Philipona & O'Regan (2006) recently proposed a linear model of surface reflectance as it is sensed by the human eyes. In their model, the tristimulus response to reflected light is accurately approximated by a linear transformation of the tristimulus response to illumination, allowing the prediction of several perceptual characteristics of human vision. Later, Vazquez-Corral et al (2012) built a bridge between Philipona & O'Regan's model and von Kries-like approaches to color constancy in computer vision by showing that the linear operators could be diagonalized in a common basis. However both of these studies required specifying a particular dataset of illuminants. We will show in this paper that it is possible to compute adequate linear operators and a common basis for diagonalization without specifying any particular set of illuminants.