Color vision and image intensities: when are changes material?

The difficulty in understanding a biological system or its components without some idea of its goals has been emphasized by Marr. In this paper, a preliminary goal for color vision is proposed and analyzed. That goal is to determine where changes of material occur in a scene (using only spectral information). The goal is challenging because the effects of many processes (shadowing, shading from surface orientation changes, highlights, variations in pigment density) are confounded with the effects of material changes in the available image intensities. We show there is a minimal and unique condition, the spectral crosspoint that rejects instances of these confounding processes. (If plots are made of image intensity versus wavelength from two image regions, and the plots intersect, we say that there is a spectral crosspoint.) An operator is designed to detect crosspoints; it turns out to resemble double-opponent cells described in primate visual cortex.