Relational color constancy refers to the constancy of the perceived
relations between the colors of surfaces of a scene under changes in
the spectral composition of the illuminant. Spatial ratios of cone
excitations provide a natural physical basis for this constancy, as, on
average, they are almost invariant under illuminant changes for large
collections of natural surfaces and illuminants. The aim of the present
work was to determine, computationally, for specific surfaces and
illuminants, the constancy limits obtained by the application of a
minimum-variance principle to cone-excitation ratios and to investigate
its validity in predicting observers' surface-color judgments.
Cone excitations and their changes due to variations in the color of
the illuminant were estimated for colored surfaces in simulated
two-dimensional scenes of colored papers and real three-dimensional
scenes of solid colored objects. For various test surfaces, scenes, and
illuminants, the estimated levels of relational color constancy
mediated by cone-excitation ratios varied significantly with the test
surface and only with certain desaturated surfaces corresponded to
ideal matches. Observers' experimental matches were compared with
predictions expressed in CIE 1976 (u′,v′)
space and were found to be generally consistent with minimum-variance
predictions.