Color Constancy and a Changing Illumination

The color constancy problem has proven to be very hard to solve. This is even true in the simple Mondriaan world where a planar patchwork of matte surfaces is viewed under a single illuminant. In this paper we consider the color constancy problem given two images of a Mondriaan viewed under different illuminants. We show that if surface reflectances are well modeled by 3 basis functions and illuminants by up to 5 basis functions then we can, theoretically, solve for color constancy given 3 surfaces viewed under 2 illuminants. The number of recoverable dimensions in the illuminant depends on the spectral characteristics of the sensors. Specifically if for a given sensor set a von Kries type, diagonal model of color constancy is sufficient then we show that at most 2 illuminant parameters can be retrieved. Recent work has demonstrated that for the human visual system a diagonal matrix is a good model of color constancy given an appropriate choice of sensor basis. We might predict therefore, that we can recover at most 2 illuminant parameters. We present simulations which indicate that this in fact the case.