-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 ision 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 itensities. 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 conspirliies of confounding processes that might mimic a material chage. 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.

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Many problems in biological information processing require the solution to a complex system of equations in many unknown variables. An equation-counting procedure is described for determining whether such a system of equations will indeed have a unique solution, and under what conditions the solution should be interpreted as ‘correct’. Three examples of the procedure are given for illustration, one from auditory signal processing and two from vision.

There are countless three-dimensional interpretations of a set of points moving in a two-dimensional image. A unique visual interpretation of motion thus requires assumptions about the types of structure likely to be found in the three-dimensional world. We propose that the human visual system favors articulated structures in its interpretations. An articulated structure is a rigid body with moving parts that themselves are rigid and rotate in fixed planes with respect to the body. (A bicycle is an example.) We claim that an image consisting of just two moving points is seen as an articulated structure (when their motion is consistent with one), even though countless other interpretations are possible, including a rigid one of a rod moving in space. An experiment is presented in support of our claim, and a well-known display from an old experiment is reinterpreted as a special case of an articulated structure.

Uniform circular (wheel) motion and pendular motion are studied as examples of a hypothesized collection of moving-part modules. A moving-part interpretation rule1 states that given two moving points Rand B in an image, if B can be interpreted as a point on a rigid body moving at constant velocity without rotation in space, and P can be reliably interpreted as the bob of a pendulum or as a point on a wheel attached to the body at a fixed hub point, a visual system should make that interpretation.