Improving gamut mapping color constancy

The color constancy problem, that is, estimating the color of the scene ii luminant from a set of image data recorded under an unknown light, is an im portant problem in computer vision and digital photography. The gamut mappi ng [10], [17] approach to color constancy is, to date, one of the most succ essful solutions to this problem. In this algorithm the set of mappings tak ing the image colors recorded under an unknown illuminant to the gamut of a ll colors observed under a standard illuminant is characterized, Then, at a second stage, a single mapping is selected from this feasible set, In the first version of this algorithm Forsyth [17] mapped sensor values recorded under one illuminant to those recorded under a second, using a three-dimens ional (3-D) diagonal matrix. However, because the intensity of the scene il luminant cannot be recovered Finlayson [10] modified Forsyth's algorithm to work in a two-dimensional (2-D) chromaticity spare and set out to recover only 2-D chromaticity mappings. While the chromaticity mapping overcomes the intensity problem it is not cl ear that something hasn't been lost in the process. After all, a 2-D constr aint isn't usually as powerful as a 3-D constraint, The first result of thi s paper is to show that only intensity information is lost. Formally, we pr ove that the feasible set calculated by Forsyth's original algorithm, proje cted into 2-D, is the same as the feasible set calculated by the 2-D algori thm. Thus, there is no advantage in using the 3-D algorithm and we can use the simpler, 2-D version of the algorithm to characterize the set of feasib le illuminants. Another problem with the chromaticity mapping is that it is perspective in nature and so chromaticities and chromaticity maps are perspectively distor ted. Previous work [13] demonstrated that the effects of perspective distor tion were serious for the 2-D algorithm. Indeed, in order to select a sensi ble single mapping from the feasible set this set must first be mapped back up to 3-D. We extend this work to the case where a constraint on the possi ble color of the illuminant is factored into the gamut mapping algorithm, H ere, the feasible set is intersected with a set of feasible illuminant maps prior to the selection task. We find that good selection is still only pos sible after undoing the perspective projection. However, matters are more c omplex than before because the illuminant constraint is nonconvex and calcu lating the intersections of nonconvex bodies is a hard problem, Fortunately , pre show here that the illumination constraint can be enforced during sel ection without explicitly intersecting the two constraint sets. In the final part of this paper we reappraise the selection task. Gamut map ping returns the set of feasible illuminant maps. Any one of these is a pla usible illuminant; that is, any member of the feasible set could be the cor rect answer. As such, we argue that the selection task should set out to fi nd the mapping that minimizes the maximum possible error. This leads to a n ew median selection method which minimizes this worst case performance. Our new algorithm is tested using real and synthetic images, The results of these tests show that the algorithm presented here delivers excellent colo r constancy.