Color constancy at a pixel

In computational terms we can solve the color constancy problem if device red, green, and blue sensor responses, or RGB's, for surfaces seen under an unknown illuminant can be mapped to corresponding RGB's under a known reference light. In recent years almost all authors have argued that this three-dimensional problem is too hard. It is argued that because a bright light striking a dark surface results in the same physical spectra as those of a dim light incident on a light surface, the magnitude of RGB's cannot be recovered. Consequently, modern color constancy algorithms attempt only to recover image chromaticities under the reference light: They solve a two-dimensional problem. While significant progress has been made toward achieving chromaticity constancy, recent work has shown that the most advanced algorithms are unable to render chromaticity stable enough so that it can be used as a cue for object recognition B. V. Funt, K. Bernard, and L. Martin, in Proceedings of the Fifth European Conference on Computer Vision (European Vision Society, Springer-Verlag, Berlin, 1998), Vol. II, p. 445. We take this reductionist approach a little further and look at the one-dimensional color constancy problem. We ask, Is there a single color coordinate, a function of image chromaticities, for which the color constancy problem can be solved? Our answer is an emphatic yes. We show that there exists a single invariant color coordinate, a function of R, G, and B, that depends only on surface reflectance. Two corollaries follow. First, given an RGB image of a scene viewed under any illuminant, we can trivially synthesize the same gray-scale image (we simply code the invariant coordinate as a gray scale). Second, this result implies that we can solve the one-dimensional color constancy problem at a pixel (in scenes with no color diversity whatsoever). We present experiments that show that invariant gray-scale histograms are a stable feature for object recognition. Indexing on invariant distributions supports almost perfect recognition for a dataset of 11 objects viewed under five colored lights. In contrast, object recognition based on chromaticity histograms (post-color constancy preprocessing) delivers much poorer recognition.