Color constancy. III. General linear recovery of spectral descriptions for lights and surfaces

We present a color-constancy algorithm that uses quantum-catch data from reflected lights to recover surface reflectance functions and illuminant spectral power distributions. The algorithm recovers both surface and light-source spectral properties simultaneously. The method works in all situations that were handled by the earlier two-stage algorithms of Maloney and Wandell [J. Opt. Soc. Am. A 3, 29 (1986)] and D'Zmura and Iverson [J. Opt. Soc. Am. A 9, 490 (1992); 10, 2148, 2166 (1993); 11, 1970 (1994)]. In addition, the method handles problems that lie outside the scope of earlier algorithms. Using this method, a trichromatic visual system can recover, when provided adequate information, spectral descriptions of arbitrarily high accuracy for lights and surfaces. We determine conditions under which bilinear models can be used to recover color properties uniquely with the new procedure, and we formulate an algorithm for checking whether a particular bilinear model provides perfect color constancy. This research extends our analysis of linear methods for color constancy begun earlier [J. Opt. Soc. Am. A 10, 2148, 2166 (1993)].