IntroductionDepth estimation is a fundamental task in computer vision, with key applications in areas such as robotics, autonomous driving, and augmented reality. Traditional stereo vision techniques rely on synchronized cameras to capture images and infer depth by finding correspondences between them. However, these methods often struggle in low-light and fast-motion conditions. Moreover, conventional cameras produce large amounts of redundant data by capturing entire images at fixed intervals, leading to inefficiencies in both data storage and processing.Unlike conventional cameras, event cameras operate asynchronously, detecting per-pixel brightness changes (called "events") [1][2][3]. This provides high temporal resolution and robustness to motion blur, making them well suited for dynamic scenes. Their sparse output enables efficient processing of only relevant areas, making them ideal for real-time tasks such as visual odometry (VO) / SLAM.Harnessing deep learning for depth estimation with event cameras has the potential to transform such applications. However, adapting neural networks to event data remains challenging due to its asynchronous stream-like nature. Moreover, the scarcity of event camera datasets with ground truth depth [4,5] results in limited training data, which can lead to overfitting [6]. While simulating data is one way to address this issue, generalizing models trained on simulation to real-world scenarios is far from trivial due to differences in data distribution [7][8][9][10]. Thus, instead of directly processing events (which is prone to overfitting and extensive training time) we rely on intermediate event representations informed by the scene geometry.One promising approach for 3D reconstruction is back-projecting events as rays into space and capturing their intersection densities as disparity space images (DSIs) [11]. DSIs from two or more cameras can be fused, eliminating the need for event synchronization between cameras. This reduces complexity and allows for more robust depth estimation. The Multi-Camera Event-based Multi-View Stereo (MC-EMVS) method [12] recently produced state-of-the-art (SOTA) results, outperforming other techniques in depth benchmarks across several metrics. To obtain pixel-wise depth estimates from a DSI, MC-EMVS selects the disparity level with the highest ray count, effectively using an argmax operation. Ray counting is used as a proxy for finding 3D edges where the rays intersect. A selective threshold filter is applied to predict depth only for pixels with sufficient ray counts.While straightforward, this approach does not fully utilize the potential of DSIs. It is susceptible to noise and cannot effectively extract cues from surrounding pixels and more complex patterns across disparity levels. Consequently, it leads to fewer pixels obtaining depth estimation and less accurate depth predictions than the DSI might potentially allow for. Therefore, we need more effective approaches for extracting depth from DSIs, that are more reliable, accurate, and produce more depth estimates, by adequately recognizing complex ray intersection patterns.Our Contribution. We propose a novel deep learning framework for event-based depth estimation that is optimized for SLAM scenarios and addresses the aforementioned limitations. An overview is illustrated in Fig. 1. Our approach estimates pixel-wise depth from a DSI using a neural network with 3D convolutions and a recurrent structure. The framework is directly applicable to both monocular and stereo settings. Our key contributions include:• Learning-based Local Processing: For each selected pixel, a small local subregion of the DSI (Sub-DSI) is used as input to the neural network. This novel design leverages the inherent sparsity of event data and DSIs to efficiently process and produce only relevant information for sparse depth-related tasks. (Sec. 3). • Enhanced Data Utilization: Our model captures complex patterns within the DSI, increasing depth prediction accuracy and the number of pixels for which depth can be reliably estimated.Limiting the input to small local subregions around selected pixels enhances generalization by preventing the network from overfitting to dynamics specific to the training scenes and augmenting the available training set, as each Sub-DSI serves as an individual data instance. • Efficiency and Scalability: By adopting our Sub-DSI approach, we obtain small independent inputs of fixed size. This enables full parallelization and provides an ultra-light network that has the ability to handle any camera resolution with constant very short inference time. Our network architecture allows the processing of DSIs of variable depth resolution. (Sec. 3.2). • Comprehensive Experiments: We evaluate our model on both monocular and stereo data from the standard datasets MVSEC [4] and DSEC [13] using cross-validation. It outperforms the state of the art by a large margin on ten figures of merit. Even using monocular data, our model achieves performance comparable to SOTA methods that require stereo data (Sec. 4). We show downstream applicability and robustness to imperfect (noisy) camera poses.To the best of our knowledge, our work is the first learning-based multi-view stereo method to (i) use camera poses along with events as input, which is crucial for accurate depth estimation over long intervals (as used in SLAM [14,15]); (ii) demonstrate successful and robust depth prediction on real-world event data from DSIs; (iii) report good generalization on all three MVSEC indoor flying sequences [5], even when compared to multi-modal methods that combine stereo intensity frames with events. We provide code, trained models and video results for clarity and reproducibility.
Related WorkStereo depth estimation with event cameras has been a captivating problem since the invention of the first event camera by Mahowald and Mead in the 1990s [3,5,16] due to their potential for high temporal resolution and robustness to motion blur. Recent approaches have addressed stereo event-based 3D reconstruction for VO and SLAM [14,[17][18][19][20][21][22]. These methods assume a static world and known camera motion, using this information to assimilate events over longer time intervals, thereby increasing parallax and producing more accurate semi-dense depth maps. A comprehensive review is provided in [5].MC-EMVS [12] introduced a novel stereo approach for depth estimation which does not require explicit data association, using DSIs generated from stereo events cameras. By leveraging the sparsity of events and fusing back-projected rays, they outperformed the event-matching-based solution of [19] and thereby achieved SOTA results in 3D reconstruction and VO [14]. Evidently, this DSIbased 3D reconstruction is robust to imperfect poses estimated using an event camera tracking method. We advance this approach by employing a compact neural network specialized to derive explicit depth from the DSIs, creating a standardized and effective framework for processing event-based data in deep learning applications that does not rely on event simultaneity or matching.Deep Learning for depth estimation from event data. Deep learning has significantly advanced depth estimation in traditional monocular and stereo camera setups, achieving remarkable results [23][24][25]. However, its application to event camera data remains relatively limited due to the sparse asynchronous nature of event streams, which require specialized frameworks [5]. For example, in monocular vision, [26] uses synthetic data on a recurrent network to capture temporal information from grid-like event inputs. Yet, mismatches between synthetic and real data degrade performance [27], and monocular depth estimation from events is an ill-posed problem, making high accuracy challenging to achieve with this learning-based framework [28].For stereo depth estimation, [6,29] present two pioneering studies. Specifically, DDES [6] introduced the first deep-learning-based supervised stereo-matching method, while [29] proposed the first unsupervised learning framework. Both methods use First-In First-Out queues to store events at each position, allowing for concurrent time and polarity reservation. Nevertheless, high event rates lead to greater processing demands and, consequently, increased model complexity and memory requirements, limiting the use of visual cues from both event cameras. Our method overcomes these challenges by maintaining constant input dimensions defined by the size of the DSI subregion around a selected pixel, regardless of the event rate. It thereby provides a significant advancement in applying deep learning to event-based depth estimation on real-world data.
MethodologyIn this section, we present our supervised-learning-based approach and the related framework in detail, for which a general overview is provided in Fig. 1. We describe the preprocessing of the data, the architecture of our network (shown in Fig. 2) and the training and inference procedures.
FrameworkAs an event camera with W ×H pixels moves through a scene, it triggers events e k = (x k , y k , t k , ± k ) and produces a near continuous-time stream of data E = {e k }. Following [11,12], this stream is sliced into time intervals. For every time interval, a DSI is created and associated with a camera viewpoint (called Reference Viewpoint) as follows: given camera poses, all events e k in the interval are back-projected into 3D space by casting rays from the moving camera optical center through the corresponding pixel (x k , y k ). The depth axis is discretized into D levels, equidistant in inverse linear space, resulting in a 3D DSI of size D × W × H voxels, whose values represent the number of rays passing through each region (i.e., voxel) of space (as shown in Fig. 1). Although input poses are required for building a DSI, they can be obtained from tracking methods or dead-reckoning [12,14,30].We consider a stereo setup with two synchronized cameras providing two perspectives of the same scene. By leveraging parallax, this configuration enhances depth perception and allows for more accurate 3D reconstruction. For each interval, we construct two DSIs (one for each camera) and fuse them by applying voxel-wise metrics (e.g., harmonic mean) as described in [12]. To compare performance, we also apply our approach to the monocular data of the left camera only.Since DSIs are typically large and sparse, depth is estimated only for pixels with sufficient information. A confidence map is generated by projecting the DSI onto a 2D grid of size W × H, where each pixel's value represents the maximum ray density among all depth levels [12] (called pixel selection map in Fig. 3). An adaptive Gaussian threshold (AGT) filter is then applied to this grid to select the pixels {p 1 , . . . , p n } with a sufficient maximum ray density for reliable depth estimation. For each selected pixel p i = (x i , y i ), a surrounding subregion Si is extracted from the DSI, including the ray counts of all pixels within L1 radii of r W , r H :Si . = DSI[ : , x i -r W : x i + r W , y i -r H : y i + r H ].Each subregion Si is then normalized individually,S i . = Si / max( Si ) ∈ [0, 1] D×(2r W +1)×(2r H +1) ,(1)and serves as input to our neural network. Using only small subregions of the DSIs as inputs leads to an efficient and compact architecture operating independently of camera resolution. Furthermore, it reduces the risk of overfitting by encouraging the model to learn generalizable patterns of ray intersections within the Sub-DSIs instead of memorizing semantics and dynamics specific to the training scene. Such localized input processing is possible because DSIs consolidate sparse events into a structured format that preserves geometric information within small spatial regions.The depth estimates z 1 , . . . , z n are computed in parallel. Since the amount of selected pixels can be controlled by the AGT filter and the dimensions of the Sub-DSIs are fixed, we achieve constant low model complexity and memory costs, regardless of the number of triggered events.
Network ArchitectureThe architecture of the neural network is illustrated in Fig. 2, with the dimensions of each layer listed in Tab. 1. The network receives the normalized Sub-DSI (1) as input. The objective is to capture local geometrical patterns in the Sub-DSI to extract more relevant depth information than the SOTA argmax approach used in [11,12]. Since established networks like U-Net [31] often include strong spatial compression and Transformers tend to impose high data demands for reliable generalization [32], we tailor an ultra-lightweight custom architecture that shares design elements with FireNet [33], adapted for very small frame sizes yet variable depth dimensions. Similarly to RAFT-Stereo [34], we adopt convolutions and a Gated Recurrent Unit (GRU) to efficiently handle different depth resolutions, enabling customization of the desired depth precision without modifying architecture.First, to capture local patterns, further reduce input size and avoid overfitting, we apply a 3D convolutional filter (3D-Conv) with a ReLU activation, a kernel size of 3 × 3 × 3 and no padding in the spatial dimensions (width and height). For the depth dimension, we set a padding of 1 and a stride of 2 to halve the number of depth layers. We use 4 output channels to capture different patterns simultaneously, resulting in the convolved version of the Sub-DSI (1):S * i = 3D-Conv(S i ) ∈ R D 2 ×4×(2r W -1)×(2r H -1) .(2)To create the DSIs, rays were cast from the representative camera location into space, passing sequentially through the different depth levels. Since mapping precision requirement may change from scene to scene, we need to deal with variable depth resolution of the DSI. To efficiently and flexibly model this interdependence of consecutive depth layers for a variable D, the convolved depth layers are flattened and successively fed into a GRU [35]. The recurrent structure of the GRU allows us to maintain a constant ultra-low count of only 70k parameters in total. It iteratively embeds each depth layer's information within the context of the previous layers, producing hidden state representations h 1 , . . . , h D/2 . We then proceed with the final hidden state h D/2 , which condenses the relevant information from all depth layers along the depth axis:h D 2 = GRU(S * i ) ∈ R 4•(2r W -1)•(2r H -1) .(3)Finally, a dense layer that preserves the dimension of h D/2 with ReLU activation and a subsequent output dense layer are applied to process the hidden state. We introduce two versions of the network for custom modification of depth estimation density. In the single-pixel version, the network predicts the normalized depth for the selected pixel z i ∈ [0, 1], while in the multi-pixel version, the output is a 3 × 3 grid Z i ∈ [0, 1] 3×3 ,
ExperimentsIn this section, we evaluate the performance and reliability of the proposed depth estimation approach. Following prior protocols, we conduct experiments on the MVSEC [4] and the DSEC [13] datasets. Ground truth (GT) depth, captured at fixed intervals using LiDAR sensors, serves as reference locations for constructing the respective DSIs over a defined time span. Pixel selection for depth estimation is based on an AGT filter, where the window size determines the surrounding pixel count considered, and a constant C is subtracted from the observed ray count. We investigate the impact of DSIs derived from both monocular and stereo settings during training and testing. Table 2 provides an overview of the key parameters used in the datasets and the training processes of the experiments. Abbreviations are: minimum depth (z min ), maximum depth (z max ), depth dimensions (D), filter window size (Window), subtractive constant (C), batch size (Batch), learning rate (LR), and loss function (LF).
MetricsThe performance of the networks is evaluated using ten standard metrics commonly employed in depth estimation tasks [12]. We calculate both mean and median errors between the estimated and GT depths, with median errors providing robustness against outliers. Additionally, we report the number of reconstructed points, reflecting the algorithm's ability to generate valid depth estimations, and the number of outliers (bad-pix [40]), representing the proportion of significant depth estimation errors. In the Appendix, we also compute the scale-invariant logarithmic error (SILog Err) to evaluate the error while considering scale, and the sum of absolute relative differences (AErrR) to assess the relative accuracy of the depth predictions. Finally, we report δ-accuracy values, which indicate the percentage of points whose estimated depth falls within specified limits relative to GT [41].
Baseline MethodsWe compare our approach against several SOTA methods that have been benchmarked on the task of long-term event-based depth estimation [5], thus evaluated under the same input conditions (events and camera poses) and output format (semi-dense depth maps) supportive of SLAM. In the absence of other deep stereo methods that learn from input camera poses, we also include comparisons against the SOTA instantaneous end-to-end learning-based stereo methods in Sec. 4.5 for completeness. We adopt the same train-test splits established in prior work and standard benchmarks [5].The Generalized Time-Based Stereovision (GTS) method [39] utilizes a two-step process: first performing stereo matching based on a time-consistency score for each event, followed by depth estimation through triangulation. The Semi-Global Matching (SGM) method [38] is adapted for event-based data by generating time images and subsequently applying stereo matching, with the depth map being refined by masking it at the locations of recent events. Another method, Eventbased Stereo Visual Odometry (ESVO) [19] (ESVO2 [42]), integrates depth estimates by employing Student-t filters, ensuring robust spatio-temporal consistency between stereo time image patches.The two closest baseline methods for performance comparison of our method are EMVS for monocular vision [11] and MC-EMVS for stereo vision [12]. Both methods extract pixel-wise depth from DSIs by applying the argmax function. To ensure consistency and fairness, we benchmark the methods following the procedure established in prior works [5].
ScenePixel selection map MC-EMVS [12] MC-EMVS [12] with Fdenser DERD-Net (Ours)Ground truth (GT)Figure 3: Depth estimation. Qualitative comparison of depth estimated using the MC-EMVS method [12], applying it to the new selected pixels F denser and our method DERD-Net, for the MVSEC indoor_flying [4] (top 3 rows) and DSEC Zurich_City_04_a (bottom row) sequences. Ground truth depth from LiDAR is masked by pixels with valid depth estimate. Our method estimates depth even at pixels with no GT depth. Depth maps are pseudo-colored, from blue (close) to red (far), in the range 1-6.5m for MVSEC and 4-50m for DSEC.
Experiments on MVSEC DatasetThis section describes the experiments conducted on the indoor_flying sequences 1,2,3 of the MVSEC dataset [4] to evaluate the performance of the proposed depth estimation method. Most stereo methods do not evaluate on indoor_flying_4 (because of noisy events from the low-texture floor as the drone flies very low) and the driving sequences (because the stereo baseline is too small for the given depth range and low camera resolution). We employed three-fold cross-validation by utilizing two sequences for supervised training and reserving the remaining sequence for testing, repeating this process for all three possible combinations of sequences to ensure robustness in our evaluation.Two pixel-selection filter settings: F orig and F denser . We first trained the single-pixel version of our network on monocular DSIs to compare its performance to EMVS [11]. Subsequently, we retrained it on stereo DSIs fused via the harmonic mean and compared its performance to MC-EMVS [12]. These two baseline methods used an AGT filter F orig with a window of 5 × 5 px and a subtractive constant of C orig = -14. Given that our network is designed to extract additional information from the geometrical patterns within the DSI, we hypothesized that it would still produce reliable depth estimates for pixels with lower confidence. To test this hypothesis, we used a larger filter window size of 9 × 9 px and a subtractive constant of C denser = -10, resulting in a less strict filter F denser , enabling depth estimation for more pixels. To ensure a representative comparison, we evaluated our networks as well as EMVS and MC-EMVS on both sets of pixels created by F orig and F denser .Multipixel vs. Morphological Filter. One apparent drawback of MC-EMVS is the limited number of pixels for which depth is estimated compared to other SOTA methods. To address this, [12] presented the option of adding a 4-neighbor morphological filter (MF), which dilates the depth estimation map to increase the number of depth-estimated pixels. We compare this with our framework's ability to further increase the number of depth-estimated pixels by training and evaluating the multi-pixel version of our network.Results. The averaged results over all three sequences are displayed in the left half of Tab. 3 for all discussed modalities, while the individual results (including performance without EL) are detailed in the Appendix, in Tabs. 12 to 14. Notably, our network's performance converges after only 3 epochs of training. This rapid convergence is particularly advantageous for future applications where the network might be trained on more heterogeneous datasets or retrained for specific scenarios.Monocular setup. On the monocular DSIs filtered by F orig , our single-pixel network achieves results comparable to those of stereo SOTA methods and significantly outperforms EMVS [11] by 30% in MAE. Remarkably, even on the 3.27 times larger set of pixels created by F denser , it still achieves better scores than EMVS at F orig for all metrics, except bad-pix. Applying EMVS to the same expanded set of pixels leads to a 76% increase in MAE compared to our framework.Stereo setup. Applying our single-pixel network to stereo DSIs filtered by F denser allows us to predict depth at significantly more pixels than any other method, except for the SGM method [38], while consistently surpassing all benchmarks across all metrics. The number of pixels increases by 242%, while the MAE and MedAE reduce by 24% and 30%, compared to MC-EMVS [12] with F orig . The only exception is the bad-pix measure, where MC-EMVS performs slightly better. When both methods are compared on the same set of pixels, our approach yields a reduction in both MAE and MedAE of 42% for F orig and 46% for F denser , respectively. Performance remains consistent when using the multi-pixel network, which increases the amount of depth-estimated pixels by a factor of 5.47 for F orig and 4.09 for F denser compared to its single-pixel version, indicating it to be a superior approach to the morphological filter of MC-EMVS, which only rises the number of points by a factor of 3.70 for F orig . As a consequence, the multi-pixel version of our framework estimates depth for almost as many pixels as the SGM method while delivering new SOTA results.Qualitative comparison. To further illustrate the effectiveness of our method, Fig. 3 compares depth maps generated by our single-pixel network against those produced by SOTA method MC-EMVS.Our network not only provides a denser depth estimation, which improves the recognition of contours, but also effectively eliminates the visible outliers produced by MC-EMVS. This improvement is evident when comparing our method to MC-EMVS applied both to the expanded and the original set of pixels, highlighting the robustness and superiority of our approach.
Experiments on DSEC DatasetTo assess the applicability of our network architecture to different data, we retrained and tested it on DSIs obtained from a stereo setting in the DSEC dataset [13]. This dataset presents unique challenges due to its outdoor driving scenarios, which differ significantly from the indoor environments of the MVSEC dataset, its higher spatial resolution (640 × 480 px) and different noise characteristics (Prophesee camera vs. DAVIS346 camera). Moreover, straight driving sequences are especially challenging for event-based multi-view stereo due to the little motion parallax present in them.Setup. We select the commonly used Zurich_City_04_a sequence to provide a focused in-depth evaluation. We split the sequence into two halves for training and testing. The DSIs were created by fusing the left and right DSIs via the harmonic mean. Analogous to Sec. 4.3, we use the original filter from MC-EMVS [12] F orig with a window size of 5 × 5 px and C orig = -4, and a denser filter F denser with a window size of 9 × 9 px and C denser = -2. First, the network was trained for 3 epochs on the DSIs of the first half of the sequence and tested on those of the second. The process was then reversed and each network was used to predict in its testing half of the data sequence.Results. The results of these experiments are displayed on the right half of Tab. 3 and illustrated in Fig. 3. Our approach drastically outperforms every other method across all metrics, with our multi-pixel network achieving even slightly better performance than the single-pixel network. For F orig , it reduces the MAE by 55% on a 1.72x higher number of pixels compared to MC-EMVS with a morphological filter. For F denser , depth estimation density is increased by an additional factor of 2.24 while performance remains mostly stable, yielding a reduction in MAE of 62% compared to the argmax operation from MC-EMVS. Remarkably, even on purely monocular DSIs filtered by F denser , our framework achieved superior performance to all benchmarked methods for every metric except MedAE. These results underscore the robustness and versatility of our approach, even in complex real-world outdoor scenes.
Robustness of DERD-Net compared to other deep-learning stereo methodsSince there are no comparable learning-based methods that use prior camera poses, Tab. 4 compares end-to-end learning-based stereo methods, which are "instantaneous" (do not take into account camera poses) and output dense depth. In order to use their output for efficient VO/SLAM, we would need an extra step of extracting features (keypoints). Instead, DERD-Net's semi-dense depth maps help avoid unnecessary computation by outputting 3D edges for direct visual odometry, as in [14]. We use the same train-test splits established as the other learning-based methods [5]. While absolute accuracy is not directly comparable, evaluating the errors in the different splits relative to each other is informative about robustness: we observe that our method is the first one to generalize robustly across all three sequences (Tab. 4).No other method reports good generalization on "split 2" of MVSEC because of the difference in dynamic characteristics of events in training and testing on that split [6,43]. This is true even when compared to hybrid approaches, despite them also using stereo intensity frames ("2E+2F" input data modality). The observed robustness of our method to such shifts may be supported by the architectural choice of processing only small subregions as input (see Tab. 2 for Sub-DSI frame size), which encourages the model to learn generalizable patterns within the Sub-DSIs rather than memorizing global scene layout or dataset-specific context.
Sensitivity AnalysesIn this section we carry out experiments varying the settings in Tab. 2. Furthermore, we analyze the robustness of our method to noisy camera poses obtained from an event-based SLAM system.Sensitivity with respect to sub-DSI size. Varying the horizontal and vertical extent of the Sub-DSIs has an impact on our method's performance. Our experiments show that the performance of DERD-Net can be improved by increasing the frame size of the Sub-DSIs, at the expense of increasing the network complexity (e.g., parameter count and computational cost). See Appendix Sec. A.1.Sensitivity with respect to DSI transformations. We analyzed how DERD-Net behaves in the case of previously unseen but structurally similar environments, obtained by means of horizontal and vertical flips of the DSIs. Although its performance worsened slightly, it still outperformed all baseline methods. This demonstrates robustness to the aforementioned transformations. See Appendix Sec. A.2.Sensitivity with respect to noisy camera poses. To assess the importance of having accurate camera poses during DSI construction, we test our framework using noisy poses with drift, mimicking real-world SLAM conditions. Instead of ground-truth (GT) poses from LiDAR-IMU odometry, we use poses estimated by the stereo event-based VO system ES-PTAM [14], which reports an Absolute Trajectory Error (ATE) of 131.62 cm over a 50 m-deep scene in the DSEC Zurich_City_04_a sequence.Running DERD-Net with these imperfect poses yields the results shown in the top rows of Tab. 5. The percentage values in parentheses denote the relative differences with respect to the performance obtained using ideal (GT) poses (Tab. 3). Remarkably, performance improved across all metrics (likely due to the slight reduction in the number of evaluated points of comparable magnitude), demonstrating strong robustness of DERD-Net to noisy poses obtained from an event-based SLAM system.We conduct an additional experiment where the original DERD-Net depth predictions were used to re-estimate the camera poses (in an offline manner, using the camera tracking module in [14]). The resulting poses were then used to build DSIs on which DERD-Net was evaluated. This "reprojection" loop allows us to assess, using standard depth-based metrics, the robustness of our method to noise in camera poses introduced by DERD-Net's own depth inaccuracies. The results are reported in the bottom rows of Tab. 5. The performance shows only minor degradation, particularly for F orig , with no metric worsening by more than 13%. Remarkably, even under such self-induced pose noise, DERD-Net's depth estimation errors remain roughly 50% lower than those of prior SOTA methods using ideal poses. These results demonstrate the practical viability of deploying DERD-Net as a depth-estimation module within a self-sustaining SLAM system. Overall, our experiments confirm that DERD-Net remains remarkably robust even when the input poses are significantly degraded, as would be expected in real-world scenarios. See also Appendix Secs. A.3 and A.4
RuntimeOur network achieved an average inference time of only 0.37 ms per Sub-DSI on an NVIDIA RTX A6000. Since predictions are made independently per pixel, inference for each Sub-DSI can be parallelized on the GPU. The total inference time to estimate a depth map of average density (500 pixels) from MVSEC with F orig is 1.12 ms. Taking MVSEC as an example (DAVIS cameras of 346×260 pixels) and DSIs back-projecting 2 million events onto D = 100 depth planes, then each DSI creation takes ≈45 ms, DSI fusion takes ≈26 ms, and pixel selection takes ≈0.2 ms on an 8-core computer with Intel Xeon(R) W-2225 CPU operating at 4.10 GHz. These values are common for both the state-of-the-art method MC-EMVS and DERD-Net. It has been shown that DSI creation does not hamper real-time performance [53] because the 3D map can be updated infrequently and on-demand.Our network adds only a very small runtime compared to the DSI creation time. This ultra-fast performance, combined with its lightweight architecture, enables efficient execution, making DERD-Net ideal for real-world applications requiring low-latency depth estimation.
ConclusionWe have developed the first learning-based multi-view stereo method for event-based depth estimation. Our approach combines input camera poses with events to produce intermediate geometric representations (DSIs) from which depth is estimated using deep learning. It is directly applicable to both monocular and stereo camera setups. By processing small independent subregions of DSIs in parallel, the framework operates independently of camera resolution and facilitates an efficient network under 1 MB in size with an inference time of only 0.37 ms.Our framework consistently demonstrated superior performance across several metrics compared to other stereo methods and achieved comparable performance when using purely monocular data. It is the first learning-based depth estimation approach that reports robust generalization on all three indoor flying sequences of the MVSEC dataset. Adaptability to different scenes was confirmed on the outdoor driving DSEC dataset, for which it drastically outperformed benchmark approaches across all metrics. Moreover, our framework significantly increased the number of points for which depth can be robustly estimated from DSIs. It also showed strong robustness to noise in camera poses.Given its exceptional performance, ultra-lightweight architecture, scalability and flexibility across different configurations, our method holds strong potential to become a standard approach for learning depth from events and is highly suitable for real-world robotic applications requiring low latency and low memory such as SLAM [15].
A Appendix: Sensitivity AnalysesIn this section we report additional experiments to assess our method's robustness to changes in hyperparameter (Tab. 6), changes in the scene (Tab. 7) and noise in camera poses (Tabs. 8 and 9). We also complement the evaluation on the downstream task of camera tracking (Tab. 10).
A.1 Sensitivity with respect to Sub-DSI SizeThe hyperparameters used for our experiments are detailed in Tab. 2. The LiDAR's sampling interval, the estimated minimum and maximum depths, and the number of depth layers D have all been defined to match the protocol in [12]. In Sec. 4.3, we already provided a comparison between the two AGT filters F orig and F denser . In this section, we therefore analyze the impact of the size of the Sub-DSI.We retrained the network for one epoch on the indoor_flying 2 and 3 sequences and compared its test performance on sequence 1 using radii r W = r H of 2, 3, and 4 px, effectively creating Sub-DSI frames of size 5 × 5, 7 × 7, and 9 × 9 px, respectively. Layer dimensions were adapted, while the overall network architecture remained fixed.  From the results reported in Tab. 6 it can be inferred that performance appears to improve as the radii increase. The network was able to achieve better results after a single epoch using a frame size of 9 × 9 than when fully trained on 7 × 7 frames (see Tab. 12 in this Appendix), highlighting its potential for further performance improvements.[cm] ↓ [cm] ↓ [%] ↓ ×100 ↓ [%] ↓ ×100 ↓ [%] ↑ [%] ↑ [%] ↑ [million]↑5Nevertheless, increasing the frame size to 9 × 9 yielded a reduction of 5% in MAE for both filters after a single training epoch. In contrast to that, the network had to apply 65% more 3D-convolutional operations and its total amount of parameters raised from 70k to 270k. We therefore decided for a 7 × 7 frame size for this study. Future research could explore the evident potential to further boost performance by optimizing the sub-DSI size, considering the trade-off between accuracy, parameter count and computational costs.
A.2 Sensitivity with respect to DSI TransformationsNext, we analyze the robustness of DERD-Net with respect to transformations of the DSI, in particular axis-aligned reflections of the DSIs generated from the indoor_flying_1 sequence of the MVSEC dataset. Specifically, we flipped the DSIs horizontally, vertically, and both horizontally and vertically. These transformations effectively generate scenes with similar geometric properties (e.g., distance ranges) but novel spatial configurations. This allows us to evaluate how well the network generalizes to previously unseen, yet structurally similar environments. We therefore purposely used no data augmentation during training to ensure a representative assessment of the network's inherent robustness. Analogous to previous experiments, we used the single-pixel network that was trained solely on the original indoor_flying 2 and 3 for evaluation. No retraining was performed.The results of these experiments are displayed in Tab. 7. Performance worsened only slightly, with results that still significantly outperform all SOTA methods for all tested configurations, indicating that our network might effectively generalize to scenes that share similar depth ranges and texture with those on which it was originally trained. 
A.3 Sensitivity with respect to Noise in Camera PosesIn Section Sec. 4.6 we summarized the sensitivity of DERD-Net with respect to noise in the camera poses used to build DSIs, on DSEC data. For completeness, we now show results on MVSEC data.We repeat the same experiment as that in the top rows of Tab. 5 on the MVSEC indoor_flying_1 sequence, for which ES-PTAM reported an ATE of 14.93 cm over a 6 m depth range. The results shown in Tab. 8, and compared to those obtained with GT poses in Tab. 12, again highlight DERD-Net's strong robustness to noisy poses estimated by an event-based SLAM system: the MAE and MedAE increased only slightly, while the bad-pix metric even improved. The most pronounced decline was in the number of evaluated points. Nevertheless, DERD-Net with F denser still predicts depth for 69% more pixels than MC-EMVS with F orig under ideal poses, while achieving a 30% lower MAE. For its multi-pixel variant, DERD-Net evaluated with noisy poses maintains superior performance over all state-of-the-art methods using GT poses, while still predicting the highest number of points. In the interest of thoroughness, we also used poses from the state-of-the-art event-based stereo visual-inertial odometry system ESVO2 [42], which is notably more accurate than ES-PTAM, to run DERD-Net on MVSEC indoor_flying_1, indoor_flying_2, and indoor_flying_3. The mean results are reported in Tab. 9. Compared to Tab. 3, DERD-Net shows only a slight decrease in depth estimation performance on F orig , while it even improves on F denser , confirming its robustness to pose noise from an event-based SLAM system integrating events and inertial data. 
A.4 Downstream Camera Tracking Performance AnalysisAs intermediate results to those in the bottom part of Tab. 5, we report offline camera tracking performance using the edge-alignment camera tracking module in [14] acting on input events and the local maps built using DERD-Net's depth predictions (from GT poses). Camera tracking performance is given in terms of ATE and Absolute Rotation Error (ARE) on the DSEC [13] driving dataset in Tab. 10. Although our model was trained only on the Zurich_City_04_a sequence, we evaluate it on all Zurich_City_04 sequences to highlight its generalization capabilities. The obtained pose errors in the 50 m depth range scenes across all sequences show strong performance of DERD-Net for downstream tasks such as pose estimation via simple photometric edge alignment on event images, as well as its robust generalization even when trained on a single sequence. Training on a more diverse set of DSEC sequences would be expected to further enhance these results. These values are not comparable to online SLAM tracking results because they assume that the 3D map was pre-built offline using DERD-Net with GT poses. Therefore, the estimated camera poses reported here do not accumulate drift.
B Appendix -Detailed per-Sequence ResultsThe average results of different SOTA methods compared to DERD-Net are presented in Tab. 11. In Tabs. 12 to 14, the individual performance on each of the respective sequences indoor_flying 1, 2, 3 from the MVSEC dataset are displayed. Table 15 presents the corresponding results for the Zurich_City_04_a sequence from the DSEC dataset.      Justification: We mention the requirement of available Ground Truth for training (Sec. 4) and explicitly point out that accuracy cannot be directly compared to end-to-end learning-based methods (Sec. 4.5). We state the need for camera pose in the construction of the DSIs (Sec. 3.1). More details about limitations of DSIs are available in the linked source [12]. Guidelines:
MVSEC AveragedRMSE δ < 1.25 δ < 1.25 2 δ < 1.25 3 #Points [cm] ↓ [cm] ↓ [%] ↓ ×100 ↓ [%] ↓ ×100 ↓ [%] ↑ [%] ↑ [%] ↑ [RMSE δ < 1.25 δ < 1.25 2 δ < 1.25 3 #Points [cm] ↓ [cm] ↓ [%] ↓ ×100 ↓ [%] ↓ ×100 ↓ [%] ↑ [%] ↑ [%] ↑ [RMSE δ < 1.25 δ < 1.25 2 δ < 1.25 3 #Points [cm] ↓ [cm] ↓ [%] ↓ ×100 ↓ [%] ↓ ×100 ↓ [%] ↑ [%] ↑ [%] ↑ [million]↑ SOTA EMVS [RMSE δ < 1.25 δ < 1.25 2 δ < 1.25 3 #Points [cm] ↓ [cm] ↓ [%] ↓ ×100 ↓ [%] ↓ ×100 ↓ [%] ↑ [%] ↑ [%] ↑ [million]↑ SOTA EMVS [RMSE δ < 1.25 δ < 1.25 2 δ < 1.25 3 #Points [m] ↓ [m] ↓ [%] ↓ ×100 ↓ [%] ↓ ×100 ↓ [%] ↑ [%] ↑ [%] ↑ [• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper. • The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. • The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. • The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon. • The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. • If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. • While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. Justification: Following standard evaluation protocols used by comparable prior methods to ensure fairness through consistent experimental settings, we do not plot error bars. Instead, we test several variations of our network and report differences in the estimation errors (Tabs. 11 to 15). We also provide a quantitative evaluation of the effects of uncertainty on our networks' accuracy by comparing the pixel selection maps -visualizations of uncertainty -to the depth maps created by the networks in Fig. 3 and the video included in the supplementary material. Furthermore, we provide an analysis of how variations to the dataset (Sec. A.2) and hyperparameters (Sec. A.1) affect the network's performance. Guidelines:• The answer NA means that the paper does not include experiments.• The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper. • The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions). • The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.) • The assumptions made should be given (e.g., Normally distributed errors). • It should be clear whether the error bar is the standard deviation or the standard error of the mean. Guidelines:• The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.• If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics. • The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction).
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SafeguardsQuestion: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)? Answer: [NA] Justification: We see no parts of our paper being at high risk for misuse. Guidelines:• The answer NA means that the paper poses no such risks.• Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters. • Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images. • We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort. 12. Licenses for existing assets Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected? Answer: [Yes] Justification: We did correctly cite the creators of MC-EMVS for the DSI approach [12] as well as the creators for the datasets of MVSEC [4] and DSEC [13].Guidelines:• The answer NA means that the paper does not use existing assets.• The authors should cite the original paper that produced the code package or dataset.• The authors should state which version of the asset is used and, if possible, include a URL. • The name of the license (e.g., CC-BY 4.0) should be included for each asset.• For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided. • If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset. • For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided. • If this information is not available online, the authors are encouraged to reach out to the asset's creators. 13. New assets Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets? Answer: [Yes] Justification: The full documentation for code and models is included in the supplementary material of our submission. Guidelines:• The answer NA means that the paper does not release new assets.• Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc. • The paper should discuss whether and how consent was obtained from people whose asset is used. Table 1 :1Network Architecture. The parameters of the network's modules are specified in Tab. 1. Details of network layers. K, P, and S stand for kernel-size, padding and stride.InputNeural NetworkOutputSub-DSI3D-ConvolutionGRU (depth layers)Dense + ReLU + DenseDepthFigure 2: LayerDimensionsDetailsSub-DSI (Input) 100 × 1 × 7 × 7 Depth × Channels × Width × Height3D-Convolution 50 × 4 × 5 × 5K = (3,3,3); P = (1,0,0); S = (2,1,1)ReLU + Flatten 50 × (4 • 5 • 5)Flattens channels and frameGRU1 × 100Selects final hidden state h 50Dense + ReLU100Maintains dimensionDense (Output)1 or 3 × 3Outputs depth value(s)
Table 2 :2Hyperparameters.DatasetDataset DetailsDSI ParametersGauss. FilterTraining ProcessSequencesResolution LiDAR ∆t Span z min z max D Sub-DSI Window C Batch Optimizer LRLF EpochsMVSEC Indoor flying 346 × 260 px50 ms1 s 1 m 6.5 m 100 7×79×9 -10 64AdamW 10 -3 MAE3DSEC Zurich04a640 × 480 px 100 ms 0.2 s 4 m 50 m 100 7×79×9-264AdamW 10 -3 MAE3
representing the normalized depth predictions of the central pixel and its 8 neighbors. Finally, normalized depth is converted into actual depth by mapping [0, 1] to [z min , z max ].3.3 Training and InferenceAs supervised loss function for training the neural network model we use the mean absolute error(MAE), with given ground truth depth (this is the case of standard real-world datasets used, such asMVSEC and DSEC -see Sec. 4). To reduce training time and further improve generalization, weadditionally employ ensemble learning (EL) [36, 37]. For training, we initialize two identical butindependent instances of our neural network with different random weights. The training set is splitinto two disjoint subsets, enabling parallel training. During testing or inference, each Sub-DSI S i isprocessed simultaneously by both networks, and the final depth estimation is obtained by averagingthe individual predictions. This helps reduce variance in the predictions, leading to more stable andaccurate results. We also present results without EL in Tabs. 11 to 14 in the Appendix Sec. B.
Table 3 :3Summarized quantitative comparison of the proposed methods with the state of the art. MVSEC indoor_flying and DSEC Zurich_City_04_a. The full comparison over ten metrics is in the Appendix Sec. B.MethodMVSECDSECAlgorithmModalityMean Err Median Err bad-pix #Points Mean Err Median Err bad-pix #Points [cm] ↓ [cm] ↓ [%] ↓ [million]↑ [m] ↓ [m] ↓ [%] ↓ [million]↑EMVS [11]monocular + F orig33.7814.353.841.275.642.5213.681.31EMVS [11]monocular + F denser 50.3220.8111.464.157.013.5624.336.09ESVO [19]stereo22.709.832.831.563.931.6210.549.40SOTASGM [38] GTS [39] MC-EMVS [12]stereo stereo stereo + F orig35.42 389.00 20.0712.35 45.43 9.536.39 38.45 1.3514.46 0.06 0.816.74 26.24 3.271.58 1.62 0.9015.25 32.56 10.758.30 0.11 1.25MC-EMVS [12]stereo + F denser28.3812.383.262.774.761.5617.424.64MC-EMVS [12] + MF stereo + F orig20.649.721.433.003.510.9611.813.83DERD-Netmonocular + F orig23.6811.552.781.213.121.605.502.10OursDERD-Net DERD-Net DERD-Netmonocular + F denser 28.52 stereo + F orig 11.69 stereo + F denser 15.2413.85 5.50 6.684.87 0.89 1.704.15 0.79 2.773.01 1.61 1.801.50 0.46 0.546.35 4.12 5.046.09 1.67 4.64DERD-Net (multi-pixel) stereo + F orig12.025.630.904.321.590.473.816.59DERD-Net (multi-pixel) stereo + F denser15.686.731.7411.331.790.544.6114.74
Table 4 :4Mean depth error [cm] of deep stereo methods on MVSEC indoor data. Values are collected from original sources.MethodModality Split 1 Split 2 Split 3DDES [6]2E16.729.427.8EIT-Net [43]2E14.2-19.4DTC-SPADE [44]2E13.5-17.1Liu et al [45]2E202531StereoSpike [46]2E16.5-18.4ASNet [47]2E20.4628.7422.15Ghosh et al. [48]2E12.1-15.6Chen et al [49]2E13.9-14.6StereoFlow-Net [50] 2E13-15EIS (ICCV 2021)2E + 2F13.7418.4322.36SCS-Net [51]2E + 2F11.4-13.5N. Uddin et al [29]2E + 2F19.7-26.4Zhao et al. [52]2E + 2F9.7-11.1DERD-Net2E11.6911.1112.28
Table 5 :5Depth estimation performance on DSEC zurich_city_04_a using poses computed by ES-PTAM or by camera tracking on DERD-Net's output ("Reprojection" rows). Relative changes with respect to Tab. 3, which reports results obtained using GT poses, are presented in parentheses.Algorithm PosesFilterMean Err Median Err bad-pix #Points [m] ↓ [m] ↓ [%] ↓ [million]↑DERD-Net ES-PTAMF orig1.56 (-3.11%) (-2.17%) (-6.8%) (-3.59%) 0.45 3.84 1.61DERD-Net ES-PTAMF denser1.74 (-3.33%) (-3.7%) (-3.97%) (-3.23%) 0.52 4.84 4.49DERD-Net Reprojection F orig1.66 (+3.11%) (+6.52%) (+1.7%) (-12.57%) 0.49 4.19 1.46DERD-Net Reprojection F denser1.95 (+8.33%) (+11.11%) (+12.1%) (-11.85%) 0.60 5.65 4.09
Table 6 :6Sensitivity analysis of DERD-Net's performance for different Sub-DSI frame sizes after one epoch of training. MVSEC indoor_flying_1.Sub-DSI ModalityMean Err Median Err bad-pix SILog Err AErrR log RMSE δ < 1.25 δ < 1.25 2 δ < 1.253 #Points frame size
Table 7 :7Performance of DERD-Net when applying axis-aligned reflections. MVSEC indoor_flying_1.ReflectionModalityMean Err Median Err bad-pix SILog Err AErrR log RMSE δ < 1.25 δ < 1.25 2 δ < 1.25 3 #Points[cm] ↓[cm] ↓[%] ↓ ×100 ↓ [%] ↓ ×100 ↓[%] ↑[%] ↑[%] ↑ [million]↑nonestereo + Forig11.695.420.860.974.909.8896.8798.8599.650.98verticalstereo + Forig12.816.270.921.065.4310.3496.5698.8099.640.98horizontalstereo + Forig14.266.811.011.235.8811.0895.8598.5699.600.98horizontal + vertical stereo + Forig14.286.791.021.235.9211.1195.7998.5399.600.98nonestereo + Fdenser 14.866.471.311.496.1412.3095.4598.2499.373.01verticalstereo + Fdenser 16.277.421.441.656.7912.9694.9198.0999.313.01horizontalstereo + Fdenser 18.237.871.601.917.3213.8493.7397.7199.253.01horizontal + vertical stereo + Fdenser 18.868.371.681.987.6414.1493.4697.6199.223.01
Table 8 :8Quantitative depth estimation performance on MVSEC indoor_flying_1 using poses computed downstream of ES-PTAM. Relative changes with respect to Tab. 12, which reports results obtained using GT poses, are presented in parentheses.AlgorithmPosesFilterMean Err Median Err bad-pix #Points [m] ↓ [m] ↓ [%] ↓ [million]↑DERD-NetES-PTAM F orig12.72 (+8.81%) (+16.79%) (-24.42%) (-30.61%) 6.33 0.65 0.68DERD-NetES-PTAM F denser15.76 (+6.06%) (+13.76%) (-10.69%) (-46.18%) 7.36 1.17 1.62DERD-Net (multi-pixel) ES-PTAM F orig13.53 (+10.27%) (+19.01%) (-24.42%) (-33.91%) 6.76 0.65 3.41DERD-Net (multi-pixel) ES-PTAM F denser16.60 (+6.62%) (+16.08%) (-11.68%) (-46.46%) 7.65 1.21 6.27
Table 9 :9Quantitative depth estimation performance averaged over MVSEC indoor_flying_1, _2, and _3 using poses computed downstream of ESVO2. Relative changes with respect to Tab. 3, which reports results obtained using GT poses, are presented in parentheses.Algorithm PosesFilterMean Err Median Err bad-pix [m] ↓ [m] ↓ [%] ↓ [million]↑ #PointsDERD-Net ESVO2 F orig11.53 (-1.37%) (+4.18%) (+22.47%) (-22.78%) 5.73 1.09 0.61DERD-Net ESVO2 F denser13.69 (-10.17%) (-5.39%) (-14.12%) (-47.65%) 6.32 1.46 1.45
Table 10 :10Camera tracking performance on DSEC zurich_city_04, without DERD-Net retraining.Sequencezc04a zc04b zc04c zc04d zc04e zc04fDuration [s]3513.45347.813.643.1ATE RMSE [cm] ↓17.077.8514.00 55.645.71 36.11ARE RMSE [deg] ↓ 0.310.080.450.670.110.72
Table 11 :11Quantitative comparison of the proposed methods with the state of the art. MVSEC indoor_flying (average).AlgorithmModalityMean Err Median Err bad-pix SILog Err AErrR log
Table 12 :12Quantitative comparison of the proposed methods with the state of the art. MVSEC indoor_flying_1.million]↑
Table 13 :13Quantitative comparison of the proposed methods with the state of the art. MVSEC indoor_flying_2.million]↑AlgorithmModality Mean Err Median Err bad-pix SILog Err AErrR log
Table 14 :14Quantitative comparison of the proposed methods with the state of the art. MVSEC indoor_flying_3.11]monocular + Forig31.4213.016.154.5613.3721.8084.0794.7297.881.17EMVS [11]monocular + Fdenser 45.6917.9614.6611.7419.8634.8172.6988.2794.013.65ESVO [19]stereo21.348.973.753.489.3219.1491.6095.8897.861.89ESVO indep. 1sstereo20.428.633.503.249.1418.3592.0396.1998.191.41SGM indep. 1sstereo32.948.758.299.5015.8231.5484.4092.3395.4816.95GTS indep. 1sstereo167.1437.2343.0871.9194.7886.9349.3660.5467.760.07MC-EMVS [12]stereo + Forig18.208.491.771.788.1313.5995.5398.1399.080.65MC-EMVS [12]stereo + Fdenser25.8110.344.653.4810.8918.9189.1095.9398.352.25MC-EMVS [12] + MF stereo + Forig18.588.681.861.818.1913.7195.2798.0799.092.42DERD-Netmonocular + Forig23.3710.434.983.3111.0718.4188.3096.2398.460.98DERD-Netmonocular + Fdenser 27.6512.758.684.6013.3921.7682.7594.3497.903.65OursDERD-Net without EL stereo + Forig DERD-Net stereo + Forig11.44 11.115.23 4.941.34 1.261.13 1.105.45 5.3410.67 10.5096.67 96.6998.60 98.6699.52 99.540.58 0.58DERD-Netstereo + Fdenser14.465.922.781.726.7413.1794.0597.8899.322.25DERD-Net multi-pixel stereo + Forig11.294.881.281.145.3910.6696.5098.6199.543.21DERD-Net multi-pixel stereo + Fdenser14.925.952.851.806.8613.4793.6797.7699.299.52MVSEC Indoor Flying 3AlgorithmModalityMean Err Median Err bad-pix SILog Err AErrR log
Table 15 :15Quantitative comparison of the proposed methods with the state of the art. DSEC Zurich_City_04_a.11]monocular + Forig30.5415.092.313.3311.5918.2788.1696.4598.471.42EMVS [11]monocular + Fdenser 44.6220.267.158.5018.2629.1578.5591.4195.574.15ESVO [19]stereo29.6212.613.784.0211.5020.2088.2894.8897.522.29ESVO indep. 1sstereo24.2910.842.813.059.8417.5491.8796.4698.161.86SGM indep. 1sstereo37.8614.695.338.5217.6529.4685.6793.3196.2114.81GTS indep. 1sstereo299.4860.6639.7572.24 102.7788.8745.0458.8666.940.08MC-EMVS [12]stereo + Forig19.4910.380.991.437.3512.0196.0998.6099.380.82MC-EMVS [12]stereo + Fdenser27.8913.652.012.8310.2516.8590.9797.0598.733.04MC-EMVS [12] + MF stereo + Forig20.0210.591.021.507.5012.3095.7998.5199.363.11DERD-Netmonocular + Forig21.9111.621.461.939.0714.0193.0298.2599.361.14DERD-Netmonocular + Fdenser 27.0113.802.582.8510.9916.9689.2397.0498.984.15OursDERD-Net without EL stereo + Forig DERD-Net stereo + Forig12.50 12.286.31 6.130.57 0.550.84 0.825.03 4.919.20 9.1197.41 97.4199.13 99.1599.72 99.740.82 0.82DERD-Netstereo + Fdenser16.397.641.021.406.3611.8495.4998.4599.483.04DERD-Net multi-pixel stereo + Forig12.506.340.560.844.939.1797.4199.1299.714.59DERD-Net multi-pixel stereo + Fdenser16.557.651.011.386.3611.7695.4498.4399.4712.77
The answer NA means that the abstract and introduction do not include the claims made in the paper.• The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers. • The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. • It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.2. LimitationsQuestion: Does the paper discuss the limitations of the work performed by the authors? Answer:[Yes]   NeurIPS Paper Checklist1. ClaimsQuestion: Do the main claims made in the abstract and introduction accurately reflect thepaper's contributions and scope?EMVS [11] Answer: [Yes] monocular + Forig5.642.5213.6813.2325.5236.4972.5687.1293.56million]↑ 1.31SOTAEMVS [11] ESVO [19] Justification: The framework and it advantages are explained in Sec. 3. The results are monocular + Fdenser 7.01 3.56 24.33 23.07 41.74 48.52 63.00 79.81 87.71 6.09 stereo 3.93 1.62 10.54 8.30 17.66 28.90 84.37 92.81 96.05 9.40 SGM [38] stereo 6.74 1.58 15.25 17.95 18.42 42.51 80.66 89.12 93.16 8.30 GTS [39] stereo 26.24 1.62 32.56 61.58 33.45 79.26 68.07 78.39 85.85 0.11 displayed in Sec. 4.MC-EMVS [12] MC-EMVS [12] Guidelines: stereo + Forig stereo + Fdenser3.27 4.760.90 1.5610.75 17.428.19 15.8417.48 30.6728.73 40.4583.30 76.3791.56 86.0195.62 90.971.25 4.64MC-EMVS [12] + MF stereo + Forig DERD-Net monocular + Forig •3.51 3.120.96 1.6011.81 5.508.89 3.9618.84 12.1929.99 19.9281.72 86.0690.68 96.2995.07 98.613.83 2.10DERD-Netmonocular + Fdenser3.011.506.354.0412.2420.1286.4696.0798.416.09OursDERD-Net DERD-Netstereo + Forig stereo + Fdenser1.61 1.800.46 0.544.12 5.042.78 2.917.03 7.5916.68 17.0693.50 92.0997.05 96.7298.66 98.561.67 4.64DERD-Net multi-pixel stereo + Forig1.590.473.812.546.7615.9393.6097.1898.786.59DERD-Net multi-pixel stereo + Fdenser1.790.544.612.767.4616.6292.3196.8298.6214.74
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