Diagonal transforms suffice for color constancy

The main result is to show that under the conditions imposed by the Maloney-Wandell color constancy algorithm, color constancy can be expressed in terms of a simple independent adjustment of the sensor responses, so long as the sensor space is first transformed to a new basis. The overall goal is to present a theoretical analysis connecting many established theories of color constancy. For the case where surface reflectances are two-dimensional and illuminants are three-dimensional, it is proved that perfect color constancy can always be solved for by an independent adjustment of sensor responses, which means that the color constancy transform can be expressed as a diagonal matrix. In addition to purely theoretical arguments, results from simulations of diagonal-matrix-based color constancy, in which the spectra of real illuminants and reflectances along with the human cone sensitivity functions were used, are presented. The simulations demonstrate that when the cone sensor space is transformed to its new basis in the appropriate manner, a diagonal matrix supports close to optimal color constancy