This paper presents some mathematical results concerning the measurement of motion of contours. A fundamental problem of motion measurement in general is that the velocity field is not determined uniquely from the changing intensity patterns. Recently Hildreth & Ullman have studied a solution to this problem based on an Extremum Principle [Hildreth (1983), Ullman & Hildreth (1983)]. That is, they formulate the measurement of motion as the computation of the smoothest velocity field consistent with the changing contour. We analyse this Extremum principle and prove that it is closely related to a matching scheme for motion measurement which matches points on the moving contour that have similar tangent vectors. We then derive necessary and sufficient conditions for the principle to yield the correct velocity field. These results have possible implications for the design of computer vision systems, and for the study of human vision.

In the last seven years a new computational approach has led to promising advances in the understanding of biological visual perception. The foundations of the approach are largely due to the work of a single man, David Marr at M.I.T. Now, after his death in Boston on November 17th 1980, research in vision will not be the same for the growing number of those who are following his lead.