Color Vision and Image Intensities: When Are Changes Material?
Marr has emphasized the difficulty in understanding a biological system or its components without some idea of its goals. 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). This goal is challenging for two reasons. First, 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. Second, material changes are essentially arbitrary. We are consequently led to a strategy of rejecting the presence of such confounding processes. We show there is a unique condition, the spectral crosspoint, that allows rejection of the hypothesis that measured image intensities arise from one of the 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.) We restrict our attention to image intensities measured from regions on opposite sides of an edge because material changes almost always cause edges. Also, by restricting our attention to luminance discontinuities, we can avoid peculiar conspiracies of confounding processes that might mimic a material change. Our crosspoint conjecture is that biological visual systems interpret spectral crosspoints across edges as material changes. A circularly symmetric operator is designed to detect crosspoints: it turns out to resemble the double-opponent cell which is commonplace in biological color vision systems.