Abstract

In a color atlas, the uniformity of color spacing between reflectances is disturbed by changes in the spectral power distribution (SPD) of the illumination. Because the atlas may still be useful under different lights, we introduce a new metric of color order that is less sensitive to change of illumination. Three reflectances with labels 1, 2, 3 map to points in chromaticity space (under a particular light) that, if not collinear, are ordered either clockwise or counterclockwise. The ordering parameter P of the reflectances is –1 for clockwise ordering, +1 for counterclockwise ordering, and 0 for collinear points. The perceptual significance of P can be tested via a dichotomous color-blindness test (such as the Farnsworth D-15 test). It has been shown mathematically¹ that the P of three reflectances depends on illumination only if, when the reflectances are treated formally as color-matching functions, the chromaticity space that results has a spectrum locus that is not everywhere convex. Illuminants affect P when one or more reflectances is purple—a vindication of the model because purples are known not to be color-constant. A color atlas is called statistically consistent if its first three principal components form a chromaticity space that is convex and well ordered in wavelength. The Munsell atlas is statistically consistent. Convexity of the spectrum locus also insures that no linear combination of the reflectances (or reflectance principal components) has more than two zero crossings. Implications of these theorems for color technology and robotic vision are noted.

© 1988 Optical Society of America