Predicting frequency of metamerism in natural scenes by entropy of colors

Estimating the frequency of metameric surfaces in natural scenes usually requires many comparisons of surface colors to determine which are visually indistinguishable under one light but distinguishable-by a certain criterion degree-under another. The aim here was to test the predictive power of a simpler approach to estimation based on the entropy of colors. In simulations with 50 hyperspectral images of natural scenes, the logarithm of the observed relative frequency of metamerism in each scene under two successive daylights was regressed on combinations of the estimated Shannon differential entropies of the colors of the scene under the same two daylights. The regression was strong, and it remained so when restricted to the estimated differential entropy under just the first daylight, providing that the criterion degree of metamerism was limited. When the criterion degree was made more extreme, however, the restricted regression failed. A possible explanation of the predictive power of differential entropy is briefly considered.