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Color discrimination, color constancy and natural scene statistics

Does the visual system allocate discriminative ability to different regions in colour space in a way that optimizes discrimination among natural colours? If so, discrimination should satisfy a " cube root rule " : in an optimized system differential sensitivity will be greatest for the most commonly encountered conditions, dropping to half its maximum under conditions of relative frequency 1/8. Quantitatively, this principle is only very roughly consistent with psychophysical data, but it does account for some of the salient findings, such as the relative sensitivity for different directions in colour space; the fit between theory and psychophysical observation is improved by considering the stimulus to be the local contrast between test field and background, rather than absolute luminance and chromatic values of individual pixels. Comparison with physiological data shows less satisfactory agreement: M cells appear to be too nonlinear, and P cells too linear, for optimal metric representations of luminance and colour respectively. The good colour discrimination of some strongly anomalous trichromats may result from an optimization, during development, of postreceptoral nonlinearity to match the limited range of inputs delivered by the anomalous photoreceptors. For natural colours under natural illuminants, the cone excitations for all surfaces in an image are scaled by approximately the same factor with a change of illumination. This allows the effect of varying illumination to be simply corrected by reciprocal adjustments of sensitivity in the different cone types. The resulting representation is illumination-invariant, but also fails to preserve information about the overall chromatic 2 cast of a scene. Yet experimentally, colouration of the image is perceptually attributed in part to the illuminant and in part to the viewed surfaces, resulting in " underconstancy ". When the statistical variation among natural illuminants and scenes is considered, underconstancy can be viewed not as a failure of constancy, but as a best guess about illuminant colour appropriately based on knowledge of relevant environmental statistics. Natural images do generate small deviations from the scaling principle. These can provide useful cues to the illuminant: statistics (other than the mean) of the distribution of an image's elements in cone excitation space can in principle resolve the ambiguity inherent in the mean alone. Experiment suggests that vision does exploit these cues.and gives them statistically justifiable weight.