Abstract

When two lights are combined additively, the color that results can be determined from the colors of the two component lights without knowledge of the nature of the actual spectra. This is not the case for a subtractive mixture, which occurs with color transparencies and colored shadows, because the spectrum of the resultant is the product of the two component spectra. Because the actual spectra cannot be known solely from colorimetric data, prediction of the subtractive mixture is an ill-posed problem. Concrete predictions can be made by adopting one of the assumptions of Maloney and Wandell's theory of color constancy (JOSA A, 1986), namely, that all naturally occurring reflectance/transmis- sion spectra can be described as a linear combination of three spectral basis functions. Under this assumption, a subtractive color mixture can be represented by a bilinear operator acting on pairs of tristimulus values. Although the detailed predictions depend to a degree on the choice of the basis functions, certain algebraic properties are obeyed by all models of this type. The model generates predictions of perceptual transparency that are analogous to those made for achromatic displays by the theories of Metelli (Scientific American, 1974) and others.

© 1990 Optical Society of America