Imaging and color measurement · Reports
Linear RGB-to-XYZ color correction: fit and held-out evaluation
The experiment this would ideally have been
The controlled version measures the specific physical chart that was photographed, on a well-characterized spectrophotometer, at the time of capture. It captures the chart under several illuminants and apertures, repeats each capture so session variation becomes a measured spread, and validates the fitted matrix against a second chart the fit never saw.
What survived is one capture session: RAW chart frames, flat-field frames, and dark frames at one aperture under one illuminant, with the illuminant spectrum recorded in the measurement sidecars. No per-unit measurement of the photographed chart was retained.
That shapes what the fit can answer. It is enough to ask whether a linear model generalizes beyond the patches it was fitted on — and to answer it — without being enough to call the result a chart calibration.
Method
Camera RGB comes from the patch-extraction path documented separately: black subtraction, bilinear demosaic, same-aperture flat correction, white balance, and rectangular sampling of patch interiors. Target XYZ comes from the spectral reference described in the reference report, rendered under the measured illuminant.
The matrix is a least-squares solution: for camera RGB r_i and target t_i,
each output-channel row of M solves the normal equations, giving XYZ = M·RGB.
Error is converted to CIELAB against the declared white and reported as
CIEDE2000.
Five-fold held-out design. Patches are assigned to five deterministic partitions. Each fold trains on four fifths and evaluates on the remaining fifth, so every patch is evaluated exactly once by a matrix that never saw it. The partitions are deterministic, not random: re-running the evaluation gives a bit-identical result, which matters because a shifting fold assignment would make the reported error irreproducible.
Results
From ccm-validation-summary.csv, mean
CIEDE2000:
| Evaluation | Patches | Fit / training | Five-fold held out |
|---|---|---|---|
| All-patch baseline | 140 | 4.099 | 4.134 |
Kept set, L* ≥ 25 |
112 | 3.170 | 3.221 |
| All patches under the kept-set fit | 140 | 4.126 | — |
| Excluded dark patches under that fit | 28 | 7.952 | — |
Held-out exceeds training by 0.035. Under these deterministic partitions, the training score is representative of patches withheld from each fit. The close scores argue against patch-fold overfit within this calculation; they do not reproduce the fit on another physical chart.
4.134 is the reported result. It belongs to the combined camera–capture–reference–model path. The archive contains no observer experiment or declared viewing condition, so the report does not translate this CIEDE2000 value into a universal visibility or just-noticeable-difference result.
The dark-patch experiment
Excluding patches below L* = 25 and refitting lowers held-out error to
3.221, 22% below the baseline. The two evaluations that follow are why that
number is not reported as the result:
- Under the restricted fit, all 140 patches change only from 4.134 to 4.126.
- The 28 excluded patches measure 7.952.
The lower kept-set score did not transfer to the complete chart; it came from leaving the hardest subset out of that average while the subset remained poorly predicted. Recording the exclusion as a flare-handling choice, rather than as a better all-patch model, is the reading these evaluations support.
Plausible contributors include flare in the bright-surround capture and mismatch between the compatible reference and the photographed chart unit. They are not separable here, and the archive does not exclude other capture-path effects.
Limitations
Fold partitions are not physical replication. All five folds draw from one capture of one chart. The 0.035 gap establishes that the model is not memorizing patches. It says nothing about a second chart, illuminant, or session.
The reference is compatible, not per-unit. See the reference report. The compatible reference differs from manufacturer nominal values by mean ΔE76 1.34 across the 140 patches — a different metric under different weighting, so not an amount to subtract from the CIEDE2000 result. The disagreement prevents camera-only attribution; it does not quantify the reference contribution.
One capture condition. One aperture, one illuminant, one session. The correction flat is measured rather than assumed, but cannot separate the illumination source from the lens and sensor, making this same-aperture correction rather than component calibration.
Numerical scope. The 3×3 solve uses normal equations with pivoted elimination and rejects a rank-deficient design. The published fit completed without that rejection, but no condition number was retained, so this report does not report a quantified numerical-stability margin. A QR or SVD solution would be the preferred extension for a conditioning study.
What would resolve it
A per-unit spectral measurement of the photographed chart, with its own uncertainty retained, would remove the product-reference substitution and make that contribution estimable. A second chart, illuminant, and capture session would extend the evaluation from patch partitions to physical replication.
Source file: reports/ccm-fit.md