An object-color space

Abstract

Putting aside metaphorical meanings of the term, color space is understood as a vector space, where lights having the same color (i.e., subjectively indistinguishable) are represented as a point. The CIE 1931 color space, empirically based on trichromatic color measurements, is a classical example. Its derivatives, such as CIELAB and sRGB, have been successfully used in many applications (e.g., in color management). However, having been designed for presenting the color of self-luminous objects, these spaces are less suitable for presenting color of reflecting objects. Specifically, they can be used to represent color of objects only for a fixed illumination. Here I put forward a color space to represent the color of objects independently of illumination. It is based on an ideal color atlas comprising the reflectance spectra taking two values: k or 1 - k (0 < or = k < or = 1), with two transitions (at wavelengths lambda(1) and lambda(2)) across the spectrum. This color atlas is complete; that is, every reflecting object is metameric to some element of the atlas. When illumination alters, the classes of metameric reflectance spectra are reshuffled but in each class there is exactly one element of the atlas. Hence, the atlas can uniquely represent the metameric classes irrespective of illumination. Each element of the atlas (thus, object color) is specified by three numbers: (i) lambda = (lambda(1) + lambda(2))/2, which correlates well with hue of object color (as dominant wavelength correlates with hue of light color); (ii) delta =/lambda(1) - lambda/, which correlates with whiteness/blackness; and (iii) alpha =/1 - 2k/, which correlates with chroma of object color (as colorimetric purity correlates with saturation of light color). Using a geographical coordinate system, each element of the atlas (thus, each object color) is geometrically represented as a radius vector so that its length equals alpha, the latitude and longitude being proportional to delta and lambda, respectively.