Classical Computer Vision

On the generated scene, 12 of the configurations score a perfect F1 of 1.000. A saturated benchmark has no power left to separate the things it is being asked to rank, so the choice among those twelve is arbitrary as far as it is concerned.

It is not arbitrary on photographs:

Identical on the benchmark, 19% apart on the real images. Pinned by test_tuning_on_shapes_costs_nineteen_percent_on_photographs and test_the_synthetic_scene_saturates.

The synthetic scene is not worthless — it is not decisive. Across the 18 settings both grids share, the correlation between synthetic F1 and photograph F is +0.751. It orders the settings roughly right and cannot pick between the good ones, which is exactly the failure mode of a benchmark everyone has already solved.

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The OpenCV tutorial's seed rule (a fraction of the global distance maximum) counts 1 coin of 24 when a lighting artefact merges the mask; local-maxima seeding counts 24 of 24 on the same broken mask. And three methods count 24 while only one measures them plausibly — watershed's smallest basin implies a 5.75 mm coin next to a 24.25 mm reference

The best method on an exact copy is the worst at every other setting: block matching scores 0.9925 IoU unrotated and 0.0000 at 2°. The decisive choice is the verifier's hypothesis, not the descriptor — identical SIFT matches score 0.794 vs 0.677 at 0° and 0.000 vs 0.499 at 90°. And rotation-robustness is paid for in false accusations: 6.3% of an untampered photo flagged, vs 0.0% for block matching

A more accurate airlight and transmission map produce a worse image — 19.50 dB falls to 18.50 dB when the airlight error is cut from 0.063 to 0.051; the two errors cancel. And CLAHE wins the contrast column (0.181 vs 0.156) while losing by 6.6 dB

Every method, without exception. Most of a photograph is smooth, and interpolating a missing colour across a smooth region is trivial — so the whole-image average is dominated by the pixels where the problem does not exist. The failure lives on the 3% of pixels that are edges, and it is 2 to 3 dB deep there.

The colour fringing column is what a viewer actually notices: a magenta or cyan halo on a high-contrast edge, caused by red, green and blue being interpolated to slightly different places. Malvar and VNG cut it roughly in half.

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Otsu's failure on shadowed pages is not because a global threshold is impossible — the best global cut scores 0.890 where Otsu scores 0.678. Also: the detector that wins on the benchmark (Otsu + contour, 1.07 px) fails on a real photograph

Every row above is one monotonic map from input level to output level. Drawing that map says more than any metric, because the oracle's curve is the correct answer and distance from it is the error:

* Global HE and histogram matching lift the shadows roughly 50 levels too far between inputs 100 and 140, then run out of range and clip. * Gamma barely has a shape — it lifts everything and is nearly flat against the oracle's slope, which is why it scores worst of all. * AHE is visibly non-monotonic. Its map depends on where the pixel is, so the median curve zig-zags; two pixels of the same input brightness come out at different levels depending on their neighbours. That is the noise amplification, drawn. * CLAHE tracks the oracle closest in the shadows and gives up at the top.

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Harris returns ~1000 keypoints and AKAZE ~357. More keypoints means more chances for one to land inside the 3 px match radius, so the natural objection is that Harris wins on density. Randomly discarding its keypoints answers it:

Flat. A tenth of the keypoints scores the same as all of them. Randomly subsampled, so the survivors are not quietly reselected for quality. Pinned by test_harris_does_not_win_by_finding_more_keypoints.

So density is not the explanation — but placement partly is. Harris's 33.5% coverage against SIFT's 80.6% says the two are not solving the same problem: Harris is answering "where are the most reliable corners", and a homography needs "where are reliable corners spread across the frame". Pinned by test_harris_trades_frame_coverage_for_repeatability.

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Choosing the best inpainting method is worth 1.1 dB; knowing where the damage is is worth 14.0 dB. Ranking detectors by IoU gets it backwards — the best-IoU detector restores to 9.88 dB, a worse-IoU one to 12.87 dB. And gray-world drives the no-reference cast to 0.04° while landing further from the truth (14.28°) than the faded input (7.72°)

Plain LK's answer is 1 pixel. At 1 px it scores 0.221 against a control of 1.118 — it is working. At 2 px it scores 1.524 against 2.236, which is two thirds of the way to having found nothing, and by 4 px it is indistinguishable from the control. The textbook's "one to two pixels" is right, and the useful half of the range is the first one.

DIS does not break anywhere in this sweep. Its error at 32 px (0.238) is lower than plain LK's at 1 px. It is also faster than Farnebäck.

### Each pyramid level roughly doubles the tractable motion

The largest displacement still handled with an EPE below half the displacement:

The 2^L story holds from level 1 onward. The first level buys a factor of 4, not 2 — the coarse level halves the displacement and blurs away the fine structure the linearisation was tripping over, so it gets paid twice. A 4-level pyramid takes a method that dies at 1 px and carries it to 32.

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` minimise |∇f − ∇source|² inside the region subject to f = target on the boundary `

whose solution satisfies ∇²f = ∇²source. Discretised, every interior pixel is the average of its four neighbours minus the source's Laplacian, so iterating that update converges to the answer.

They agree to 0.0066 — two independent implementations of the same equation, which is the only real check that either is right — and the transparent one costs 38× the time.

Converged by 50 iterations and flat thereafter; the slight rise past 200 is float accumulation in the Jacobi update, not further progress.

### The one line that makes it Poisson blending

`python f = sub.copy() # target everywhere, INCLUDING the boundary ring f[interior] = patch[interior] # a starting guess, interior only `

Seeding the boundary from the source instead — f[region_mask] = patch[...] — makes f = source an exact fixed point of the iteration, because the solution of ∇²f = ∇²g with f = g on the boundary is g.

The solver then "converged" in zero steps to the copy-paste answer and reported a seam visibility of 2.8046 — identical to the control, to four decimal places — with nothing at all to indicate it had not run. It is the quietest failure in this repository: a method that is a no-op, reporting a plausible number, in a table where another row happens to carry the same one.

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The natural thing to measure is IoU against a foreground mask. Doing that gives this table:

A grid of rectangles that has never looked at the image scores 0.914 and beats five of the six real methods. It beats mean-shift, the best method by boundary F, by 0.54.

Two things conspire to produce that.

The region-to-foreground conversion uses the truth. labels_to_foreground assigns each region to foreground or background by which it overlaps more. That is deliberately generous — so a low score cannot be blamed on the conversion — and the consequence is that the more regions a method returns, the more the oracle assignment can do for it. At one region per pixel the score is 1.0 for any method whatsoever.

And the binary target was wrong in the first place. A human segmentation is a labelling, not a figure/ground split. dominant_foreground takes the largest annotated region to be the background and inverts it, which fails whenever that is not true: on memorial_arch the largest region covers 24.5% of the frame, so the "foreground" is 75.5% of the picture and corresponds to nothing anyone drew. Methods returning sensible regions score 0.000 against it.

Boundary F is the metric BSDS was built for and the one every published number on it uses. It does not reward region count, and under it the grid sits last. Pinned by test_a_grid_of_rectangles_beats_most_real_methods_on_iou and test_boundary_recall_separates_what_iou_cannot.

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The truth (dashed) swings between 36 and 243 across four pixels. Every method draws a smooth line through the middle of it. Nearest visibly steps and the rest ramp — that difference is the 0.49 dB — but next to the original they are the same curve.

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At a tenth of the brightness NCC still localises every template and SSD normalised localises none. Dividing by the standard deviation is exactly a scale invariance, and the sweep has to reach 10× before the claim is visible at all — at the usual gentle 0.9 every method still works.

> ZNCC holds 1.000 at every negative offset; NCC falls to 0.458. Subtracting > the mean is exactly an offset invariance, and NCC does not subtract the mean. > > It takes a negative offset to show it. Brightening clips at white and > destroys the structure for everyone — at +0.4 NCC and ZNCC both sit at 0.958 > and the difference between them is invisible. Darkening clips only in the > shadows, which leaves enough for a mean-subtracting method and not enough for > anything else. A sweep over positive offsets alone would have reported that > NCC and ZNCC are equivalent.

The algebra says the same thing with no image search involved. ZNCC of a patch against a·patch + b is 1.0 for any positive a and any b:

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The gap is real and large. A perfectly flat spectrum would put 0.10 in the top 10%; noise scores 0.44 because the largest samples of a Gaussian are still larger than the rest, and every photograph scores 0.69 or above. Thresholding really can separate them.

That is what makes the result interesting rather than disappointing: the method's justification is sound, and the Haar basis is still not a good enough one.

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