A theory of selection for gamut mapping colour constancy

Gamut mapping colour constancy attempts to determine the set of diagonal matrices taking the gamut of image colours under an unknown illuminant into the gamut of colours observed under a standard illuminant. Forsyth (1990) developed such an algorithm in rgb sensor space which Finlayson (1996) later modified to work in a 2-d chromaticity space. In this paper we prove that Forsyth's 3-d solution gamut is, when projected to 2-d, identical to the gamut recovered by the 2-d algorithm. Whilst this implies that there is no inherent disadvantage in working in chromaticity space, this algorithm has a number of problems; the 2-d solution set is distorted and contains practically non-feasible illuminants. These problems have been addressed separately in previous works; we address them together in this paper. Non-feasible illuminants are discarded by intersecting the solution gamut with a non-convex gamut of common illuminants. In 2-d this intersection is relatively simple, but to remove the distortion, both these sets should be represented as 3-d cones of mappings, and the intersection is more difficult. We present an algorithm which avoids performing this intersection explicitly and which is simple to implement. Tests of this algorithm on both real and synthetic images show that it performs significantly better than the best current algorithms.