Color constancy in diagonal chromaticity space

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Abstract
Simple constraints on the sets of possible surface reflectances and illuminants are exploited in a new color constancy algorithm that builds upon Forsyth's (1990) theory of color constancy. The goal defined for a color constancy algorithm is to discount variations in the color and intensity of the incident illumination and thereby extract illumination-independent descriptors of surface colors from images. Forsyth's method is based on two constraints: first, the surface colors under a canonical illuminant all fall within an established maximal convex gamut of possible colors and second that a diagonal matrix accurately maps colors between illuminants. These constraints taken together turn out to be very effective in solving for color constancy; however, other strong assumptions about the scenes are required for the method to work-the illumination must be uniform, the surfaces must be planar, and there can be no specularities. We show that these restrictions are necessary only because Forsyth sets out to recover the intensity of descriptors. At the outset we abandon 3-dimensional descriptor recovery in favor of recovering only orientation (i.e. 2 dimensions). Intensity information is factored out of the problem by mapping 3-dimensional (r, g, b) camera responses onto 2-dimensional chromaticities; specifically (r/b, g/b). We show that this "diagonal chromaticity space" has two important properties: first, gamut convexity is preserved and second illumination change is still described by a diagonal matrix. It follows that Forsyth's algorithm can be directly applied to the recover chromaticity descriptors and from these the 3D descriptor orientations can be derived. The basic algorithm is then extended to include a maximal gamut constraint on the set of illuminants that is analogous to the gamut constraint on surface colors. The diagonal chromaticity space facilitates the expression of the illumination constraint in the algorithm. Tests on real images show that the algorithm provides good color constancy.

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