Exploiting Spatial and Spectral Image Regularities for Color Constancy

We study the problem of color constancy–inferring from an image the spectrum of the illumination and the reflectance spectra of all the depicted surfaces. This estimation problem is underdetermined: many surface and illumination spectra can be described as a linear combination of 3 basis functions, giving 3 unknowns per pixel, plus 3 parameters for a global illumination. A trichromatic visual system makes fewer measurements than there are unknowns. We address this problem by writing the reflectance spectra of small groups of pixels as linear combinations of ”spatio-spectral” basis functions. These aggregated surface reflectance spectra require fewer parameters to describe than the sum of the spectral parameters for the individual surface pixels, giving us more measurements than unknown parameters. We explore this problem in a Bayesian context, showing when the problem is over or underdetermined based on analyzing the local curvature characteristics of the log-likelihood function. We show how using the spatio-spectral basis functions might give us improved reflectance and illumination spectral estimates when applied to real image data.