Color constancy: generalized diagonal transforms suffice

Abstract

This study’s main result is to show that under the conditions imposed by the Maloney–Wandell color constancy algorithm, whereby illuminants are three dimensional and reflectances two dimensional (the 3–2 world), color constancy can be expressed in terms of a simple independent adjustment of the sensor responses (in other words, as a von Kries adaptation type of coefficient rule algorithm) as long as the sensor space is first transformed to a new basis. A consequence of this result is that any color constancy algorithm that makes 3–2 assumptions, such as the Maloney–Wandell subspace algorithm, Forsyth’s MWEXT, and the Funt–Drew lightness algorithm, must effectively calculate a simple von Kries-type scaling of sensor responses, i.e., a diagonal matrix. Our results are strong in the sense that no constraint is placed on the initial spectral sensitivities of the sensors. In addition to purely theoretical arguments, we present results from simulations of von Kries-type color constancy in which the spectra of real illuminants and reflectances along with the human-cone-sensitivity functions are used. The simulations demonstrate that when the cone sensor space is transformed to its new basis in the appropriate manner a diagonal matrix supports nearly optimal color constancy.