Improving gamut mapping color constancy

The color constancy problem, that is, estimating the color of the scene illuminant from a set of image data recorded under an unknown light, is an important problem in computer vision and digital photography. The gamut mapping [10], [17] approach to color constancy is, to date, one of the most successful solutions to this problem. In this algorithm the set of mappings taking the image colors recorded under an unknown illuminant to the gamut of all 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-dimensional (3-D) diagonal matrix. However, because the intensity of the scene illuminant cannot be recovered Finlayson [10] modified Forsyth’s algorithm to work in a two-dimensional (2-D) chromaticity space and set out to recover only 2-D chromaticity mappings. While the chromaticity mapping overcomes the intensity problem it is not clear that something hasn’t been lost in the process. After all, a 2-D constraint isn’t usually as powerful as a 3-D constraint. The first result of this paper is to show that only intensity information is lost. Formally, we prove that the feasible set calculated by Forsyth’s original algorithm, projected into 2-D, is the same as the feasible set calculated by the 2-D algorithm. 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 feasible illuminants. Another problem with the chromaticity mapping is that it is perspective in nature and so chromaticities and chromaticity maps are perspectively distorted. Previous work [13] demonstrated that the effects of perspective distortion were serious for the 2-D algorithm. Indeed, in order to select a sensible 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 possible color of the illuminant is factored into the gamut mapping algorithm. Here, 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 possible after undoing the perspective projection. However, matters are more complex than before because the illuminant constraint is nonconvex and calculating the intersections of nonconvex bodies is a hard problem. Fortunately, we show here that the illumination constraint can be enforced during selection without explicitly intersecting the two constraint sets. In the final part of this paper we reappraise the selection task. Gamut mapping returns the set of feasible illuminant maps. Any one of these is a plausible illuminant; that is, any member of the feasible set could be the correct answer. As such, we argue that the selection task should set out to find the mapping that minimizes the maximum possible error. This leads to a new 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 color constancy.