trafo: restore the x-only scx affine model; make the inverses exact

[alexlib]

Problem

Commit 8321647 (2025-03-21) rewrote distort_brown_affin so that scx scales both axes and the shear term:

*x1 = ap.scx * (x_dist - sin_she * y_dist);
*y1 = ap.scx * cos_she * y_dist;

Until then liboptv, like the Tcl/Tk 3DPTV trafo.c it was ported from, used:

*x1 = ap.scx * x - sin(ap.she) * y;
*y1 = cos(ap.she) * y;

scx is the x-only scale factor of the El-Hakim (1986) / Grün & Beyer (1986) affine pair. It compensated the pixel-clock vs. frame-grabber mismatch, which stretches only the scan-line direction. Applied to both axes it duplicates cc. orientation.c's Jacobian (∂y/∂scx = 0) still assumes the original model, so the fit and the projection disagree.

The same commit left correct_brown_affine_exact (used by dist_to_flat) inverting the original model. flat_to_dist → dist_to_flat therefore misses by 0.04 mm (≈ 8 px at 5 µm pixels) at scx = 1.02. Every round-trip test used scx = 1, where the two models coincide, so nothing caught it.

Change

• Restore the original affine step in distort_brown_affin.
• Make correct_brown_affin and correct_brown_affine_exact exact inverses of it, in both the initial guess and the iteration target.
• Decentering stays evaluated at one undistorted point (Brown 1971), as in 8321647. The pre-2025 code updated x in place before the y line; that difference is second order.

Tests

check_trafo.c gains three tests:

• affine_matches_3dptv: forward equals the Tcl/Tk formula.
• scx_scales_x_only: changing scx leaves y unchanged.
• affine_round_trip: scx = 1.02, she = 0.01, radial + decentering, through both correct_brown_affin and dist_to_flat.

Verified locally with a standalone harness compiled against trafo.c over 5 (scx, she) combinations × 3 points:

	master	this branch
forward vs. 3DPTV formula	0.04–0.06 mm off when scx ≠ 1	≤ 9e-16
dist_to_flat round trip	0.04–0.06 mm	2e-13
failing cases	12 / 15	0 / 15

The check suite itself was not run locally (no check/cmake on this machine), so CI is the first full run. Note that tests/testing_fodder/track/cal/cam{1,2}.tif.addpar have scx ≈ 1.0016–1.0020. Their tracking expectations predate 2025, so they should agree with the restored model, but CI needs to confirm that.

The same fix is in openptv2 (fix/brown-affine-scx-x-only), where the formula was also inlined in the tracking kernels.

🤖 Generated with Claude Code

[Copilot]

🟢 Approval recommended

The forward and inverse formulas are algebraically consistent and adequately covered by targeted tests.

0 open findings

What changed in this PR

Restores the x-only Brown affine scale model and aligns inverse transformations with it.

Changes:

• Applies scx only to the x-coordinate.
• Corrects both inverse affine calculations.
• Adds regression and round-trip tests.

File	Description
liboptv/​src/​trafo.c	Restores and exactly inverts the original affine model.
liboptv/​tests/​check_trafo.c	Adds affine-model and inverse regression tests.

🧠 Review effort: Balanced

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[alexlib]

Local run of the full C test suite (all 17 check_*.c compiled against liboptv/src with a minimal stand-in for check.h; libcheck isn't installed here): master 84 ok / 3 fail, this branch 87 ok (+3 new trafo tests) / the same 3 fail (test_volumedimension, track3d_test_cavity, track3d_test_burgers, all already failing on master). In particular check_track, which uses the scx ≈ 1.0016–1.0020 cameras, passes with the restored model. CI with the real libcheck is still the authority.