---
license: apache-2.0
pretty_name: cyclegraph flow gain
language:
  - en
size_categories:
  - n<1K
tags:
  - optical-flow
  - benchmark
  - synthetic
  - ergonomics
  - egocentric
  - fisheye
configs:
  - config_name: displacement_gain
    data_files: data/displacement_gain.jsonl
  - config_name: displacement_gain_raft
    data_files: data/displacement_gain_raft.jsonl
  - config_name: gain_by_resolution
    data_files: data/gain_by_resolution.jsonl
  - config_name: estimator_benchmark
    data_files: data/estimator_benchmark.jsonl
  - config_name: geometry_floor
    data_files: data/geometry_floor.jsonl
---
# cyclegraph flow gain

**How much of a hand's motion a dense optical flow estimator actually recovers, and what it
reports instead once it stops.** Rendered under the corpus's own fisheye, where the true flow
field is known exactly, which is the only reason a gain is measurable at all.

The finding, in one line: past a displacement knee the estimator reports the **background**,
at a gain equal to hand distance over background distance
(0.45 / 2.5 = 0.18) — and the ego-motion
correction that ought to catch this subtracts the background, so the error cancels into a small
plausible number rather than a loud one.

**Run it against your own estimator.** The harness ships in this repository, needs numpy and
nothing else, and needs no corpus, no token and no GPU.

```python
from cyclegraph_flow_gain import gain_curve

def my_estimator(first, second):   # -> (H, W, 2) float32, or None on failure
    ...

curve = gain_curve(my_estimator, width=960)
print(curve.knee_px, curve.floor_gain, curve.floor_ratio_expected)
print(curve.verdict(operating_displacement_px=12.0))
```

Passing is **not** gain near 1.0 everywhere; no dense estimator does that. Passing is your knee
sitting outside the displacements your work actually produces, which is why `verdict()` takes
that displacement instead of assuming one.

## The knee belongs to the estimator, the floor belongs to the geometry

Both files below share the 0.25 s pair baseline, so they compare directly.

| hand displacement | farneback-cv2 | raft-small |
|---|---|---|
| 22.794 px | 0.9925 | 0.9946 |
| 34.181 px | 0.2024 | 0.9738 |
| 45.539 px | 0.2323 | 0.32 |
| 68.025 px | 0.1773 | 0.1724 |

RAFT-small buys roughly one more doubling of usable displacement and lands on the same floor.
A better estimator moves where the cliff is and does not touch what is underneath it.

## Higher decode resolution is not better

At 0.236 of the hand box width, the same physical displacement at four decode sizes:

| decode | 480x270 | 960x540 | 1440x810 | 1920x1080 |
|---|---|---|---|---|
| gain | 0.7656 | 0.9925 | 0.2036 | 0.1978 |

960x540 is a measured optimum.
1920x1080 does worse than
480x270.

## The lens does most of the work

`BENCHMARK_CARD.md` carries the argument. Under pure rotation at 10 degrees per second the corpus fisheye leaves 10.0916 mm/s of apparent hand speed, where a narrow lens leaves 0.1328 mm/s. That is 76 times more from the same scalar-median subtraction, because rotational flow on a fisheye varies with radius and a scalar cannot cancel a field that does.

The exact-geometry residual is the control: 1.1461 px,
computed closed-form with no estimator involved. `farneback-cv2` reports
1.2171 px and `raft-small` reports
1.014 px — **below** the floor an ideal
estimator would leave, which is under-recovery rather than accuracy.

## Configs

| config | rows | what one row is |
|---|---|---|
| `displacement_gain` | 18 | farneback, one decode scale and displacement, 0.25 s baseline |
| `displacement_gain_raft` | 18 | raft-small, same sweep and baseline |
| `gain_by_resolution` | 36 | farneback across four decode sizes, 0.0333333 s baseline |
| `estimator_benchmark` | 2 | one estimator: its A14 rotation residual against the exact-geometry floor |
| `geometry_floor` | 20 | closed-form apparent speed under one camera motion |

**On baselines.** `displacement_gain` and `displacement_gain_raft` use the
0.25 s pair interval; `gain_by_resolution` uses the clip's own rate,
0.0333333 s. Displacements and gains are identical either way — the interval
only rescales `true_speed_mm_s`. Compare estimators on `hand_displacement_px` and never across
files on mm/s. Every row carries its own `pair_interval_s`.

## What this cannot tell you

- **Whether a real hand crosses the knee.** That depends on your frame rate and your work. The
  harness reports the knee for your geometry; it does not know your job.
- **Anything about the corpus.** No corpus frame was decoded for any number here. The
  measurement cyclegraph exists to make is blocked on cost and one human step, and has not run.
- **Whether the ergonomic instrument is valid.** No ergonomist scored anything.
- **The corpus's real ego-motion distribution.** The floor table assumes a camera motion.
- **Whether synthetic texture behaves like factory video.** The lens is the corpus's. The
  content is not.

The depth planes — 0.45 m and 2.5 m — are stated
assumptions about workstation geometry, not measurements, and the floor sits at their ratio, so
a different workstation gives a different floor. That is a prediction and it is untested.

## Provenance and terms

Apache-2.0, as is `builddotai/Egocentric-10K` itself. The lens calibration is the vendor's
published `intrinsics.json`, identical for all 2,144 shipped workers. `ETHICS.md` in this
repository records the limit of what the licence settles:

> Apache-2.0 is the vendor's licence to grant. It is not a worker's consent, and section 2 records that the consent instrument is unknown.

No frame, no worker, no factory and no pilot value appears in this release.

- Repository, including what is blocked and why: https://github.com/caiotheodoro/cyclegraph
- The data behind every table above, interactively: https://huggingface.co/spaces/caiotheodoro/cyclegraph