Diagonal versus Affine Transformations for Color Correction

Funt, B.V., and Lewis, B.C. "Diagonal versus Affine Transformations for Color Correction", Journal of the Optical Society of America A, Vol 17, No. 11, Nov. 2000.


Standard methods for color correction involve the use of a diagonal-matrix transformation. Zaidi proposes the use of a two-parameter affine model; we show that this offers no improvement in terms of accuracy over the diagonal model, especially if a sharpening transformation is also used. In Zaidi’s model, the sensor responses are combined into a luminance channel and two color channels in MacLeod–Boynton2 chromaticity space. These are referred to as the rg and yv coordinates. To account for changes in illumination, these coordinates are transformed into illumination-independent color descriptors with an affine transformation that involves a scaling of one coordinate and a translation of the other. This is an interesting approach, which we will examine to see whether it offers any improvements over the performance of the more standard diagonal-matrix transform (DMT). Zaidi’s model accounts for illumination change by a two-parameter affine transformation. Using two parameters, instead of the three parameters implicit in a typical von Kries scaling of the cone signals, is an interesting approach, but the affine model is not the only twoparameter model available. We consider as an alternative a two-parameter diagonal model and find it to model illumination change more accurately than Zaidi’s affine model, especially when used in conjunction with a technique known as spectral sharpening.

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