + "content": "and scanning, making these methods more efficient for the 3D industry.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 415, + 504, + 460 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 416, + 504, + 427 + ], + "spans": [ + { + "bbox": [ + 107, + 418, + 437, + 426 + ], + "type": "text", + "content": "Compared to existing AM generation work, they directly estimate the distribution", + "score": 1.0 + }, + { + "bbox": [ + 439, + 416, + 474, + 427 + ], + "type": "inline_equation", + "content": "p ( \\mathcal { M } | \\mathcal { C } )", + "score": 0.7474 + }, + { + "bbox": [ + 474, + 417, + 504, + 426 + ], + "type": "text", + "content": ", where", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 105, + 427, + 504, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 504, + 438 + ], + "type": "text", + "content": "C denotes conditions such as images, text or empty sets for unconditional generation. However,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 437, + 504, + 449 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 150, + 449 + ], + "type": "text", + "content": "estimating", + "score": 1.0 + }, + { + "bbox": [ + 150, + 437, + 186, + 449 + ], + "type": "inline_equation", + "content": "p ( \\mathcal { M } | \\mathcal { C } )", + "score": 0.7211 + }, + { + "bbox": [ + 187, + 439, + 504, + 449 + ], + "type": "text", + "content": "requires an understanding of both the underlying shape, i.e., S, and complex", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 450, + 414, + 460 + ], + "spans": [ + { + "bbox": [ + 107, + 450, + 414, + 460 + ], + "type": "text", + "content": "topological structures M. Given this, we made the following approximation:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 255, + 477, + 504, + 490 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 255, + 477, + 504, + 490 + ], + "spans": [ + { + "bbox": [ + 255, + 477, + 504, + 490 + ], + "type": "interline_equation", + "content": "p (\\mathcal {M} | \\mathcal {C}) \\approx p (\\mathcal {M}, \\mathcal {S} | \\mathcal {C}). \\tag {1}", + "image_path": "493a0c9d88aa65dcd239591329191f0301e4dc8b32e2e11b7d2da81339584820.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 493, + 257, + 504 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 494, + 257, + 504 + ], + "spans": [ + { + "bbox": [ + 107, + 494, + 257, + 504 + ], + "type": "text", + "content": "According to the chain rule, we have:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 232, + 510, + 504, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 232, + 510, + 504, + 525 + ], + "spans": [ + { + "bbox": [ + 232, + 510, + 504, + 525 + ], + "type": "interline_equation", + "content": "p (\\mathcal {M}, \\mathcal {S} | \\mathcal {C}) = p (\\mathcal {M} | \\mathcal {S}, \\mathcal {C}) \\cdot p (\\mathcal {S} | \\mathcal {C}). \\tag {2}", + "image_path": "8bf78913402038647174d8a506688d62b1cd01fa3b660b42209a6e0a26a2d109.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 529, + 504, + 553 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 530, + 504, + 541 + ], + "spans": [ + { + "bbox": [ + 107, + 531, + 170, + 540 + ], + "type": "text", + "content": "For distribution", + "score": 1.0 + }, + { + "bbox": [ + 171, + 530, + 217, + 541 + ], + "type": "inline_equation", + "content": "p ( \\mathcal { M } | \\mathcal { S } , \\mathcal { C } )", + "score": 0.7875 + }, + { + "bbox": [ + 217, + 531, + 504, + 540 + ], + "type": "text", + "content": ", given that S is a much stronger and more direct condition than C, we", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 542, + 264, + 552 + ], + "spans": [ + { + "bbox": [ + 107, + 542, + 264, + 552 + ], + "type": "text", + "content": "can make the following approximation:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 255, + 559, + 504, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 255, + 559, + 504, + 571 + ], + "spans": [ + { + "bbox": [ + 255, + 559, + 504, + 571 + ], + "type": "interline_equation", + "content": "p (\\mathcal {M} | \\mathcal {S}, \\mathcal {C}) \\approx p (\\mathcal {M} | \\mathcal {S}). \\tag {3}", + "image_path": "692ba251dac9eba24e7bc0d46470586f9e081c12ae578e1c30704831cc446a96.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 577, + 197, + 589 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 107, + 578, + 197, + 589 + ], + "spans": [ + { + "bbox": [ + 107, + 578, + 197, + 589 + ], + "type": "text", + "content": "Combining 1, 2 and 3:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 243, + 588, + 504, + 602 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 243, + 588, + 504, + 602 + ], + "spans": [ + { + "bbox": [ + 243, + 588, + 504, + 602 + ], + "type": "interline_equation", + "content": "p (\\mathcal {M} | \\mathcal {C}) \\approx p (\\mathcal {M} | \\mathcal {S}) \\cdot p (\\mathcal {S} | \\mathcal {C}), \\tag {4}", + "image_path": "cab409b95b2f03f76571481178ea0ec0675bd3d29957f6ddcfd8c06a15828a9c.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 605, + 504, + 639 + ], + "type": "text", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 106, + 605, + 504, + 616 + ], + "spans": [ + { + "bbox": [ + 106, + 606, + 144, + 615 + ], + "type": "text", + "content": "in which", + "score": 1.0 + }, + { + "bbox": [ + 146, + 605, + 181, + 616 + ], + "type": "inline_equation", + "content": "p ( \\mathcal { M } | S )", + "score": 0.8358 + }, + { + "bbox": [ + 184, + 606, + 504, + 615 + ], + "type": "text", + "content": "is the focus of our shape-conditioned mesh generation. As shown in Fig. 3,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 616, + 504, + 628 + ], + "spans": [ + { + "bbox": [ + 107, + 617, + 149, + 627 + ], + "type": "text", + "content": "estimating", + "score": 1.0 + }, + { + "bbox": [ + 151, + 616, + 186, + 628 + ], + "type": "inline_equation", + "content": "p ( \\mathcal { M } | S )", + "score": 0.4659 + }, + { + "bbox": [ + 187, + 617, + 297, + 627 + ], + "type": "text", + "content": "is much more simpler than", + "score": 1.0 + }, + { + "bbox": [ + 298, + 616, + 331, + 628 + ], + "type": "inline_equation", + "content": "p ( \\mathcal { M } | \\mathcal { C } )", + "score": 0.6907 + }, + { + "bbox": [ + 332, + 617, + 504, + 628 + ], + "type": "text", + "content": ", proving that our setting is much easier to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 628, + 259, + 637 + ], + "spans": [ + { + "bbox": [ + 107, + 628, + 259, + 637 + ], + "type": "text", + "content": "train than settings in privous methods.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 643, + 505, + 733 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 107, + 645, + 504, + 654 + ], + "spans": [ + { + "bbox": [ + 107, + 645, + 504, + 654 + ], + "type": "text", + "content": "As for p(S|C), In the 3D community, numerous large models Team (2024); Tang et al. (2024); Xu", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 655, + 504, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 504, + 666 + ], + "type": "text", + "content": "et al. (2024); Siddiqui et al. (2023) aim to estimate using various 3D representations and demonstrate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 667, + 503, + 676 + ], + "spans": [ + { + "bbox": [ + 107, + 667, + 503, + 676 + ], + "type": "text", + "content": "excellent results. Besides, some single scene 3D asset production methods Mildenhall et al. (2020);", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 678, + 503, + 687 + ], + "spans": [ + { + "bbox": [ + 107, + 678, + 503, + 687 + ], + "type": "text", + "content": "Kerbl et al. (2023b); Barron et al. (2021; 2022); Poole et al. (2023); Liu et al. (2023b); Sun et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 689, + 503, + 697 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 503, + 697 + ], + "type": "text", + "content": "(2023) can also provide samples from this distribution. By integrating our framework with these", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 504, + 709 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 504, + 709 + ], + "type": "text", + "content": "existing methods, we can leverage their capabilities to enhance our mesh generation process. This", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 709, + 504, + 721 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 361, + 720 + ], + "type": "text", + "content": "integration allows for a more resource-efficient way to estimate", + "score": 1.0 + }, + { + "bbox": [ + 362, + 709, + 396, + 721 + ], + "type": "inline_equation", + "content": "p ( \\mathcal { M } | \\mathcal { C } )", + "score": 0.7845 + }, + { + "bbox": [ + 396, + 712, + 504, + 720 + ], + "type": "text", + "content": ", significantly reducing the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 722, + 371, + 732 + ], + "spans": [ + { + "bbox": [ + 107, + 722, + 371, + 732 + ], + "type": "text", + "content": "complexity and resources required compared to previous methods.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 81, + 500, + 158 + ], + "blocks": [ + { + "bbox": [ + 111, + 81, + 500, + 158 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 81, + 500, + 158 + ], + "spans": [ + { + "bbox": [ + 111, + 81, + 500, + 158 + ], + "type": "image", + "content": "```mermaid\ngraph LR\n A[\"Training\"] --> B[\"VQ Encoder\"]\n B --> C[\"Artist-Created Mesh\"]\n C --> D[\"Sample from surface\"]\n D --> E[\"Inference\"]\n E --> F[\"NeRF 3D GS\"]\n F --> G[\"Sample\"]\n G --> H[\"Point Cloud\"]\n H --> I[\"Feature\"]\n I --> J[\"Mesh Autoregressive Transformer\"]\n J --> K[\"...\"]\n K -.-> L[\"Cross-Entropy Loss\"]\n L --> M[\"Cross-Entropy Loss\"]\n M --> N[\"Cross-Entropy Loss\"]\n N --> O[\"Cross-Entropy Loss\"]\n O --> P[\"VQ Decoder\"]\n P --> Q[\"Generated Mesh\"]\n```", + "image_path": "ed7acb9369bfcc2c48faff57b105d6db318c21dfbb1b16f91c12ef6419bebbfe.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 170, + 504, + 226 + ], + "type": "image_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 171, + 504, + 181 + ], + "spans": [ + { + "bbox": [ + 107, + 171, + 504, + 181 + ], + "type": "text", + "content": "Figure 4: Pipeline Overview. We introduce MeshAnything, an autoregressive transformer capable", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 182, + 504, + 193 + ], + "spans": [ + { + "bbox": [ + 107, + 182, + 504, + 193 + ], + "type": "text", + "content": "of generating Artist-Created Meshes that adhere to given 3D shapes. During training, we inject point", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 194, + 504, + 203 + ], + "spans": [ + { + "bbox": [ + 107, + 194, + 504, + 203 + ], + "type": "text", + "content": "clouds features into a decoder-only transformer and supervise it using token sequences derived from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 205, + 504, + 214 + ], + "spans": [ + { + "bbox": [ + 107, + 205, + 504, + 214 + ], + "type": "text", + "content": "the Artist-Created meshes. After training, MeshAnything takes point clouds sampled from various", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 217, + 398, + 224 + ], + "spans": [ + { + "bbox": [ + 107, + 217, + 398, + 224 + ], + "type": "text", + "content": "3D representations as input and generates aligned Artist-Created meshes.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_type": "flowchart" + }, + { + "bbox": [ + 105, + 247, + 173, + 259 + ], + "type": "title", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 106, + 248, + 173, + 260 + ], + "spans": [ + { + "bbox": [ + 106, + 248, + 173, + 260 + ], + "type": "text", + "content": "4 METHOD", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 274, + 504, + 308 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 106, + 275, + 504, + 285 + ], + "spans": [ + { + "bbox": [ + 106, + 275, + 504, + 285 + ], + "type": "text", + "content": "In this section, we detail our shape condition strategy in Section 4.1. After that, we provide a detailed", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 286, + 504, + 297 + ], + "spans": [ + { + "bbox": [ + 107, + 286, + 504, + 297 + ], + "type": "text", + "content": "description for MeshAnything, which consists of a VQVAE with our newly proposed noise-resistant", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 297, + 457, + 307 + ], + "spans": [ + { + "bbox": [ + 107, + 297, + 457, + 307 + ], + "type": "text", + "content": "decoder (Section 4.2) and a shape-conditioned autoregressive transformer (Section 4.3).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 323, + 353, + 333 + ], + "type": "title", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 324, + 351, + 333 + ], + "spans": [ + { + "bbox": [ + 107, + 324, + 351, + 333 + ], + "type": "text", + "content": "4.1 SHAPE ENCODING FOR CONDITIONAL GENERATION", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 344, + 504, + 378 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 345, + 504, + 355 + ], + "spans": [ + { + "bbox": [ + 107, + 345, + 504, + 355 + ], + "type": "text", + "content": "We begin by describing our shape condition strategy. MeshAnything targets learning p(M|S), so", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 356, + 504, + 366 + ], + "spans": [ + { + "bbox": [ + 107, + 356, + 504, + 366 + ], + "type": "text", + "content": "we need to pair each mesh M with a corresponding S, i.e., the shape condition. Choosing an", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 367, + 481, + 377 + ], + "spans": [ + { + "bbox": [ + 107, + 367, + 481, + 377 + ], + "type": "text", + "content": "appropriate 3D representation for S is non-trivial and should satisfy the following conditions:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 127, + 388, + 505, + 500 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 129, + 388, + 504, + 423 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 131, + 391, + 504, + 399 + ], + "spans": [ + { + "bbox": [ + 131, + 391, + 504, + 399 + ], + "type": "text", + "content": "1. It should be easily extracted from various 3D representations. This ensures that the trained", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 401, + 504, + 411 + ], + "spans": [ + { + "bbox": [ + 142, + 401, + 504, + 411 + ], + "type": "text", + "content": "models can be integrated with a wide range of 3D asset production pipelines Mildenhall", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 412, + 504, + 422 + ], + "spans": [ + { + "bbox": [ + 143, + 412, + 504, + 422 + ], + "type": "text", + "content": "et al. (2020); Kerbl et al. (2023b); Hong et al. (2023); Poole et al. (2023); Tang et al. (2024).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 128, + 427, + 504, + 461 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 129, + 429, + 504, + 439 + ], + "spans": [ + { + "bbox": [ + 129, + 429, + 504, + 439 + ], + "type": "text", + "content": "2. It should be suitable for data augmentation to prevent overfitting. To ensure the effec-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 141, + 439, + 504, + 450 + ], + "spans": [ + { + "bbox": [ + 141, + 439, + 504, + 450 + ], + "type": "text", + "content": "tiveness of S during training, any data augmentation applied to M must be equivalently", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 451, + 206, + 460 + ], + "spans": [ + { + "bbox": [ + 143, + 451, + 206, + 460 + ], + "type": "text", + "content": "applicable to S.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 128, + 466, + 504, + 500 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 129, + 467, + 504, + 477 + ], + "spans": [ + { + "bbox": [ + 129, + 467, + 504, + 477 + ], + "type": "text", + "content": "3. It should be efficiently and conveniently input into the model as a condition. To ensure", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 478, + 504, + 488 + ], + "spans": [ + { + "bbox": [ + 142, + 478, + 504, + 488 + ], + "type": "text", + "content": "the model comprehends the shape information and to maintain efficient training, S must be", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 490, + 317, + 498 + ], + "spans": [ + { + "bbox": [ + 143, + 490, + 317, + 498 + ], + "type": "text", + "content": "easily and effectively encoded into features.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 104, + 511, + 504, + 599 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 513, + 503, + 521 + ], + "spans": [ + { + "bbox": [ + 107, + 513, + 503, + 521 + ], + "type": "text", + "content": "Considering the first and second points, S should be in an explicit representation. Further consid-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 523, + 503, + 533 + ], + "spans": [ + { + "bbox": [ + 107, + 523, + 503, + 533 + ], + "type": "text", + "content": "ering the third point, the main explicit 3D representations that can be easily encoded as features", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 535, + 504, + 544 + ], + "spans": [ + { + "bbox": [ + 107, + 535, + 504, + 544 + ], + "type": "text", + "content": "are voxels and point clouds. Both representations are suitable, but voxels typically require a high", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 546, + 503, + 555 + ], + "spans": [ + { + "bbox": [ + 107, + 546, + 503, + 555 + ], + "type": "text", + "content": "resolution to accurately represent shapes, and processing high-resolution voxels into features is com-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 556, + 504, + 566 + ], + "spans": [ + { + "bbox": [ + 107, + 556, + 504, + 566 + ], + "type": "text", + "content": "putationally expensive. Additionally, voxels, being a discrete representation, are less precise for data", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 567, + 504, + 577 + ], + "spans": [ + { + "bbox": [ + 106, + 567, + 504, + 577 + ], + "type": "text", + "content": "augmentation compared to point clouds. Therefore, we chose point clouds as the representation for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 578, + 504, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 578, + 504, + 588 + ], + "type": "text", + "content": "S. To enhance the expressive power of the point clouds, we also include normals into the point cloud", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 590, + 166, + 598 + ], + "spans": [ + { + "bbox": [ + 107, + 590, + 166, + 598 + ], + "type": "text", + "content": "representation.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 605, + 504, + 661 + ], + "type": "text", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 107, + 606, + 503, + 616 + ], + "spans": [ + { + "bbox": [ + 107, + 606, + 503, + 616 + ], + "type": "text", + "content": "To obtain point clouds from the ground truth mesh for training, we could simply sample point clouds", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "spans": [ + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "type": "text", + "content": "directly from the surface of M. However, this would create problems during inference: the surfaces", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 629, + 503, + 637 + ], + "spans": [ + { + "bbox": [ + 107, + 629, + 503, + 637 + ], + "type": "text", + "content": "of automatically generated 3D assets are often rougher than those of AMs. For example, in AMs,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 639, + 504, + 649 + ], + "spans": [ + { + "bbox": [ + 107, + 639, + 504, + 649 + ], + "type": "text", + "content": "we would sample a series of points on a flat plane, whereas automatically generated 3D assets would", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 651, + 410, + 659 + ], + "spans": [ + { + "bbox": [ + 107, + 651, + 410, + 659 + ], + "type": "text", + "content": "have uneven surfaces, causing a domain gap between training and inference.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 666, + 505, + 733 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 107, + 667, + 504, + 676 + ], + "spans": [ + { + "bbox": [ + 107, + 667, + 504, + 676 + ], + "type": "text", + "content": "Therefore, we need to ensure that S extracted from the ground truth M during training has a similar", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 677, + 504, + 688 + ], + "spans": [ + { + "bbox": [ + 107, + 677, + 504, + 688 + ], + "type": "text", + "content": "domain to the S extracted during inference. To bring their domains closer, we intentionally construct", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 689, + 504, + 698 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 504, + 698 + ], + "type": "text", + "content": "coarse meshes from AMs. We first extract the signed distance function from M with Wang et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 504, + 709 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 504, + 709 + ], + "type": "text", + "content": "(2022), then convert it into a relatively coarse mesh using Marching Cubes Lorensen & Cline (1987)", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 712, + 504, + 720 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 504, + 720 + ], + "type": "text", + "content": "to destroy the ground truth topology. Finally, we sample point cloud and its normals from the coarse", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 721, + 504, + 731 + ], + "spans": [ + { + "bbox": [ + 107, + 721, + 504, + 731 + ], + "type": "text", + "content": "mesh. This approach also helps to avoid overfitting, as AMs typically have fewer faces, and each", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 751, + 308, + 760 + ], + "type": "page_number", + "angle": 0, + "index": 13, + "lines": [] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6, + "para_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 81, + 500, + 158 + ], + "blocks": [ + { + "bbox": [ + 111, + 81, + 500, + 158 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 81, + 500, + 158 + ], + "spans": [ + { + "bbox": [ + 111, + 81, + 500, + 158 + ], + "type": "image", + "content": "```mermaid\ngraph LR\n A[\"Training\"] --> B[\"VQ Encoder\"]\n B --> C[\"Artist-Created Mesh\"]\n C --> D[\"Sample from surface\"]\n D --> E[\"Inference\"]\n E --> F[\"NeRF 3D GS\"]\n F --> G[\"Sample\"]\n G --> H[\"Point Cloud\"]\n H --> I[\"Feature\"]\n I --> J[\"Mesh Autoregressive Transformer\"]\n J --> K[\"...\"]\n K -.-> L[\"Cross-Entropy Loss\"]\n L --> M[\"Cross-Entropy Loss\"]\n M --> N[\"Cross-Entropy Loss\"]\n N --> O[\"Cross-Entropy Loss\"]\n O --> P[\"VQ Decoder\"]\n P --> Q[\"Generated Mesh\"]\n```", + "image_path": "ed7acb9369bfcc2c48faff57b105d6db318c21dfbb1b16f91c12ef6419bebbfe.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 170, + 504, + 226 + ], + "type": "image_caption", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 171, + 504, + 181 + ], + "spans": [ + { + "bbox": [ + 107, + 171, + 504, + 181 + ], + "type": "text", + "content": "Figure 4: Pipeline Overview. We introduce MeshAnything, an autoregressive transformer capable", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 182, + 504, + 193 + ], + "spans": [ + { + "bbox": [ + 107, + 182, + 504, + 193 + ], + "type": "text", + "content": "of generating Artist-Created Meshes that adhere to given 3D shapes. During training, we inject point", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 194, + 504, + 203 + ], + "spans": [ + { + "bbox": [ + 107, + 194, + 504, + 203 + ], + "type": "text", + "content": "clouds features into a decoder-only transformer and supervise it using token sequences derived from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 205, + 504, + 214 + ], + "spans": [ + { + "bbox": [ + 107, + 205, + 504, + 214 + ], + "type": "text", + "content": "the Artist-Created meshes. After training, MeshAnything takes point clouds sampled from various", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 217, + 398, + 224 + ], + "spans": [ + { + "bbox": [ + 107, + 217, + 398, + 224 + ], + "type": "text", + "content": "3D representations as input and generates aligned Artist-Created meshes.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 0, + "sub_type": "flowchart" + }, + { + "bbox": [ + 105, + 247, + 173, + 259 + ], + "type": "title", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 106, + 248, + 173, + 260 + ], + "spans": [ + { + "bbox": [ + 106, + 248, + 173, + 260 + ], + "type": "text", + "content": "4 METHOD", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 274, + 504, + 308 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 106, + 275, + 504, + 285 + ], + "spans": [ + { + "bbox": [ + 106, + 275, + 504, + 285 + ], + "type": "text", + "content": "In this section, we detail our shape condition strategy in Section 4.1. After that, we provide a detailed", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 286, + 504, + 297 + ], + "spans": [ + { + "bbox": [ + 107, + 286, + 504, + 297 + ], + "type": "text", + "content": "description for MeshAnything, which consists of a VQVAE with our newly proposed noise-resistant", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 297, + 457, + 307 + ], + "spans": [ + { + "bbox": [ + 107, + 297, + 457, + 307 + ], + "type": "text", + "content": "decoder (Section 4.2) and a shape-conditioned autoregressive transformer (Section 4.3).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 323, + 353, + 333 + ], + "type": "title", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 324, + 351, + 333 + ], + "spans": [ + { + "bbox": [ + 107, + 324, + 351, + 333 + ], + "type": "text", + "content": "4.1 SHAPE ENCODING FOR CONDITIONAL GENERATION", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 344, + 504, + 378 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 345, + 504, + 355 + ], + "spans": [ + { + "bbox": [ + 107, + 345, + 504, + 355 + ], + "type": "text", + "content": "We begin by describing our shape condition strategy. MeshAnything targets learning p(M|S), so", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 356, + 504, + 366 + ], + "spans": [ + { + "bbox": [ + 107, + 356, + 504, + 366 + ], + "type": "text", + "content": "we need to pair each mesh M with a corresponding S, i.e., the shape condition. Choosing an", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 367, + 481, + 377 + ], + "spans": [ + { + "bbox": [ + 107, + 367, + 481, + 377 + ], + "type": "text", + "content": "appropriate 3D representation for S is non-trivial and should satisfy the following conditions:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 127, + 388, + 505, + 500 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 129, + 388, + 504, + 423 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 131, + 391, + 504, + 399 + ], + "spans": [ + { + "bbox": [ + 131, + 391, + 504, + 399 + ], + "type": "text", + "content": "1. It should be easily extracted from various 3D representations. This ensures that the trained", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 401, + 504, + 411 + ], + "spans": [ + { + "bbox": [ + 142, + 401, + 504, + 411 + ], + "type": "text", + "content": "models can be integrated with a wide range of 3D asset production pipelines Mildenhall", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 412, + 504, + 422 + ], + "spans": [ + { + "bbox": [ + 143, + 412, + 504, + 422 + ], + "type": "text", + "content": "et al. (2020); Kerbl et al. (2023b); Hong et al. (2023); Poole et al. (2023); Tang et al. (2024).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 128, + 427, + 504, + 461 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 129, + 429, + 504, + 439 + ], + "spans": [ + { + "bbox": [ + 129, + 429, + 504, + 439 + ], + "type": "text", + "content": "2. It should be suitable for data augmentation to prevent overfitting. To ensure the effec-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 141, + 439, + 504, + 450 + ], + "spans": [ + { + "bbox": [ + 141, + 439, + 504, + 450 + ], + "type": "text", + "content": "tiveness of S during training, any data augmentation applied to M must be equivalently", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 451, + 206, + 460 + ], + "spans": [ + { + "bbox": [ + 143, + 451, + 206, + 460 + ], + "type": "text", + "content": "applicable to S.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 128, + 466, + 504, + 500 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 129, + 467, + 504, + 477 + ], + "spans": [ + { + "bbox": [ + 129, + 467, + 504, + 477 + ], + "type": "text", + "content": "3. It should be efficiently and conveniently input into the model as a condition. To ensure", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 142, + 478, + 504, + 488 + ], + "spans": [ + { + "bbox": [ + 142, + 478, + 504, + 488 + ], + "type": "text", + "content": "the model comprehends the shape information and to maintain efficient training, S must be", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 143, + 490, + 317, + 498 + ], + "spans": [ + { + "bbox": [ + 143, + 490, + 317, + 498 + ], + "type": "text", + "content": "easily and effectively encoded into features.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 104, + 511, + 504, + 599 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 513, + 503, + 521 + ], + "spans": [ + { + "bbox": [ + 107, + 513, + 503, + 521 + ], + "type": "text", + "content": "Considering the first and second points, S should be in an explicit representation. Further consid-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 523, + 503, + 533 + ], + "spans": [ + { + "bbox": [ + 107, + 523, + 503, + 533 + ], + "type": "text", + "content": "ering the third point, the main explicit 3D representations that can be easily encoded as features", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 535, + 504, + 544 + ], + "spans": [ + { + "bbox": [ + 107, + 535, + 504, + 544 + ], + "type": "text", + "content": "are voxels and point clouds. Both representations are suitable, but voxels typically require a high", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 546, + 503, + 555 + ], + "spans": [ + { + "bbox": [ + 107, + 546, + 503, + 555 + ], + "type": "text", + "content": "resolution to accurately represent shapes, and processing high-resolution voxels into features is com-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 556, + 504, + 566 + ], + "spans": [ + { + "bbox": [ + 107, + 556, + 504, + 566 + ], + "type": "text", + "content": "putationally expensive. Additionally, voxels, being a discrete representation, are less precise for data", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 567, + 504, + 577 + ], + "spans": [ + { + "bbox": [ + 106, + 567, + 504, + 577 + ], + "type": "text", + "content": "augmentation compared to point clouds. Therefore, we chose point clouds as the representation for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 578, + 504, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 578, + 504, + 588 + ], + "type": "text", + "content": "S. To enhance the expressive power of the point clouds, we also include normals into the point cloud", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 590, + 166, + 598 + ], + "spans": [ + { + "bbox": [ + 107, + 590, + 166, + 598 + ], + "type": "text", + "content": "representation.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 605, + 504, + 661 + ], + "type": "text", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 107, + 606, + 503, + 616 + ], + "spans": [ + { + "bbox": [ + 107, + 606, + 503, + 616 + ], + "type": "text", + "content": "To obtain point clouds from the ground truth mesh for training, we could simply sample point clouds", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "spans": [ + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "type": "text", + "content": "directly from the surface of M. However, this would create problems during inference: the surfaces", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 629, + 503, + 637 + ], + "spans": [ + { + "bbox": [ + 107, + 629, + 503, + 637 + ], + "type": "text", + "content": "of automatically generated 3D assets are often rougher than those of AMs. For example, in AMs,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 639, + 504, + 649 + ], + "spans": [ + { + "bbox": [ + 107, + 639, + 504, + 649 + ], + "type": "text", + "content": "we would sample a series of points on a flat plane, whereas automatically generated 3D assets would", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 651, + 410, + 659 + ], + "spans": [ + { + "bbox": [ + 107, + 651, + 410, + 659 + ], + "type": "text", + "content": "have uneven surfaces, causing a domain gap between training and inference.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 666, + 505, + 733 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 107, + 667, + 504, + 676 + ], + "spans": [ + { + "bbox": [ + 107, + 667, + 504, + 676 + ], + "type": "text", + "content": "Therefore, we need to ensure that S extracted from the ground truth M during training has a similar", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 677, + 504, + 688 + ], + "spans": [ + { + "bbox": [ + 107, + 677, + 504, + 688 + ], + "type": "text", + "content": "domain to the S extracted during inference. To bring their domains closer, we intentionally construct", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 689, + 504, + 698 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 504, + 698 + ], + "type": "text", + "content": "coarse meshes from AMs. We first extract the signed distance function from M with Wang et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 504, + 709 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 504, + 709 + ], + "type": "text", + "content": "(2022), then convert it into a relatively coarse mesh using Marching Cubes Lorensen & Cline (1987)", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 712, + 504, + 720 + ], + "spans": [ + { + "bbox": [ + 107, + 712, + 504, + 720 + ], + "type": "text", + "content": "to destroy the ground truth topology. Finally, we sample point cloud and its normals from the coarse", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 721, + 504, + 731 + ], + "spans": [ + { + "bbox": [ + 107, + 721, + 504, + 731 + ], + "type": "text", + "content": "mesh. This approach also helps to avoid overfitting, as AMs typically have fewer faces, and each", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 83, + 503, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 503, + 95 + ], + "type": "text", + "content": "face can often sample multiple points. The network can easily recognize the ground truth topology", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 95, + 333, + 104 + ], + "spans": [ + { + "bbox": [ + 107, + 95, + 333, + 104 + ], + "type": "text", + "content": "by determining whether the points lie on the same plane.", + "score": 1.0, + "cross_page": true + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "bbox": [ + 104, + 83, + 504, + 106 + ], + "type": "text", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 106, + 83, + 503, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 503, + 95 + ], + "type": "text", + "content": "face can often sample multiple points. The network can easily recognize the ground truth topology", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 95, + 333, + 104 + ], + "spans": [ + { + "bbox": [ + 107, + 95, + 333, + 104 + ], + "type": "text", + "content": "by determining whether the points lie on the same plane.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 110, + 504, + 156 + ], + "type": "text", + "angle": 0, + "index": 1, + "lines": [ + { + "bbox": [ + 107, + 111, + 503, + 121 + ], + "spans": [ + { + "bbox": [ + 107, + 111, + 503, + 121 + ], + "type": "text", + "content": "Since almost all 3D representations can be converted into a coarse mesh using Marching", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 122, + 504, + 132 + ], + "spans": [ + { + "bbox": [ + 106, + 122, + 504, + 132 + ], + "type": "text", + "content": "Cubes Lorensen & Cline (1987) or sampled into point clouds, this ensures that the domain of S", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 133, + 504, + 143 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 504, + 143 + ], + "type": "text", + "content": "is consistent during both training and inference. We pair the point clouds extracted as S with M to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 142, + 280, + 156 + ], + "spans": [ + { + "bbox": [ + 107, + 144, + 178, + 153 + ], + "type": "text", + "content": "create a data item", + "score": 1.0 + }, + { + "bbox": [ + 179, + 142, + 227, + 156 + ], + "type": "inline_equation", + "content": "\\big \\{ ( { \\mathcal { M } } _ { i } , { \\mathcal { S } } _ { i } ) \\big \\} ", + "score": 0.9047 + }, + { + "bbox": [ + 228, + 145, + 280, + 154 + ], + "type": "text", + "content": "i for training.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 167, + 324, + 179 + ], + "type": "title", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 106, + 169, + 323, + 179 + ], + "spans": [ + { + "bbox": [ + 106, + 169, + 323, + 179 + ], + "type": "text", + "content": "4.2 VQ-VAE WITH NOISE-RESISTANT DECODER", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 188, + 504, + 255 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 190, + 504, + 198 + ], + "spans": [ + { + "bbox": [ + 107, + 190, + 504, + 198 + ], + "type": "text", + "content": "Following MeshGPT Siddiqui et al. (2023), we first train a VQ-VAE Van Den Oord et al. (2017) to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 201, + 503, + 209 + ], + "spans": [ + { + "bbox": [ + 107, + 201, + 503, + 209 + ], + "type": "text", + "content": "learn a vocabulary of geometric embeddings for better transformer Vaswani et al. (2017) learning.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 212, + 504, + 220 + ], + "spans": [ + { + "bbox": [ + 107, + 212, + 504, + 220 + ], + "type": "text", + "content": "Different to MeshGPT, which uses graph convolutional networks Wu et al. (2019) and ResNet He", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 222, + 504, + 232 + ], + "spans": [ + { + "bbox": [ + 107, + 222, + 504, + 232 + ], + "type": "text", + "content": "et al. (2016) as the encoder and decoder respectively, we employ transformers with identical struc-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 232, + 504, + 243 + ], + "spans": [ + { + "bbox": [ + 107, + 232, + 504, + 243 + ], + "type": "text", + "content": "tures for both the encoder and decoder. 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(2023); Liu et al. (2024a); Xu et al. (2023); Guo et al. (2023), we first encode the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 626, + 504, + 635 + ], + "spans": [ + { + "bbox": [ + 107, + 626, + 504, + 635 + ], + "type": "text", + "content": "point cloud into a fixed-length token sequence with a point cloud encoder P and then concatenate it", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 636, + 504, + 647 + ], + "spans": [ + { + "bbox": [ + 106, + 636, + 504, + 647 + ], + "type": "text", + "content": "to the front of the embedding sequence from T VQ-VAE as the final input embedding sequence for", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 648, + 171, + 658 + ], + "spans": [ + { + "bbox": [ + 107, + 648, + 171, + 658 + ], + "type": "text", + "content": "the transformer:", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 257, + 658, + 504, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 257, + 658, + 504, + 670 + ], + "spans": [ + { + "bbox": [ + 257, + 658, + 504, + 670 + ], + "type": "interline_equation", + "content": "\\mathcal {T} ^ {\\prime} = \\operatorname{concat} (\\mathcal {P} (\\mathcal {S}), \\mathcal {T}) \\tag {9}", + "image_path": "2aab9c62c96846b493f2510a53f4eef3cdf119891dda2a8cd383b2125d12d63f.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 670, + 306, + 682 + ], + "type": "text", + "angle": 0, + "index": 17, + "lines": [ + { + "bbox": [ + 107, + 670, + 305, + 681 + ], + "spans": [ + { + "bbox": [ + 107, + 671, + 132, + 681 + ], + "type": "text", + "content": "where", + "score": 1.0 + }, + { + "bbox": [ + 133, + 670, + 145, + 681 + ], + "type": "inline_equation", + "content": "\\tau ^ { \\prime }", + "score": 0.8649 + }, + { + "bbox": [ + 145, + 671, + 305, + 681 + ], + "type": "text", + "content": "is the training input for the transformer.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 688, + 505, + 733 + ], + "type": "text", + "angle": 0, + "index": 18, + "lines": [ + { + "bbox": [ + 107, + 689, + 504, + 699 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 504, + 699 + ], + "type": "text", + "content": "We borrow a pretrained point encoder from Zhao et al. 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(2023), we first train a VQ-VAE Van Den Oord et al. (2017) to", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 201, + 503, + 209 + ], + "spans": [ + { + "bbox": [ + 107, + 201, + 503, + 209 + ], + "type": "text", + "content": "learn a vocabulary of geometric embeddings for better transformer Vaswani et al. (2017) learning.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 212, + 504, + 220 + ], + "spans": [ + { + "bbox": [ + 107, + 212, + 504, + 220 + ], + "type": "text", + "content": "Different to MeshGPT, which uses graph convolutional networks Wu et al. (2019) and ResNet He", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 222, + 504, + 232 + ], + "spans": [ + { + "bbox": [ + 107, + 222, + 504, + 232 + ], + "type": "text", + "content": "et al. 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As shown in the left table, compared to the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 91, + 504, + 102 + ], + "spans": [ + { + "bbox": [ + 106, + 91, + 504, + 102 + ], + "type": "text", + "content": "baseline Artist-Created Mesh Generation method, the meshes generated by MeshAnything are better", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 104, + 504, + 113 + ], + "spans": [ + { + "bbox": [ + 107, + 104, + 504, + 113 + ], + "type": "text", + "content": "aligned with human preferences. In the right table, we compare MeshAnything with mesh extraction", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 114, + 464, + 123 + ], + "spans": [ + { + "bbox": [ + 107, + 114, + 464, + 123 + ], + "type": "text", + "content": "baselines, and it received the most votes. 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MethodShape↑Topology↑
PolyGen12.7%11.1%
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MethodShape↑Topology↑
MarchingCubes38.1%10.2%
Shape As Points17.3%6.2%
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MethodShape↑Topology↑
PolyGen12.7%11.1%
MeshGPT24.1%28.2%
MeshAnything63.2%60.7%
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MethodShape↑Topology↑
MarchingCubes38.1%10.2%
Shape As Points17.3%6.2%
MeshAnything44.6%83.6%
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(2018), while we", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 601, + 503, + 609 + ], + "spans": [ + { + "bbox": [ + 107, + 601, + 503, + 609 + ], + "type": "text", + "content": "choose OPT-350M Zhang et al. (2022) as our autoregressive transformer architecture. The residual", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 611, + 470, + 620 + ], + "spans": [ + { + "bbox": [ + 107, + 611, + 470, + 620 + ], + "type": "text", + "content": "vector quantization Zeghidour et al. (2021) depth is set to 3, with a codebook size of 8,192.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 626, + 504, + 682 + ], + "type": "text", + "angle": 0, + "index": 14, + "lines": [ + { + "bbox": [ + 107, + 628, + 503, + 637 + ], + "spans": [ + { + "bbox": [ + 107, + 628, + 503, + 637 + ], + "type": "text", + "content": "Our point encoder is based on the pretrained point encoder from Zhao et al. (2024), which has", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 639, + 503, + 649 + ], + "spans": [ + { + "bbox": [ + 107, + 639, + 503, + 649 + ], + "type": "text", + "content": "been trained on Objaverse and thus can handle general shapes. This point encoder outputs a fixed-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 650, + 503, + 659 + ], + "spans": [ + { + "bbox": [ + 107, + 650, + 503, + 659 + ], + "type": "text", + "content": "length token sequence of 257 tokens, with 256 tokens primarily containing shape information and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 661, + 503, + 671 + ], + "spans": [ + { + "bbox": [ + 107, + 661, + 503, + 671 + ], + "type": "text", + "content": "an additional head token containing semantic information about the shape. We sample 4096 points", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 673, + 189, + 681 + ], + "spans": [ + { + "bbox": [ + 107, + 673, + 189, + 681 + ], + "type": "text", + "content": "for each point cloud.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 687, + 504, + 732 + ], + "type": "text", + "angle": 0, + "index": 15, + "lines": [ + { + "bbox": [ + 107, + 689, + 504, + 698 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 504, + 698 + ], + "type": "text", + "content": "The training batch size for both the VQ-VAE and the transformer is set to 8 per GPU. The VQ-VAE", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 105, + 700, + 504, + 709 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 504, + 709 + ], + "type": "text", + "content": "is trained on 8 A100 GPUs for 12 hours, after which we separately finetune the decoder part of the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 710, + 504, + 720 + ], + "spans": [ + { + "bbox": [ + 107, + 710, + 504, + 720 + ], + "type": "text", + "content": "VQ-VAE into a noise-resistant decoder, as detailed in Section 4.2. Following this, the transformer", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 721, + 260, + 731 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 260, + 731 + ], + "type": "text", + "content": "is trained on 8 A100 GPUs for 4 days.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 168, + 111, + 440, + 169 + ], + "blocks": [ + { + "bbox": [ + 104, + 79, + 504, + 103 + ], + "type": "table_caption", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 106, + 80, + 503, + 91 + ], + "spans": [ + { + "bbox": [ + 106, + 80, + 503, + 91 + ], + "type": "text", + "content": "Table 2: Quantitative Comparisons with Prior Arts on Objaverse. MeshAnything significantly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 91, + 413, + 102 + ], + "spans": [ + { + "bbox": [ + 106, + 91, + 413, + 102 + ], + "type": "text", + "content": "outperforms prior methods across all metrics. MMD, KID are scaled by 103.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 168, + 111, + 440, + 169 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 168, + 111, + 440, + 169 + ], + "spans": [ + { + "bbox": [ + 168, + 111, + 440, + 169 + ], + "type": "table", + "html": "
MethodCOV↑MMD↓1-NNA↓FID↓KID↓
PolyGen23.26.2288.248.827.7
MeshGPT41.73.8367.325.16.11
MeshAnything53.12.7255.714.51.89
", + "image_path": "cbf54f8daa7c24b2a3d45e6d3135a4ff3686aa78f4c49f65629cd4b147f96acd.jpg" + } + ] + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 188, + 254, + 201 + ], + "type": "title", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 190, + 253, + 200 + ], + "spans": [ + { + "bbox": [ + 107, + 190, + 253, + 200 + ], + "type": "text", + "content": "5.3 QUALITATIVE EXPERIMENTS", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 209, + 504, + 266 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 210, + 503, + 220 + ], + "spans": [ + { + "bbox": [ + 107, + 210, + 503, + 220 + ], + "type": "text", + "content": "As shown in Fig. 1, MeshAnything effectively generates AMs from various 3D representations.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 221, + 504, + 231 + ], + "spans": [ + { + "bbox": [ + 107, + 221, + 504, + 231 + ], + "type": "text", + "content": "In our experiments, we use Rodin Team (2024) as the text-to-3D and image-to-3D method, and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 232, + 504, + 242 + ], + "spans": [ + { + "bbox": [ + 107, + 232, + 504, + 242 + ], + "type": "text", + "content": "employ Mildenhall et al. (2020) and Kerbl et al. (2023a) as the 3D reconstruction pipeline to obtain", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 244, + 503, + 253 + ], + "spans": [ + { + "bbox": [ + 107, + 244, + 503, + 253 + ], + "type": "text", + "content": "the corresponding NeRF and Gaussian Splatting models. For additional qualitative results, please", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 254, + 364, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 254, + 364, + 264 + ], + "type": "text", + "content": "refer to A.2 combined with other 3D asset production pipelines.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 277, + 261, + 289 + ], + "type": "title", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 280, + 259, + 289 + ], + "spans": [ + { + "bbox": [ + 107, + 280, + 259, + 289 + ], + "type": "text", + "content": "5.4 QUANTITATIVE EXPERIMENTS", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 298, + 504, + 344 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 300, + 504, + 309 + ], + "spans": [ + { + "bbox": [ + 107, + 300, + 504, + 309 + ], + "type": "text", + "content": "From the generative model perspective, MeshAnything is a shape-conditioned mesh generation", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 311, + 504, + 320 + ], + "spans": [ + { + "bbox": [ + 107, + 311, + 504, + 320 + ], + "type": "text", + "content": "model. From the mesh extraction perspective, it extracts artist-created meshes from point clouds.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 322, + 504, + 332 + ], + "spans": [ + { + "bbox": [ + 107, + 322, + 504, + 332 + ], + "type": "text", + "content": "Consequently, we compare MeshAnything with both types of methods. Additional experiments can", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 332, + 247, + 342 + ], + "spans": [ + { + "bbox": [ + 106, + 332, + 247, + 342 + ], + "type": "text", + "content": "be found in Appendix Section A.2.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 348, + 504, + 437 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 350, + 503, + 359 + ], + "spans": [ + { + "bbox": [ + 107, + 350, + 503, + 359 + ], + "type": "text", + "content": "User Study. As shown in Tab. 1, we conducted two user studies, comparing with mesh generation", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 361, + 504, + 369 + ], + "spans": [ + { + "bbox": [ + 107, + 361, + 504, + 369 + ], + "type": "text", + "content": "baselines Nash et al. (2020); Siddiqui et al. (2023) and mesh extraction baselines Lorensen & Cline", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 372, + 504, + 381 + ], + "spans": [ + { + "bbox": [ + 107, + 372, + 504, + 381 + ], + "type": "text", + "content": "(1987); Peng et al. (2021), respectively. The mesh generation baselines are trained on ShapeNet,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 383, + 503, + 392 + ], + "spans": [ + { + "bbox": [ + 107, + 383, + 503, + 392 + ], + "type": "text", + "content": "and to ensure a fair comparison, we retrained them on Objaverse using the same transformer model", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 393, + 504, + 403 + ], + "spans": [ + { + "bbox": [ + 107, + 393, + 504, + 403 + ], + "type": "text", + "content": "as MeshAnything. Since the mesh generation baselines are all unconditional mesh generation meth-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 403, + 503, + 415 + ], + "spans": [ + { + "bbox": [ + 107, + 403, + 503, + 415 + ], + "type": "text", + "content": "ods, whereas MeshAnything is a shape-conditioned mesh generation method, we sampled shapes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 415, + 503, + 424 + ], + "spans": [ + { + "bbox": [ + 107, + 415, + 503, + 424 + ], + "type": "text", + "content": "randomly from the evaluation set of Objaverse as inputs for MeshAnything, while for the baseline", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 427, + 307, + 436 + ], + "spans": [ + { + "bbox": [ + 107, + 427, + 307, + 436 + ], + "type": "text", + "content": "methods, we performed random sampling directly.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 441, + 504, + 487 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 105, + 443, + 504, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 504, + 453 + ], + "type": "text", + "content": "In the mesh extraction baseline, since our method can also be viewed as a point cloud to mesh ap-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 454, + 504, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 454, + 504, + 464 + ], + "type": "text", + "content": "proach, we included Peng et al. (2021), a point cloud to mesh method, as a baseline. Additionally, we", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 465, + 504, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 465, + 504, + 475 + ], + "type": "text", + "content": "optimized the results from the mesh extraction baseline using the Blender remesh method Blender", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 476, + 315, + 487 + ], + "spans": [ + { + "bbox": [ + 107, + 476, + 315, + 487 + ], + "type": "text", + "content": "Development Team (2024) to simplify the topology.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 491, + 504, + 548 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 492, + 504, + 502 + ], + "spans": [ + { + "bbox": [ + 107, + 492, + 504, + 502 + ], + "type": "text", + "content": "We collected 30 results from each method and asked users to vote for the best one in terms of shape", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 504, + 504, + 514 + ], + "spans": [ + { + "bbox": [ + 107, + 504, + 504, + 514 + ], + "type": "text", + "content": "quality and topology quality. A total of 41 users participated, providing 1,230 valid comparisons.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 515, + 504, + 525 + ], + "spans": [ + { + "bbox": [ + 107, + 515, + 504, + 525 + ], + "type": "text", + "content": "Both user studies demonstrated the superiority of our method. The only difference between the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 525, + 504, + 535 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 504, + 535 + ], + "type": "text", + "content": "retrained MeshGPT and MeshAnything is whether they are shape-conditioned, further proving the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 537, + 351, + 547 + ], + "spans": [ + { + "bbox": [ + 107, + 537, + 351, + 547 + ], + "type": "text", + "content": "advantages of the shape-conditioned mesh generation setting.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 552, + 504, + 575 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 554, + 503, + 563 + ], + "spans": [ + { + "bbox": [ + 107, + 554, + 503, + 563 + ], + "type": "text", + "content": "Metrics. We follow the metric setting of Chen et al. (2022); Siddiqui et al. (2023). We detail this", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 565, + 240, + 574 + ], + "spans": [ + { + "bbox": [ + 107, + 565, + 240, + 574 + ], + "type": "text", + "content": "setting in Appendix Section. A.1.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 580, + 504, + 647 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 582, + 504, + 590 + ], + "spans": [ + { + "bbox": [ + 107, + 582, + 504, + 590 + ], + "type": "text", + "content": "Comparison with Mesh Generation Pipelines. We use the same retrained models from the user", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 593, + 504, + 601 + ], + "spans": [ + { + "bbox": [ + 107, + 593, + 504, + 601 + ], + "type": "text", + "content": "study for comparison. As shown in Tab. 2, MeshAnything significantly outperforms prior meth-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 603, + 504, + 613 + ], + "spans": [ + { + "bbox": [ + 107, + 603, + 504, + 613 + ], + "type": "text", + "content": "ods Nash et al. (2020); Siddiqui et al. (2023), indicating that it’s superior in both the shape and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 614, + 504, + 624 + ], + "spans": [ + { + "bbox": [ + 106, + 614, + 504, + 624 + ], + "type": "text", + "content": "topology quality. Since the only difference between the retrained MeshGPT and MeshAnything", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 626, + 503, + 634 + ], + "spans": [ + { + "bbox": [ + 107, + 626, + 503, + 634 + ], + "type": "text", + "content": "is the inclusion of shape conditioning, the superior performance of MeshAnything further demon-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 637, + 487, + 646 + ], + "spans": [ + { + "bbox": [ + 107, + 637, + 487, + 646 + ], + "type": "text", + "content": "strates that Shape-Conditioned Mesh Generation is a more suitable setting for mesh generation.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 663, + 195, + 675 + ], + "type": "title", + "angle": 0, + "index": 11, + "lines": [ + { + "bbox": [ + 105, + 663, + 195, + 675 + ], + "spans": [ + { + "bbox": [ + 105, + 663, + 195, + 675 + ], + "type": "text", + "content": "6 CONCLUSION", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 687, + 504, + 733 + ], + "type": "text", + "angle": 0, + "index": 12, + "lines": [ + { + "bbox": [ + 105, + 689, + 503, + 699 + ], + "spans": [ + { + "bbox": [ + 105, + 689, + 503, + 699 + ], + "type": "text", + "content": "In this work, we propose a novel setting for improved mesh extraction and mesh generation, namely", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 503, + 709 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 503, + 709 + ], + "type": "text", + "content": "Shape-Conditioned Artist-Created Mesh (AM) Generation. Following this setting, we introduce Me-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 711, + 504, + 720 + ], + "spans": [ + { + "bbox": [ + 107, + 711, + 504, + 720 + ], + "type": "text", + "content": "shAnything, a model capable of generating AMs that adhere to given 3D assets. MeshAnything can", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 721, + 504, + 731 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 504, + 731 + ], + "type": "text", + "content": "convert 3D assets in any 3D representation into AMs and thus can be integrated with diverse 3D", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 300, + 750, + 311, + 760 + ], + "type": "page_number", + "angle": 0, + "index": 13, + "lines": [ + { + "bbox": [ + 299, + 751, + 312, + 761 + ], + "spans": [ + { + "bbox": [ + 299, + 751, + 312, + 761 + ], + "type": "text", + "content": "10", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9, + "para_blocks": [ + { + "type": "table", + "bbox": [ + 168, + 111, + 440, + 169 + ], + "blocks": [ + { + "bbox": [ + 104, + 79, + 504, + 103 + ], + "type": "table_caption", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 106, + 80, + 503, + 91 + ], + "spans": [ + { + "bbox": [ + 106, + 80, + 503, + 91 + ], + "type": "text", + "content": "Table 2: Quantitative Comparisons with Prior Arts on Objaverse. MeshAnything significantly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 91, + 413, + 102 + ], + "spans": [ + { + "bbox": [ + 106, + 91, + 413, + 102 + ], + "type": "text", + "content": "outperforms prior methods across all metrics. MMD, KID are scaled by 103.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 168, + 111, + 440, + 169 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 168, + 111, + 440, + 169 + ], + "spans": [ + { + "bbox": [ + 168, + 111, + 440, + 169 + ], + "type": "table", + "html": "
MethodCOV↑MMD↓1-NNA↓FID↓KID↓
PolyGen23.26.2288.248.827.7
MeshGPT41.73.8367.325.16.11
MeshAnything53.12.7255.714.51.89
", + "image_path": "cbf54f8daa7c24b2a3d45e6d3135a4ff3686aa78f4c49f65629cd4b147f96acd.jpg" + } + ] + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 188, + 254, + 201 + ], + "type": "title", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 190, + 253, + 200 + ], + "spans": [ + { + "bbox": [ + 107, + 190, + 253, + 200 + ], + "type": "text", + "content": "5.3 QUALITATIVE EXPERIMENTS", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 209, + 504, + 266 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 210, + 503, + 220 + ], + "spans": [ + { + "bbox": [ + 107, + 210, + 503, + 220 + ], + "type": "text", + "content": "As shown in Fig. 1, MeshAnything effectively generates AMs from various 3D representations.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 221, + 504, + 231 + ], + "spans": [ + { + "bbox": [ + 107, + 221, + 504, + 231 + ], + "type": "text", + "content": "In our experiments, we use Rodin Team (2024) as the text-to-3D and image-to-3D method, and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 232, + 504, + 242 + ], + "spans": [ + { + "bbox": [ + 107, + 232, + 504, + 242 + ], + "type": "text", + "content": "employ Mildenhall et al. (2020) and Kerbl et al. (2023a) as the 3D reconstruction pipeline to obtain", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 244, + 503, + 253 + ], + "spans": [ + { + "bbox": [ + 107, + 244, + 503, + 253 + ], + "type": "text", + "content": "the corresponding NeRF and Gaussian Splatting models. For additional qualitative results, please", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 254, + 364, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 254, + 364, + 264 + ], + "type": "text", + "content": "refer to A.2 combined with other 3D asset production pipelines.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 277, + 261, + 289 + ], + "type": "title", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 280, + 259, + 289 + ], + "spans": [ + { + "bbox": [ + 107, + 280, + 259, + 289 + ], + "type": "text", + "content": "5.4 QUANTITATIVE EXPERIMENTS", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 298, + 504, + 344 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 300, + 504, + 309 + ], + "spans": [ + { + "bbox": [ + 107, + 300, + 504, + 309 + ], + "type": "text", + "content": "From the generative model perspective, MeshAnything is a shape-conditioned mesh generation", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 311, + 504, + 320 + ], + "spans": [ + { + "bbox": [ + 107, + 311, + 504, + 320 + ], + "type": "text", + "content": "model. From the mesh extraction perspective, it extracts artist-created meshes from point clouds.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 322, + 504, + 332 + ], + "spans": [ + { + "bbox": [ + 107, + 322, + 504, + 332 + ], + "type": "text", + "content": "Consequently, we compare MeshAnything with both types of methods. Additional experiments can", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 332, + 247, + 342 + ], + "spans": [ + { + "bbox": [ + 106, + 332, + 247, + 342 + ], + "type": "text", + "content": "be found in Appendix Section A.2.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 348, + 504, + 437 + ], + "type": "text", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 350, + 503, + 359 + ], + "spans": [ + { + "bbox": [ + 107, + 350, + 503, + 359 + ], + "type": "text", + "content": "User Study. As shown in Tab. 1, we conducted two user studies, comparing with mesh generation", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 361, + 504, + 369 + ], + "spans": [ + { + "bbox": [ + 107, + 361, + 504, + 369 + ], + "type": "text", + "content": "baselines Nash et al. (2020); Siddiqui et al. (2023) and mesh extraction baselines Lorensen & Cline", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 372, + 504, + 381 + ], + "spans": [ + { + "bbox": [ + 107, + 372, + 504, + 381 + ], + "type": "text", + "content": "(1987); Peng et al. (2021), respectively. The mesh generation baselines are trained on ShapeNet,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 383, + 503, + 392 + ], + "spans": [ + { + "bbox": [ + 107, + 383, + 503, + 392 + ], + "type": "text", + "content": "and to ensure a fair comparison, we retrained them on Objaverse using the same transformer model", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 393, + 504, + 403 + ], + "spans": [ + { + "bbox": [ + 107, + 393, + 504, + 403 + ], + "type": "text", + "content": "as MeshAnything. 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(2021), a point cloud to mesh method, as a baseline. Additionally, we", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 465, + 504, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 465, + 504, + 475 + ], + "type": "text", + "content": "optimized the results from the mesh extraction baseline using the Blender remesh method Blender", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 476, + 315, + 487 + ], + "spans": [ + { + "bbox": [ + 107, + 476, + 315, + 487 + ], + "type": "text", + "content": "Development Team (2024) to simplify the topology.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 491, + 504, + 548 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 492, + 504, + 502 + ], + "spans": [ + { + "bbox": [ + 107, + 492, + 504, + 502 + ], + "type": "text", + "content": "We collected 30 results from each method and asked users to vote for the best one in terms of shape", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 504, + 504, + 514 + ], + "spans": [ + { + "bbox": [ + 107, + 504, + 504, + 514 + ], + "type": "text", + "content": "quality and topology quality. A total of 41 users participated, providing 1,230 valid comparisons.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 515, + 504, + 525 + ], + "spans": [ + { + "bbox": [ + 107, + 515, + 504, + 525 + ], + "type": "text", + "content": "Both user studies demonstrated the superiority of our method. The only difference between the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 525, + 504, + 535 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 504, + 535 + ], + "type": "text", + "content": "retrained MeshGPT and MeshAnything is whether they are shape-conditioned, further proving the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 537, + 351, + 547 + ], + "spans": [ + { + "bbox": [ + 107, + 537, + 351, + 547 + ], + "type": "text", + "content": "advantages of the shape-conditioned mesh generation setting.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 552, + 504, + 575 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 554, + 503, + 563 + ], + "spans": [ + { + "bbox": [ + 107, + 554, + 503, + 563 + ], + "type": "text", + "content": "Metrics. We follow the metric setting of Chen et al. (2022); Siddiqui et al. (2023). We detail this", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 565, + 240, + 574 + ], + "spans": [ + { + "bbox": [ + 107, + 565, + 240, + 574 + ], + "type": "text", + "content": "setting in Appendix Section. A.1.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 580, + 504, + 647 + ], + "type": "text", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 107, + 582, + 504, + 590 + ], + "spans": [ + { + "bbox": [ + 107, + 582, + 504, + 590 + ], + "type": "text", + "content": "Comparison with Mesh Generation Pipelines. We use the same retrained models from the user", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 593, + 504, + 601 + ], + "spans": [ + { + "bbox": [ + 107, + 593, + 504, + 601 + ], + "type": "text", + "content": "study for comparison. As shown in Tab. 2, MeshAnything significantly outperforms prior meth-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 603, + 504, + 613 + ], + "spans": [ + { + "bbox": [ + 107, + 603, + 504, + 613 + ], + "type": "text", + "content": "ods Nash et al. (2020); Siddiqui et al. (2023), indicating that it’s superior in both the shape and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 614, + 504, + 624 + ], + "spans": [ + { + "bbox": [ + 106, + 614, + 504, + 624 + ], + "type": "text", + "content": "topology quality. 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(a) further demonstrates our capability to achieve highly control-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 439, + 503, + 448 + ], + "spans": [ + { + "bbox": [ + 107, + 439, + 503, + 448 + ], + "type": "text", + "content": "lable mesh generation when combined with 3D asset production pipelines. Besides, we compare", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 450, + 504, + 460 + ], + "spans": [ + { + "bbox": [ + 107, + 450, + 504, + 460 + ], + "type": "text", + "content": "our reseults with ground truth in (b) and (c). In (b), MeshAnything generates meshes with better", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 461, + 503, + 471 + ], + "spans": [ + { + "bbox": [ + 107, + 461, + 503, + 471 + ], + "type": "text", + "content": "topology and fewer faces than the ground truth. 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In contrast, our Noise-Resistant Decoder, aided by shape conditions, has the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 617, + 444, + 627 + ], + "spans": [ + { + "bbox": [ + 107, + 617, + 444, + 627 + ], + "type": "text", + "content": "ability to resist these low-quality token sequences, producing higher-quality meshes.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 5, + "sub_type": "text_image" + }, + { + "bbox": [ + 105, + 651, + 174, + 660 + ], + "type": "title", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 107, + 651, + 173, + 661 + ], + "spans": [ + { + "bbox": [ + 107, + 651, + 173, + 661 + ], + "type": "text", + "content": "A.1 METRICS", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 670, + 504, + 693 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 672, + 504, + 681 + ], + "spans": [ + { + "bbox": [ + 107, + 672, + 504, + 681 + ], + "type": "text", + "content": "We follow the evaluation metric setting of Siddiqui et al. (2023) in mesh generation experiments and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 683, + 362, + 692 + ], + "spans": [ + { + "bbox": [ + 107, + 683, + 362, + 692 + ], + "type": "text", + "content": "the setting of Chen et al. (2022) in mesh extraction experiments.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 698, + 504, + 732 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 700, + 504, + 710 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 504, + 710 + ], + "type": "text", + "content": "We quantitatively evaluate mesh quality by uniformly sampling 100K points from the faces of both", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 711, + 504, + 720 + ], + "spans": [ + { + "bbox": [ + 107, + 711, + 504, + 720 + ], + "type": "text", + "content": "the ground truth meshes and the predicted meshes, and then computing a set of metrics to assess", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 722, + 254, + 731 + ], + "spans": [ + { + "bbox": [ + 107, + 722, + 254, + 731 + ], + "type": "text", + "content": "various aspects of the reconstruction.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 300, + 751, + 311, + 760 + ], + "type": "page_number", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 299, + 751, + 312, + 761 + ], + "spans": [ + { + "bbox": [ + 299, + 751, + 312, + 761 + ], + "type": "text", + "content": "16", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 15, + "para_blocks": [ + { + "type": "image", + "bbox": [ + 112, + 110, + 504, + 251 + ], + "blocks": [ + { + "bbox": [ + 106, + 81, + 183, + 92 + ], + "type": "image_caption", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 106, + 82, + 182, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 182, + 94 + ], + "type": "text", + "content": "A APPENDIX", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 112, + 110, + 504, + 251 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 110, + 504, + 251 + ], + "spans": [ + { + "bbox": [ + 112, + 110, + 504, + 251 + ], + "type": "image", + "content": "Collection of 3D wireframe models and 3D mesh designs including point cloud, image, and dense mesh (no text or symbols)", + "image_path": "7ab65c46fed251beed13c7e66df489ff073504f84d285a2b7c7eda53b00ac28c.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 259, + 504, + 283 + ], + "type": "image_caption", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 107, + 260, + 504, + 270 + ], + "spans": [ + { + "bbox": [ + 107, + 260, + 504, + 270 + ], + "type": "text", + "content": "Figure 5: Additional qualitative results of MeshAnything. As shown, MeshAnything can be", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 273, + 488, + 281 + ], + "spans": [ + { + "bbox": [ + 107, + 273, + 488, + 281 + ], + "type": "text", + "content": "integrated with various 3D production pipelines to achieve highly controllable mesh generation.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 1, + "sub_type": "natural_image" + }, + { + "type": "image", + "bbox": [ + 109, + 300, + 506, + 417 + ], + "blocks": [ + { + "bbox": [ + 109, + 300, + 506, + 417 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 300, + 506, + 417 + ], + "spans": [ + { + "bbox": [ + 109, + 300, + 506, + 417 + ], + "type": "image", + "content": "Point Cloud Condition\nImage Condition\nImage Condition\n(a)\n312 faces\nOurs\n518 faces\nGT\n612 faces\nOurs\n529 faces\nGT\n(b)\n(c)", + "image_path": "862aeab2050e05c2e08496535a396d53ce14ba0421ede1b90aa189a88547daac.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 427, + 504, + 495 + ], + "type": "image_caption", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 427, + 503, + 437 + ], + "spans": [ + { + "bbox": [ + 107, + 427, + 503, + 437 + ], + "type": "text", + "content": "Figure 6: Qualitative Results. (a) further demonstrates our capability to achieve highly control-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 439, + 503, + 448 + ], + "spans": [ + { + "bbox": [ + 107, + 439, + 503, + 448 + ], + "type": "text", + "content": "lable mesh generation when combined with 3D asset production pipelines. Besides, we compare", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 450, + 504, + 460 + ], + "spans": [ + { + "bbox": [ + 107, + 450, + 504, + 460 + ], + "type": "text", + "content": "our reseults with ground truth in (b) and (c). In (b), MeshAnything generates meshes with better", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 461, + 503, + 471 + ], + "spans": [ + { + "bbox": [ + 107, + 461, + 503, + 471 + ], + "type": "text", + "content": "topology and fewer faces than the ground truth. In (c), we produce meshes with a completely differ-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 472, + 504, + 482 + ], + "spans": [ + { + "bbox": [ + 107, + 472, + 504, + 482 + ], + "type": "text", + "content": "ent topology while achieving a similar shape, proving that our method does not simply overfit but", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 483, + 354, + 493 + ], + "spans": [ + { + "bbox": [ + 107, + 483, + 354, + 493 + ], + "type": "text", + "content": "understands how to construct meshes using efficient topology.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 3, + "sub_type": "text_image" + }, + { + "type": "image", + "bbox": [ + 111, + 510, + 500, + 575 + ], + "blocks": [ + { + "bbox": [ + 111, + 510, + 500, + 575 + ], + "type": "image_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 510, + 500, + 575 + ], + "spans": [ + { + "bbox": [ + 111, + 510, + 500, + 575 + ], + "type": "image", + "content": "W.O. Noise-Resistant Decoder\nOurs\nW.O. Noise-Resistant Decoder\nOurs\nW.O. Noise-Resistant Decoder\nOurs", + "image_path": "eb9f539a645e6b2e3c176b61b49ba88020584ef19f05df2c9ea2f6addf7bca86.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 583, + 504, + 628 + ], + "type": "image_caption", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 106, + 584, + 504, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 584, + 504, + 594 + ], + "type": "text", + "content": "Figure 7: Ablation on Noise-Resistant Decoder. The decoder-only transformer may generate low-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 595, + 504, + 605 + ], + "spans": [ + { + "bbox": [ + 107, + 595, + 504, + 605 + ], + "type": "text", + "content": "quality token sequences, and the decoder of VQ-VAE would typically produce flawed meshes based", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 606, + 504, + 616 + ], + "spans": [ + { + "bbox": [ + 107, + 606, + 504, + 616 + ], + "type": "text", + "content": "on these sequences. In contrast, our Noise-Resistant Decoder, aided by shape conditions, has the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 617, + 444, + 627 + ], + "spans": [ + { + "bbox": [ + 107, + 617, + 444, + 627 + ], + "type": "text", + "content": "ability to resist these low-quality token sequences, producing higher-quality meshes.", + "score": 1.0 + } + ] + } + ] + } + ], + "index": 5, + "sub_type": "text_image" + }, + { + "bbox": [ + 105, + 651, + 174, + 660 + ], + "type": "title", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 107, + 651, + 173, + 661 + ], + "spans": [ + { + "bbox": [ + 107, + 651, + 173, + 661 + ], + "type": "text", + "content": "A.1 METRICS", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 670, + 504, + 693 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 672, + 504, + 681 + ], + "spans": [ + { + "bbox": [ + 107, + 672, + 504, + 681 + ], + "type": "text", + "content": "We follow the evaluation metric setting of Siddiqui et al. (2023) in mesh generation experiments and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 683, + 362, + 692 + ], + "spans": [ + { + "bbox": [ + 107, + 683, + 362, + 692 + ], + "type": "text", + "content": "the setting of Chen et al. 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Please refer to A.1 for metrics explanation.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 140, + 111, + 470, + 196 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 111, + 470, + 196 + ], + "spans": [ + { + "bbox": [ + 140, + 111, + 470, + 196 + ], + "type": "table", + "html": "
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", + "image_path": "0f72e96f0ce4abc9816ff609fb6b53f38a109b826510443cc8109a04076fc291.jpg" + } + ] + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 217, + 227, + 391, + 285 + ], + "blocks": [ + { + "bbox": [ + 126, + 205, + 483, + 217 + ], + "type": "table_caption", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 128, + 207, + 481, + 217 + ], + "spans": [ + { + "bbox": [ + 128, + 207, + 481, + 217 + ], + "type": "text", + "content": "Table 4: Ablation on Noise-Resistant (NR) Decoder for the Quality of Mesh Generation.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 217, + 227, + 391, + 285 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 217, + 227, + 391, + 285 + ], + "spans": [ + { + "bbox": [ + 217, + 227, + 391, + 285 + ], + "type": "table", + "html": "
Method\\mathbf{CD}↓(×10^{-2})\\mathbf{ECD}↓(×10^{-2})\\mathbf{NC}↑
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", + "image_path": "4c8edf4f1e0648c2ebb129bfe07d83d794970f16251239b451977c0b2d640628.jpg" + } + ] + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 304, + 504, + 372 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 308, + 503, + 315 + ], + "spans": [ + { + "bbox": [ + 107, + 308, + 503, + 315 + ], + "type": "text", + "content": "For mesh extraction, we report the following metrics: Chamfer Distance (CD) to evaluate the overall", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 317, + 504, + 327 + ], + "spans": [ + { + "bbox": [ + 107, + 317, + 504, + 327 + ], + "type": "text", + "content": "quality of a reconstructed mesh; Edge Chamfer Distance (ECD) to assess the preservation of sharp", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 328, + 504, + 338 + ], + "spans": [ + { + "bbox": [ + 107, + 328, + 504, + 338 + ], + "type": "text", + "content": "edges by sampling points near sharp edges and corners; and Normal Consistency (NC) to evaluate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 339, + 504, + 349 + ], + "spans": [ + { + "bbox": [ + 107, + 339, + 504, + 349 + ], + "type": "text", + "content": "the quality of the surface normals. Additionally, we report the number of mesh vertices (#V) and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 350, + 504, + 360 + ], + "spans": [ + { + "bbox": [ + 107, + 350, + 504, + 360 + ], + "type": "text", + "content": "the number of mesh faces (#F). We also provide the ratio of the estimated number of vertices to the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 361, + 410, + 371 + ], + "spans": [ + { + "bbox": [ + 107, + 361, + 410, + 371 + ], + "type": "text", + "content": "ground truth number of vertices (#V R) and the same ratio for faces (#F R).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 376, + 506, + 465 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 106, + 378, + 504, + 388 + ], + "spans": [ + { + "bbox": [ + 106, + 378, + 504, + 388 + ], + "type": "text", + "content": "For mesh generation, Coverage (COV) captures the diversity of generated meshes and is sensitive", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 389, + 504, + 398 + ], + "spans": [ + { + "bbox": [ + 106, + 389, + 504, + 398 + ], + "type": "text", + "content": "to mode dropping, but it does not reflect the quality of the results. Minimum Matching Distance", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 400, + 503, + 409 + ], + "spans": [ + { + "bbox": [ + 107, + 400, + 503, + 409 + ], + "type": "text", + "content": "(MMD) measures the average distance between the reference set and their nearest neighbors in the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 411, + 504, + 421 + ], + "spans": [ + { + "bbox": [ + 107, + 411, + 504, + 421 + ], + "type": "text", + "content": "generated set, though it lacks sensitivity to low-quality outputs. The 1-Nearest Neighbor Accuracy", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 422, + 504, + 432 + ], + "spans": [ + { + "bbox": [ + 107, + 422, + 504, + 432 + ], + "type": "text", + "content": "(1-NNA) assesses both quality and diversity between the generated and reference sets. To evaluate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 433, + 504, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 433, + 504, + 442 + ], + "type": "text", + "content": "topology quality, we render the ground truth meshes and generated meshes with their wireframes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 445, + 503, + 453 + ], + "spans": [ + { + "bbox": [ + 107, + 445, + 503, + 453 + ], + "type": "text", + "content": "visualized. We then employ Frechet Inception Distance (FID) and Kernel Inception Distance (KID)", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 455, + 400, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 455, + 400, + 464 + ], + "type": "text", + "content": "on rendered images. MMD, and KID scores are scaled by a factor of 103.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 479, + 195, + 490 + ], + "type": "title", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 480, + 195, + 490 + ], + "spans": [ + { + "bbox": [ + 107, + 480, + 195, + 490 + ], + "type": "text", + "content": "A.2 EXPERIMENTS", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 500, + 504, + 544 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 107, + 501, + 503, + 511 + ], + "spans": [ + { + "bbox": [ + 107, + 501, + 503, + 511 + ], + "type": "text", + "content": "Additional Qualitative Experiments We present more qualitative results of MeshAnything here.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 513, + 504, + 522 + ], + "spans": [ + { + "bbox": [ + 107, + 513, + 504, + 522 + ], + "type": "text", + "content": "As shown in Fig. 5 and Fig. 6, MeshAnything effectively generates AMs from various 3D repre-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 524, + 503, + 533 + ], + "spans": [ + { + "bbox": [ + 107, + 524, + 503, + 533 + ], + "type": "text", + "content": "sentations. When integrated with different 3D assets production pipelines, our method effectively", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 535, + 306, + 544 + ], + "spans": [ + { + "bbox": [ + 107, + 535, + 306, + 544 + ], + "type": "text", + "content": "achieves mesh generation with diverse conditions.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 550, + 506, + 650 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 551, + 503, + 560 + ], + "spans": [ + { + "bbox": [ + 107, + 551, + 503, + 560 + ], + "type": "text", + "content": "Next, Fig. 6 demonstrates that MeshAnything does not simply overfit but understands how to gener-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 563, + 503, + 572 + ], + "spans": [ + { + "bbox": [ + 107, + 563, + 503, + 572 + ], + "type": "text", + "content": "ate meshes with efficient topology that conform to the given shape. To prove this, we use manually-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 574, + 504, + 582 + ], + "spans": [ + { + "bbox": [ + 107, + 574, + 504, + 582 + ], + "type": "text", + "content": "created meshes as ground truth and use their shapes as conditions to test whether our model can", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 584, + 504, + 594 + ], + "spans": [ + { + "bbox": [ + 107, + 584, + 504, + 594 + ], + "type": "text", + "content": "generate meshes with comparable topology. To effectively use the ground truth as conditions, we", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 594, + 504, + 605 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 504, + 605 + ], + "type": "text", + "content": "first convert them into dense meshes using Marching Cubes Lorensen & Cline (1987) to disrupt their", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 607, + 503, + 615 + ], + "spans": [ + { + "bbox": [ + 107, + 607, + 503, + 615 + ], + "type": "text", + "content": "face structure. Then, we sample point clouds with normals from the dense meshes to serve as shape", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 616, + 504, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 504, + 628 + ], + "type": "text", + "content": "conditions. The experimental results in Fig. 6 show that MeshAnything is capable of generating", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 628, + 504, + 637 + ], + "spans": [ + { + "bbox": [ + 107, + 628, + 504, + 637 + ], + "type": "text", + "content": "meshes comparable to or even surpassing those modeled by human artists, exhibiting diverse and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 639, + 238, + 649 + ], + "spans": [ + { + "bbox": [ + 107, + 639, + 238, + 649 + ], + "type": "text", + "content": "strong 3D modeling capabilities.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 654, + 506, + 733 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 656, + 504, + 665 + ], + "spans": [ + { + "bbox": [ + 107, + 656, + 504, + 665 + ], + "type": "text", + "content": "Comparison with mesh extraction baselines. Our method is related to various mesh extraction", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 666, + 504, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 504, + 677 + ], + "type": "text", + "content": "methods Lorensen & Cline (1987); Chen & Zhang (2021); Chen et al. (2022); Shen et al. (2023);", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 678, + 503, + 688 + ], + "spans": [ + { + "bbox": [ + 107, + 678, + 503, + 688 + ], + "type": "text", + "content": "Peng et al. (2021) since we also convert other 3D representations into meshes. However, it is im-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 689, + 504, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 504, + 699 + ], + "type": "text", + "content": "portant to note that previous approaches are reconstruction-like methods that produce dense meshes,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 504, + 709 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 504, + 709 + ], + "type": "text", + "content": "while our approach is generative, creating Artist-Created Meshes (AMs) that are significantly more", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 711, + 503, + 720 + ], + "spans": [ + { + "bbox": [ + 107, + 711, + 503, + 720 + ], + "type": "text", + "content": "complex to produce than dense meshes. Therefore, strictly speaking, our method cannot be con-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 721, + 503, + 731 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 503, + 731 + ], + "type": "text", + "content": "sidered the same as these reconstruction-based mesh extraction methods. The main purpose of this", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ], + "discarded_blocks": [ + { + "bbox": [ + 300, + 750, + 311, + 760 + ], + "type": "page_number", + "angle": 0, + "index": 10, + "lines": [ + { + "bbox": [ + 299, + 751, + 312, + 761 + ], + "spans": [ + { + "bbox": [ + 299, + 751, + 312, + 761 + ], + "type": "text", + "content": "17", + "score": 1.0 + } + ] + } + ] + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 16, + "para_blocks": [ + { + "type": "table", + "bbox": [ + 140, + 111, + 470, + 196 + ], + "blocks": [ + { + "bbox": [ + 104, + 79, + 504, + 103 + ], + "type": "table_caption", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 107, + 82, + 503, + 90 + ], + "spans": [ + { + "bbox": [ + 107, + 82, + 503, + 90 + ], + "type": "text", + "content": "Table 3: Reconstruction Performance under Different Noise Levels with and without Noise-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 92, + 379, + 102 + ], + "spans": [ + { + "bbox": [ + 107, + 92, + 379, + 102 + ], + "type": "text", + "content": "Resistant (NR) Decoder. Please refer to A.1 for metrics explanation.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 140, + 111, + 470, + 196 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 111, + 470, + 196 + ], + "spans": [ + { + "bbox": [ + 140, + 111, + 470, + 196 + ], + "type": "table", + "html": "
Noise Level\\mathbf{CD}(\\times 10^{-2})\\downarrow\\mathbf{ECD}(\\times 10^{-2})\\downarrow\\mathbf{NC}\\uparrow
W/O NRW/ NRW/O NRW/ NRW/O NRW/ NR
0.00.0110.0070.0350.0230.9870.993
0.10.1870.0280.6130.1380.9730.991
0.51.1670.6392.5381.3290.9640.981
1.02.1311.7984.3172.3160.9520.969
", + "image_path": "0f72e96f0ce4abc9816ff609fb6b53f38a109b826510443cc8109a04076fc291.jpg" + } + ] + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 217, + 227, + 391, + 285 + ], + "blocks": [ + { + "bbox": [ + 126, + 205, + 483, + 217 + ], + "type": "table_caption", + "angle": 0, + "index": 2, + "lines": [ + { + "bbox": [ + 128, + 207, + 481, + 217 + ], + "spans": [ + { + "bbox": [ + 128, + 207, + 481, + 217 + ], + "type": "text", + "content": "Table 4: Ablation on Noise-Resistant (NR) Decoder for the Quality of Mesh Generation.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 217, + 227, + 391, + 285 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 217, + 227, + 391, + 285 + ], + "spans": [ + { + "bbox": [ + 217, + 227, + 391, + 285 + ], + "type": "table", + "html": "
Method\\mathbf{CD}↓(×10^{-2})\\mathbf{ECD}↓(×10^{-2})\\mathbf{NC}↑
W/O NR2.4236.4140.883
W/ NR2.2566.2450.902
", + "image_path": "4c8edf4f1e0648c2ebb129bfe07d83d794970f16251239b451977c0b2d640628.jpg" + } + ] + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 304, + 504, + 372 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 308, + 503, + 315 + ], + "spans": [ + { + "bbox": [ + 107, + 308, + 503, + 315 + ], + "type": "text", + "content": "For mesh extraction, we report the following metrics: Chamfer Distance (CD) to evaluate the overall", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 317, + 504, + 327 + ], + "spans": [ + { + "bbox": [ + 107, + 317, + 504, + 327 + ], + "type": "text", + "content": "quality of a reconstructed mesh; Edge Chamfer Distance (ECD) to assess the preservation of sharp", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 328, + 504, + 338 + ], + "spans": [ + { + "bbox": [ + 107, + 328, + 504, + 338 + ], + "type": "text", + "content": "edges by sampling points near sharp edges and corners; and Normal Consistency (NC) to evaluate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 339, + 504, + 349 + ], + "spans": [ + { + "bbox": [ + 107, + 339, + 504, + 349 + ], + "type": "text", + "content": "the quality of the surface normals. Additionally, we report the number of mesh vertices (#V) and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 350, + 504, + 360 + ], + "spans": [ + { + "bbox": [ + 107, + 350, + 504, + 360 + ], + "type": "text", + "content": "the number of mesh faces (#F). We also provide the ratio of the estimated number of vertices to the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 361, + 410, + 371 + ], + "spans": [ + { + "bbox": [ + 107, + 361, + 410, + 371 + ], + "type": "text", + "content": "ground truth number of vertices (#V R) and the same ratio for faces (#F R).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 376, + 506, + 465 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 106, + 378, + 504, + 388 + ], + "spans": [ + { + "bbox": [ + 106, + 378, + 504, + 388 + ], + "type": "text", + "content": "For mesh generation, Coverage (COV) captures the diversity of generated meshes and is sensitive", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 389, + 504, + 398 + ], + "spans": [ + { + "bbox": [ + 106, + 389, + 504, + 398 + ], + "type": "text", + "content": "to mode dropping, but it does not reflect the quality of the results. Minimum Matching Distance", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 400, + 503, + 409 + ], + "spans": [ + { + "bbox": [ + 107, + 400, + 503, + 409 + ], + "type": "text", + "content": "(MMD) measures the average distance between the reference set and their nearest neighbors in the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 411, + 504, + 421 + ], + "spans": [ + { + "bbox": [ + 107, + 411, + 504, + 421 + ], + "type": "text", + "content": "generated set, though it lacks sensitivity to low-quality outputs. The 1-Nearest Neighbor Accuracy", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 422, + 504, + 432 + ], + "spans": [ + { + "bbox": [ + 107, + 422, + 504, + 432 + ], + "type": "text", + "content": "(1-NNA) assesses both quality and diversity between the generated and reference sets. To evaluate", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 433, + 504, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 433, + 504, + 442 + ], + "type": "text", + "content": "topology quality, we render the ground truth meshes and generated meshes with their wireframes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 445, + 503, + 453 + ], + "spans": [ + { + "bbox": [ + 107, + 445, + 503, + 453 + ], + "type": "text", + "content": "visualized. We then employ Frechet Inception Distance (FID) and Kernel Inception Distance (KID)", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 455, + 400, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 455, + 400, + 464 + ], + "type": "text", + "content": "on rendered images. MMD, and KID scores are scaled by a factor of 103.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 479, + 195, + 490 + ], + "type": "title", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 480, + 195, + 490 + ], + "spans": [ + { + "bbox": [ + 107, + 480, + 195, + 490 + ], + "type": "text", + "content": "A.2 EXPERIMENTS", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 500, + 504, + 544 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 107, + 501, + 503, + 511 + ], + "spans": [ + { + "bbox": [ + 107, + 501, + 503, + 511 + ], + "type": "text", + "content": "Additional Qualitative Experiments We present more qualitative results of MeshAnything here.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 513, + 504, + 522 + ], + "spans": [ + { + "bbox": [ + 107, + 513, + 504, + 522 + ], + "type": "text", + "content": "As shown in Fig. 5 and Fig. 6, MeshAnything effectively generates AMs from various 3D repre-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 524, + 503, + 533 + ], + "spans": [ + { + "bbox": [ + 107, + 524, + 503, + 533 + ], + "type": "text", + "content": "sentations. When integrated with different 3D assets production pipelines, our method effectively", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 535, + 306, + 544 + ], + "spans": [ + { + "bbox": [ + 107, + 535, + 306, + 544 + ], + "type": "text", + "content": "achieves mesh generation with diverse conditions.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 550, + 506, + 650 + ], + "type": "text", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 551, + 503, + 560 + ], + "spans": [ + { + "bbox": [ + 107, + 551, + 503, + 560 + ], + "type": "text", + "content": "Next, Fig. 6 demonstrates that MeshAnything does not simply overfit but understands how to gener-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 563, + 503, + 572 + ], + "spans": [ + { + "bbox": [ + 107, + 563, + 503, + 572 + ], + "type": "text", + "content": "ate meshes with efficient topology that conform to the given shape. To prove this, we use manually-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 574, + 504, + 582 + ], + "spans": [ + { + "bbox": [ + 107, + 574, + 504, + 582 + ], + "type": "text", + "content": "created meshes as ground truth and use their shapes as conditions to test whether our model can", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 584, + 504, + 594 + ], + "spans": [ + { + "bbox": [ + 107, + 584, + 504, + 594 + ], + "type": "text", + "content": "generate meshes with comparable topology. To effectively use the ground truth as conditions, we", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 594, + 504, + 605 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 504, + 605 + ], + "type": "text", + "content": "first convert them into dense meshes using Marching Cubes Lorensen & Cline (1987) to disrupt their", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 607, + 503, + 615 + ], + "spans": [ + { + "bbox": [ + 107, + 607, + 503, + 615 + ], + "type": "text", + "content": "face structure. Then, we sample point clouds with normals from the dense meshes to serve as shape", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 616, + 504, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 504, + 628 + ], + "type": "text", + "content": "conditions. The experimental results in Fig. 6 show that MeshAnything is capable of generating", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 628, + 504, + 637 + ], + "spans": [ + { + "bbox": [ + 107, + 628, + 504, + 637 + ], + "type": "text", + "content": "meshes comparable to or even surpassing those modeled by human artists, exhibiting diverse and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 639, + 238, + 649 + ], + "spans": [ + { + "bbox": [ + 107, + 639, + 238, + 649 + ], + "type": "text", + "content": "strong 3D modeling capabilities.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 654, + 506, + 733 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 656, + 504, + 665 + ], + "spans": [ + { + "bbox": [ + 107, + 656, + 504, + 665 + ], + "type": "text", + "content": "Comparison with mesh extraction baselines. Our method is related to various mesh extraction", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 666, + 504, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 504, + 677 + ], + "type": "text", + "content": "methods Lorensen & Cline (1987); Chen & Zhang (2021); Chen et al. (2022); Shen et al. (2023);", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 678, + 503, + 688 + ], + "spans": [ + { + "bbox": [ + 107, + 678, + 503, + 688 + ], + "type": "text", + "content": "Peng et al. (2021) since we also convert other 3D representations into meshes. However, it is im-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 689, + 504, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 504, + 699 + ], + "type": "text", + "content": "portant to note that previous approaches are reconstruction-like methods that produce dense meshes,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 700, + 504, + 709 + ], + "spans": [ + { + "bbox": [ + 107, + 700, + 504, + 709 + ], + "type": "text", + "content": "while our approach is generative, creating Artist-Created Meshes (AMs) that are significantly more", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 711, + 503, + 720 + ], + "spans": [ + { + "bbox": [ + 107, + 711, + 503, + 720 + ], + "type": "text", + "content": "complex to produce than dense meshes. Therefore, strictly speaking, our method cannot be con-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 721, + 503, + 731 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 503, + 731 + ], + "type": "text", + "content": "sidered the same as these reconstruction-based mesh extraction methods. The main purpose of this", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 298, + 504, + 308 + ], + "spans": [ + { + "bbox": [ + 107, + 298, + 504, + 308 + ], + "type": "text", + "content": "comparison is to use these mesh extraction methods as a reference for evaluating the quality of the", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 310, + 503, + 319 + ], + "spans": [ + { + "bbox": [ + 107, + 310, + 503, + 319 + ], + "type": "text", + "content": "meshes generated by MeshAnything in terms of shape. We compare MeshAnything with Lorensen", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 320, + 504, + 329 + ], + "spans": [ + { + "bbox": [ + 107, + 320, + 504, + 329 + ], + "type": "text", + "content": "& Cline (1987); Shen et al. (2023); Peng et al. (2021). Among these, MarchingCubes is the most", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 106, + 331, + 504, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 504, + 340 + ], + "type": "text", + "content": "popular mesh extraction method, FlexiCubes represents the state-of-the-art in mesh extraction, and", + "score": 1.0, + "cross_page": true + } + ] + }, + { + "bbox": [ + 107, + 342, + 410, + 352 + ], + "spans": [ + { + "bbox": [ + 107, + 342, + 410, + 352 + ], + "type": "text", + "content": "Shape as Points is the leading method for extracting mesh from point cloud.", + "score": 1.0, + "cross_page": true + } + ] + } + ], + "merge_prev": false + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 112, + 121, + 496, + 269 + ], + "blocks": [ + { + "bbox": [ + 104, + 79, + 504, + 114 + ], + "type": "table_caption", + "angle": 0, + "index": 0, + "lines": [ + { + "bbox": [ + 107, + 82, + 503, + 91 + ], + "spans": [ + { + "bbox": [ + 107, + 82, + 503, + 91 + ], + "type": "text", + "content": "Table 5: Quantitative evaluation with mesh extraction baselines. MC, FC, SAP refer to Marching", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 91, + 504, + 102 + ], + "spans": [ + { + "bbox": [ + 106, + 91, + 504, + 102 + ], + "type": "text", + "content": "Cubes Lorensen & Cline (1987), FlexiCubes Shen et al. (2023), and Shape As Points Peng et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 104, + 363, + 113 + ], + "spans": [ + { + "bbox": [ + 107, + 104, + 363, + 113 + ], + "type": "text", + "content": "(2021), respectively. Please refer to A.1 for metrics explanation.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 112, + 121, + 496, + 269 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 121, + 496, + 269 + ], + "spans": [ + { + "bbox": [ + 112, + 121, + 496, + 269 + ], + "type": "table", + "html": "
Method\\mathbf{CD}\\downarrow(\\times 10^{-2})\\mathbf{ECD}\\downarrow(\\times 10^{-2})\\mathbf{NC}\\uparrow\\#V\\downarrow(\\times 10^{3})\\#F\\downarrow(\\times 10^{3})\\mathbf{V\\_R}\\downarrow\\mathbf{F\\_R}\\downarrow
(a) Marching Cubes1.5326.7330.95473.22146.0440.2462.2
(b) MC+Remesh (0.005)2.1747.8130.912127.8167.9748.1534.6
(c) MC+Remesh (0.010)2.0837.5780.92939.0141.78225.4132.3
(d) MC+Remesh (0.030)2.9158.3290.8635.8484.41034.3814.05
(e) MC+Remesh (0.050)4.1798.1380.8142.2991.53813.644.920
(f) MC+Remesh (0.100)7.31210.7710.7480.6250.3593.7351.149
(g) FC1.1906.1210.96759.12121.1378.2391.1
(h) FC+Remesh (0.010)1.8616.9400.93337.9840.19205.5124.2
(i) SAP1.7717.1120.93979.12152.3481.2489.3
(j) SAP+Remesh (0.010)2.3677.8620.92539.1742.87239.1136.6
(k) MeshAnything2.2566.2450.9020.1720.3180.8880.871
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Among these, MarchingCubes is the most", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 331, + 504, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 504, + 340 + ], + "type": "text", + "content": "popular mesh extraction method, FlexiCubes represents the state-of-the-art in mesh extraction, and", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 342, + 410, + 352 + ], + "spans": [ + { + "bbox": [ + 107, + 342, + 410, + 352 + ], + "type": "text", + "content": "Shape as Points is the leading method for extracting mesh from point cloud.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 357, + 506, + 479 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 359, + 503, + 368 + ], + "spans": [ + { + "bbox": [ + 107, + 359, + 503, + 368 + ], + "type": "text", + "content": "We also combined these methods with the remesh technique to test whether they could significantly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 370, + 504, + 380 + ], + "spans": [ + { + "bbox": [ + 107, + 370, + 504, + 380 + ], + "type": "text", + "content": "reduce the number of faces while maintaining shape quality. We used Blender Remesh in voxel", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 380, + 504, + 391 + ], + "spans": [ + { + "bbox": [ + 106, + 380, + 504, + 391 + ], + "type": "text", + "content": "mode Community (2018); Blender Development Team (2024), specifically using Blender version", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 392, + 504, + 401 + ], + "spans": [ + { + "bbox": [ + 106, + 392, + 504, + 401 + ], + "type": "text", + "content": "4.1, as the remesh method. Since our evaluation dataset includes non-watertight meshes, we first", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 403, + 503, + 411 + ], + "spans": [ + { + "bbox": [ + 107, + 403, + 503, + 411 + ], + "type": "text", + "content": "extract the signed distance fields (SDF) of all ground truth meshes using Wang et al. (2022), which", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 414, + 504, + 423 + ], + "spans": [ + { + "bbox": [ + 106, + 414, + 504, + 423 + ], + "type": "text", + "content": "can handle non-watertight meshes. We then apply Marching Cubes with a resolution of 128 on", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 425, + 503, + 434 + ], + "spans": [ + { + "bbox": [ + 107, + 425, + 503, + 434 + ], + "type": "text", + "content": "these SDFs. Next, we apply Blender remesh Blender Development Team (2024) with different", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 435, + 503, + 446 + ], + "spans": [ + { + "bbox": [ + 107, + 435, + 503, + 446 + ], + "type": "text", + "content": "voxel sizes to the Marching Cubes results, as both the remesh method and our approach are capable", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 447, + 504, + 456 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 504, + 456 + ], + "type": "text", + "content": "of simplifying topology. Additionally, the Marching Cubes result is used as the shape condition", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 458, + 503, + 467 + ], + "spans": [ + { + "bbox": [ + 106, + 458, + 503, + 467 + ], + "type": "text", + "content": "input to MeshAnything to obtain our results. The settings of Shen et al. (2023) and Peng et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 468, + 214, + 478 + ], + "spans": [ + { + "bbox": [ + 107, + 468, + 214, + 478 + ], + "type": "text", + "content": "(2021) follow their papers.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 484, + 506, + 638 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 486, + 503, + 495 + ], + "spans": [ + { + "bbox": [ + 107, + 486, + 503, + 495 + ], + "type": "text", + "content": "As shown in Tab. 5, we found that these methods require hundreds of times more faces to achieve", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 496, + 503, + 506 + ], + "spans": [ + { + "bbox": [ + 107, + 496, + 503, + 506 + ], + "type": "text", + "content": "results comparable to our method. Comparing (a), (g), (i) and (k), our method lags in Chamfer", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 507, + 503, + 517 + ], + "spans": [ + { + "bbox": [ + 107, + 507, + 503, + 517 + ], + "type": "text", + "content": "Distance (CD) and Normal Consistency (NC), mainly due to our method’s inherent failure cases", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 518, + 504, + 528 + ], + "spans": [ + { + "bbox": [ + 107, + 518, + 504, + 528 + ], + "type": "text", + "content": "as a generative model, which makes it less robust than these reconstruction-based mesh extraction", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 529, + 503, + 538 + ], + "spans": [ + { + "bbox": [ + 107, + 529, + 503, + 538 + ], + "type": "text", + "content": "methods. When comparing with remesh methods, we observe that they incur a high cost to achieve", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 541, + 504, + 550 + ], + "spans": [ + { + "bbox": [ + 107, + 541, + 504, + 550 + ], + "type": "text", + "content": "a face count similar to ours. Comparing (f) and (k), we find that even when remesh methods achieve", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 551, + 504, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 551, + 504, + 561 + ], + "type": "text", + "content": "a comparable face count, the number of vertices is still several times higher than ours, indicating", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 563, + 504, + 572 + ], + "spans": [ + { + "bbox": [ + 107, + 563, + 504, + 572 + ], + "type": "text", + "content": "that the topology efficiency of remesh methods is far inferior to ours, as they completely ignore", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 574, + 503, + 582 + ], + "spans": [ + { + "bbox": [ + 107, + 574, + 503, + 582 + ], + "type": "text", + "content": "the shape characteristics of the 3D assets. 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Additionally, we surprisingly find that our method can produce results", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 606, + 503, + 615 + ], + "spans": [ + { + "bbox": [ + 107, + 606, + 503, + 615 + ], + "type": "text", + "content": "with fewer faces than the ground truth, demonstrating that MeshAnything is not overfitting to the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "spans": [ + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "type": "text", + "content": "data but instead learns an efficient topology representation, occasionally surpassing the ground truth", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 628, + 140, + 637 + ], + "spans": [ + { + "bbox": [ + 106, + 628, + 140, + 637 + ], + "type": "text", + "content": "meshes.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 643, + 506, + 733 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 644, + 503, + 654 + ], + "spans": [ + { + "bbox": [ + 107, + 644, + 503, + 654 + ], + "type": "text", + "content": "Ablations on Noise-Resistant Conditional Decoder. 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We then perform ablation between two settings: one where the decoder", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 678, + 503, + 687 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 503, + 687 + ], + "type": "text", + "content": "remains unchanged and unaware of the shape condition, and another where the shape condition is", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 689, + 503, + 697 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 503, + 697 + ], + "type": "text", + "content": "injected into the transformer, as described in Section 4.2. Next, we randomly sample a noise from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 700, + 504, + 709 + ], + "spans": [ + { + "bbox": [ + 106, + 700, + 504, + 709 + ], + "type": "text", + "content": "gumbel distribution and add it to codebook sampling logits during the vector quantization process", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 711, + 504, + 720 + ], + "spans": [ + { + "bbox": [ + 106, + 711, + 504, + 720 + ], + "type": "text", + "content": "to simulate the potential low-quality token sequences generated by the transformer. 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MC, FC, SAP refer to Marching", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 91, + 504, + 102 + ], + "spans": [ + { + "bbox": [ + 106, + 91, + 504, + 102 + ], + "type": "text", + "content": "Cubes Lorensen & Cline (1987), FlexiCubes Shen et al. (2023), and Shape As Points Peng et al.", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 104, + 363, + 113 + ], + "spans": [ + { + "bbox": [ + 107, + 104, + 363, + 113 + ], + "type": "text", + "content": "(2021), respectively. Please refer to A.1 for metrics explanation.", + "score": 1.0 + } + ] + } + ] + }, + { + "bbox": [ + 112, + 121, + 496, + 269 + ], + "type": "table_body", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 121, + 496, + 269 + ], + "spans": [ + { + "bbox": [ + 112, + 121, + 496, + 269 + ], + "type": "table", + "html": "
Method\\mathbf{CD}\\downarrow(\\times 10^{-2})\\mathbf{ECD}\\downarrow(\\times 10^{-2})\\mathbf{NC}\\uparrow\\#V\\downarrow(\\times 10^{3})\\#F\\downarrow(\\times 10^{3})\\mathbf{V\\_R}\\downarrow\\mathbf{F\\_R}\\downarrow
(a) Marching Cubes1.5326.7330.95473.22146.0440.2462.2
(b) MC+Remesh (0.005)2.1747.8130.912127.8167.9748.1534.6
(c) MC+Remesh (0.010)2.0837.5780.92939.0141.78225.4132.3
(d) MC+Remesh (0.030)2.9158.3290.8635.8484.41034.3814.05
(e) MC+Remesh (0.050)4.1798.1380.8142.2991.53813.644.920
(f) MC+Remesh (0.100)7.31210.7710.7480.6250.3593.7351.149
(g) FC1.1906.1210.96759.12121.1378.2391.1
(h) FC+Remesh (0.010)1.8616.9400.93337.9840.19205.5124.2
(i) SAP1.7717.1120.93979.12152.3481.2489.3
(j) SAP+Remesh (0.010)2.3677.8620.92539.1742.87239.1136.6
(k) MeshAnything2.2566.2450.9020.1720.3180.8880.871
", + "image_path": "570664b3881998a3dd6868c6ee55bf8d42bd6333a7d525ab86e65793864941da.jpg" + } + ] + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 297, + 504, + 353 + ], + "type": "text", + "angle": 0, + "index": 2, + "lines": [], + "merge_prev": false, + "lines_deleted": true + }, + { + "bbox": [ + 104, + 357, + 506, + 479 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 359, + 503, + 368 + ], + "spans": [ + { + "bbox": [ + 107, + 359, + 503, + 368 + ], + "type": "text", + "content": "We also combined these methods with the remesh technique to test whether they could significantly", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 370, + 504, + 380 + ], + "spans": [ + { + "bbox": [ + 107, + 370, + 504, + 380 + ], + "type": "text", + "content": "reduce the number of faces while maintaining shape quality. 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Next, we apply Blender remesh Blender Development Team (2024) with different", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 435, + 503, + 446 + ], + "spans": [ + { + "bbox": [ + 107, + 435, + 503, + 446 + ], + "type": "text", + "content": "voxel sizes to the Marching Cubes results, as both the remesh method and our approach are capable", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 447, + 504, + 456 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 504, + 456 + ], + "type": "text", + "content": "of simplifying topology. Additionally, the Marching Cubes result is used as the shape condition", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 458, + 503, + 467 + ], + "spans": [ + { + "bbox": [ + 106, + 458, + 503, + 467 + ], + "type": "text", + "content": "input to MeshAnything to obtain our results. The settings of Shen et al. 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Comparing (a), (g), (i) and (k), our method lags in Chamfer", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 507, + 503, + 517 + ], + "spans": [ + { + "bbox": [ + 107, + 507, + 503, + 517 + ], + "type": "text", + "content": "Distance (CD) and Normal Consistency (NC), mainly due to our method’s inherent failure cases", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 518, + 504, + 528 + ], + "spans": [ + { + "bbox": [ + 107, + 518, + 504, + 528 + ], + "type": "text", + "content": "as a generative model, which makes it less robust than these reconstruction-based mesh extraction", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 529, + 503, + 538 + ], + "spans": [ + { + "bbox": [ + 107, + 529, + 503, + 538 + ], + "type": "text", + "content": "methods. When comparing with remesh methods, we observe that they incur a high cost to achieve", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 541, + 504, + 550 + ], + "spans": [ + { + "bbox": [ + 107, + 541, + 504, + 550 + ], + "type": "text", + "content": "a face count similar to ours. Comparing (f) and (k), we find that even when remesh methods achieve", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 551, + 504, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 551, + 504, + 561 + ], + "type": "text", + "content": "a comparable face count, the number of vertices is still several times higher than ours, indicating", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 563, + 504, + 572 + ], + "spans": [ + { + "bbox": [ + 107, + 563, + 504, + 572 + ], + "type": "text", + "content": "that the topology efficiency of remesh methods is far inferior to ours, as they completely ignore", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 574, + 503, + 582 + ], + "spans": [ + { + "bbox": [ + 107, + 574, + 503, + 582 + ], + "type": "text", + "content": "the shape characteristics of the 3D assets. It’s important to note that the metrics in mesh etraction", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 584, + 503, + 594 + ], + "spans": [ + { + "bbox": [ + 107, + 584, + 503, + 594 + ], + "type": "text", + "content": "can only indicate the quality of shape alignment, which do not effectively reflect the topological", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 596, + 503, + 605 + ], + "spans": [ + { + "bbox": [ + 107, + 596, + 503, + 605 + ], + "type": "text", + "content": "advantages of our method. Additionally, we surprisingly find that our method can produce results", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 606, + 503, + 615 + ], + "spans": [ + { + "bbox": [ + 107, + 606, + 503, + 615 + ], + "type": "text", + "content": "with fewer faces than the ground truth, demonstrating that MeshAnything is not overfitting to the", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "spans": [ + { + "bbox": [ + 107, + 617, + 504, + 627 + ], + "type": "text", + "content": "data but instead learns an efficient topology representation, occasionally surpassing the ground truth", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 628, + 140, + 637 + ], + "spans": [ + { + "bbox": [ + 106, + 628, + 140, + 637 + ], + "type": "text", + "content": "meshes.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 643, + 506, + 733 + ], + "type": "text", + "angle": 0, + "index": 5, + "lines": [ + { + "bbox": [ + 107, + 644, + 503, + 654 + ], + "spans": [ + { + "bbox": [ + 107, + 644, + 503, + 654 + ], + "type": "text", + "content": "Ablations on Noise-Resistant Conditional Decoder. We perform ablation experiments to verify", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 655, + 503, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 503, + 666 + ], + "type": "text", + "content": "the effectiveness of the Noise-Resistant Decoder. We begin with a VQ-VAE trained without any", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 667, + 503, + 676 + ], + "spans": [ + { + "bbox": [ + 107, + 667, + 503, + 676 + ], + "type": "text", + "content": "noise or conditioning. 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Next, we randomly sample a noise from", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 700, + 504, + 709 + ], + "spans": [ + { + "bbox": [ + 106, + 700, + 504, + 709 + ], + "type": "text", + "content": "gumbel distribution and add it to codebook sampling logits during the vector quantization process", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 711, + 504, + 720 + ], + "spans": [ + { + "bbox": [ + 106, + 711, + 504, + 720 + ], + "type": "text", + "content": "to simulate the potential low-quality token sequences generated by the transformer. 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The test method used dense meshes derived from corrupted GT meshes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 266, + 504, + 276 + ], + "spans": [ + { + "bbox": [ + 107, + 266, + 504, + 276 + ], + "type": "text", + "content": "as the condition for generating new meshes. The generated meshes were then assessed for shape", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 277, + 503, + 285 + ], + "spans": [ + { + "bbox": [ + 107, + 277, + 503, + 285 + ], + "type": "text", + "content": "alignment with the conditional shape. 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The experiment in (d) further demonstrates that MeshAnything", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 454, + 457, + 462 + ], + "spans": [ + { + "bbox": [ + 107, + 454, + 457, + 462 + ], + "type": "text", + "content": "can tolerate generated point clouds and effectively integrate with 3D generation models.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 476, + 191, + 487 + ], + "type": "title", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 478, + 190, + 487 + ], + "spans": [ + { + "bbox": [ + 107, + 478, + 190, + 487 + ], + "type": "text", + "content": "A.3 LIMITATIONS", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 497, + 504, + 542 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 107, + 498, + 504, + 507 + ], + "spans": [ + { + "bbox": [ + 107, + 498, + 504, + 507 + ], + "type": "text", + "content": "Our method cannot generate meshes that exceed the maximum face count limit, so it cannot convert", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 510, + 504, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 510, + 504, + 519 + ], + "type": "text", + "content": "large scenes and particularly complex objects into meshes. 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Method\\mathbf{CD}↓(×10^{-2})\\mathbf{ECD}↓(×10^{-2})\\mathbf{NC}↑#V↓(×10^{3})#F↓(×10^{3})V\\_R↓F\\_R↓
(a) Noise scale 0.0052.3516.4120.8970.1750.3210.8950.880
(b) Noise scale 0.0202.9806.9700.8810.1800.3300.9010.910
(c) Noise scale 0.0504.9108.5560.7550.1620.2840.8110.802
(d) Rodin2.5526.6220.8330.1850.3420.9190.923
(e) MeshAnything2.2566.2450.9020.1720.3180.8880.871
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This indicates that the shape condition", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 226, + 433, + 237 + ], + "spans": [ + { + "bbox": [ + 106, + 226, + 433, + 237 + ], + "type": "text", + "content": "helps the decoder identify and correct imperfections in the input token sequences.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 243, + 504, + 298 + ], + "type": "text", + "angle": 0, + "index": 3, + "lines": [ + { + "bbox": [ + 107, + 245, + 503, + 253 + ], + "spans": [ + { + "bbox": [ + 107, + 245, + 503, + 253 + ], + "type": "text", + "content": "Next, we verify whether the Noise-Resistant Decoder indeed enhances the transformer’s perfor-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 255, + 503, + 263 + ], + "spans": [ + { + "bbox": [ + 107, + 255, + 503, + 263 + ], + "type": "text", + "content": "mance during inference. The test method used dense meshes derived from corrupted GT meshes", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 266, + 504, + 276 + ], + "spans": [ + { + "bbox": [ + 107, + 266, + 504, + 276 + ], + "type": "text", + "content": "as the condition for generating new meshes. The generated meshes were then assessed for shape", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 277, + 503, + 285 + ], + "spans": [ + { + "bbox": [ + 107, + 277, + 503, + 285 + ], + "type": "text", + "content": "alignment with the conditional shape. As shown in Tab. 4, the model with Noise-Resistant Decoder", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 288, + 197, + 296 + ], + "spans": [ + { + "bbox": [ + 107, + 288, + 197, + 296 + ], + "type": "text", + "content": "achieved better results.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 104, + 303, + 506, + 403 + ], + "type": "text", + "angle": 0, + "index": 4, + "lines": [ + { + "bbox": [ + 107, + 304, + 503, + 313 + ], + "spans": [ + { + "bbox": [ + 107, + 304, + 503, + 313 + ], + "type": "text", + "content": "Experiments on the Impact of Input Point Cloud Quality on Generated Results. MeshAny-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 316, + 503, + 325 + ], + "spans": [ + { + "bbox": [ + 107, + 316, + 503, + 325 + ], + "type": "text", + "content": "thing takes point clouds as input, and its robustness to point cloud quality determines its versatility", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 327, + 504, + 336 + ], + "spans": [ + { + "bbox": [ + 107, + 327, + 504, + 336 + ], + "type": "text", + "content": "across various applications. We design two experiments to evaluate its tolerance to input point cloud", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 338, + 504, + 346 + ], + "spans": [ + { + "bbox": [ + 107, + 338, + 504, + 346 + ], + "type": "text", + "content": "quality: First, keeping the other evaluation settings unchanged, we apply Gaussian noise to the input", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 348, + 504, + 357 + ], + "spans": [ + { + "bbox": [ + 107, + 348, + 504, + 357 + ], + "type": "text", + "content": "point cloud coordinates and normals. 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The experiment in (d) further demonstrates that MeshAnything", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 454, + 457, + 462 + ], + "spans": [ + { + "bbox": [ + 107, + 454, + 457, + 462 + ], + "type": "text", + "content": "can tolerate generated point clouds and effectively integrate with 3D generation models.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 476, + 191, + 487 + ], + "type": "title", + "angle": 0, + "index": 6, + "lines": [ + { + "bbox": [ + 107, + 478, + 190, + 487 + ], + "spans": [ + { + "bbox": [ + 107, + 478, + 190, + 487 + ], + "type": "text", + "content": "A.3 LIMITATIONS", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 497, + 504, + 542 + ], + "type": "text", + "angle": 0, + "index": 7, + "lines": [ + { + "bbox": [ + 107, + 498, + 504, + 507 + ], + "spans": [ + { + "bbox": [ + 107, + 498, + 504, + 507 + ], + "type": "text", + "content": "Our method cannot generate meshes that exceed the maximum face count limit, so it cannot convert", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 510, + 504, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 510, + 504, + 519 + ], + "type": "text", + "content": "large scenes and particularly complex objects into meshes. Additionally, due to its generative nature,", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 521, + 503, + 529 + ], + "spans": [ + { + "bbox": [ + 107, + 521, + 503, + 529 + ], + "type": "text", + "content": "our method is not as stable as reconstruction-based mesh extraction methods like Lorensen & Cline", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 532, + 211, + 540 + ], + "spans": [ + { + "bbox": [ + 107, + 532, + 211, + 540 + ], + "type": "text", + "content": "(1987); Shen et al. (2023).", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + }, + { + "bbox": [ + 105, + 555, + 203, + 566 + ], + "type": "title", + "angle": 0, + "index": 8, + "lines": [ + { + "bbox": [ + 107, + 555, + 201, + 566 + ], + "spans": [ + { + "bbox": [ + 107, + 555, + 201, + 566 + ], + "type": "text", + "content": "A.4 SOCIAL IMPACT", + "score": 1.0 + } + ] + } + ], + "level": 2 + }, + { + "bbox": [ + 104, + 575, + 505, + 621 + ], + "type": "text", + "angle": 0, + "index": 9, + "lines": [ + { + "bbox": [ + 107, + 577, + 504, + 586 + ], + "spans": [ + { + "bbox": [ + 107, + 577, + 504, + 586 + ], + "type": "text", + "content": "Our method points to a promising approach for the automatically generation of Artist-Created", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 106, + 588, + 504, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 588, + 504, + 597 + ], + "type": "text", + "content": "Meshes, which has the potential to significantly reduce labor costs in the 3D industry, thereby facil-", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 600, + 504, + 608 + ], + "spans": [ + { + "bbox": [ + 107, + 600, + 504, + 608 + ], + "type": "text", + "content": "itating advancements in industries such as gaming, film, and the metaverse. However, the reduced", + "score": 1.0 + } + ] + }, + { + "bbox": [ + 107, + 610, + 466, + 619 + ], + "spans": [ + { + "bbox": [ + 107, + 610, + 466, + 619 + ], + "type": "text", + "content": "cost of obtaining 3D Artist-Created meshes could also lead to potential criminal activities.", + "score": 1.0 + } + ] + } + ], + "merge_prev": false + } + ] + } + ], + "_backend": "hybrid", + "_effort": "high", + "_ocr_enable": false, + "_version_name": "3.4.4" +} \ No newline at end of file diff --git a/papers/markdown/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers/hybrid_auto/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers_model.json b/papers/markdown/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers/hybrid_auto/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers_model.json new file mode 100644 index 0000000000000000000000000000000000000000..69f37b8f73c98249af0db7e1b808170c374e8d72 --- /dev/null +++ b/papers/markdown/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers/hybrid_auto/2406.10163_MeshAnything_Artist-Created_Mesh_Generation_with_Autoregressive_Transformers_model.json @@ -0,0 +1,11866 @@ +[ + [ + { + "type": "aside_text", + "bbox": [ + 0.023, + 0.271, + 0.06, + 0.701 + ], + "angle": 270, + "content": "arXiv:2406.10163v2 [cs.CV] 9 Oct 2024" + }, + { + "type": "doc_title", + "bbox": [ + 0.173, + 0.1, + 0.825, + 0.147 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.17, + 0.777, + 0.258 + ], + "angle": 0, + "content": null, + "merge_prev": false + }, + { + "type": "image", + "bbox": [ + 0.174, + 0.285, + 0.827, + 0.729 + ], + "angle": 0, + "content": "```mermaid\ngraph LR\n A[\"Text Condition: A commode\"] --> B[\"NeRF\"]\n B --> C[\"3D GS\"]\n C --> D[\"Image\"]\n D --> E[\"Dense Mesh\"]\n E --> 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G[\"Sample\"]\n G --> H[\"Point Cloud\"]\n H --> I[\"Feature\"]\n I --> J[\"Mesh Autoregressive Transformer\"]\n J --> K[\"...\"]\n K -.-> L[\"Cross-Entropy Loss\"]\n L --> M[\"Cross-Entropy Loss\"]\n M --> N[\"Cross-Entropy Loss\"]\n N --> O[\"Cross-Entropy Loss\"]\n O --> P[\"VQ Decoder\"]\n P --> Q[\"Generated Mesh\"]\n```", + "sub_type": "flowchart" + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.215, + 0.825, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "paragraph_title", + "bbox": [ + 0.172, + 0.313, + 0.283, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.346, + 0.825, + 0.389 + ], + "angle": 0, + "content": null, + "merge_prev": false + }, + { + "type": "paragraph_title", + "bbox": [ + 0.172, + 0.408, + 0.578, + 0.421 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.435, + 0.825, + 0.478 + ], + "angle": 0, + "content": null, + "merge_prev": false + }, + { + 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Noise Level\\mathbf{CD}(\\times 10^{-2})\\downarrow\\mathbf{ECD}(\\times 10^{-2})\\downarrow\\mathbf{NC}\\uparrow
W/O NRW/ NRW/O NRW/ NRW/O NRW/ NR
0.00.0110.0070.0350.0230.9870.993
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0.51.1670.6392.5381.3290.9640.981
1.02.1311.7984.3172.3160.9520.969
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W/O NR2.4236.4140.883
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(a) Marching Cubes1.5326.7330.95473.22146.0440.2462.2
(b) MC+Remesh (0.005)2.1747.8130.912127.8167.9748.1534.6
(c) MC+Remesh (0.010)2.0837.5780.92939.0141.78225.4132.3
(d) MC+Remesh (0.030)2.9158.3290.8635.8484.41034.3814.05
(e) MC+Remesh (0.050)4.1798.1380.8142.2991.53813.644.920
(f) MC+Remesh (0.100)7.31210.7710.7480.6250.3593.7351.149
(g) FC1.1906.1210.96759.12121.1378.2391.1
(h) FC+Remesh (0.010)1.8616.9400.93337.9840.19205.5124.2
(i) SAP1.7717.1120.93979.12152.3481.2489.3
(j) SAP+Remesh (0.010)2.3677.8620.92539.1742.87239.1136.6
(k) MeshAnything2.2566.2450.9020.1720.3180.8880.871
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Method\\mathbf{CD}↓(×10^{-2})\\mathbf{ECD}↓(×10^{-2})\\mathbf{NC}↑#V↓(×10^{3})#F↓(×10^{3})V\\_R↓F\\_R↓
(a) Noise scale 0.0052.3516.4120.8970.1750.3210.8950.880
(b) Noise scale 0.0202.9806.9700.8810.1800.3300.9010.910
(c) Noise scale 0.0504.9108.5560.7550.1620.2840.8110.802
(d) Rodin2.5526.6220.8330.1850.3420.9190.923
(e) MeshAnything2.2566.2450.9020.1720.3180.8880.871
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