The goal of color constancy is to take the color responses (for example camera rgb triplets) of surfaces viewed under an unknown illuminant and map them to illuminant independent descriptors. In existing theories this mapping is either a general linear 3 \Theta 3 matrix or a simple diagonal matrix of scaling coefficients. The general theories have the advantage that the illuminant can be accurately discounted but have the disadvantage that nine parameters must be recovered. Conversely while the coefficient theories have only three unknowns, a diagonal matrix may only partially discount the illuminant. My staring point in this thesis is to generalize the coefficient approach; the goal is to retain its inherent simplicity while at the same time increasing its expressive power. Under the generalized coefficient scheme, I propose that a visual system transforms responses to a new sensor basis before applying the scaling coefficients. I present methods for choosing the best coefficient basis for a variety of statistical models of color responses. These models are rich enough that the generalized coefficient approach
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