Uniqueness, the minimum norm constraint, and analog networks for optical flow along contours

E. Hildreth's (1984) method of computing optical flow along contours cannot resolve the aperture problem for a rigidly translating straight line contour. The authors propose an additional constraint, which they call the minimum norm constraint, as a means of resolving the ambiguity for such a contour. The minimum norm constraint tends to drive the velocity estimate towards the direction normal to the contour everywhere along the contour, i.e., it counters the effect of the smoothness constraint. This is in accord with recent psychophysical studies of K. Nakayama and G. Silverman (1988) which have revealed the presence of such a tendency in the human visual system. The authors propose an analog network for computing contour based optical flow in real-time. They illustrate the minimum norm constraint through experiments.<<ETX>>

[1]  K. Nakayama,et al.  The aperture problem—I. Perception of nonrigidity and motion direction in translating sinusoidal lines , 1988, Vision Research.

[2]  Christof Koch,et al.  Seeing Chips: Analog VLSI Circuits for Computer Vision , 1989, Neural Computation.

[3]  K. Nakayama,et al.  The aperture problem—II. Spatial integration of velocity information along contours , 1988, Vision Research.

[4]  John L. Wyatt,et al.  Criteria for Robust Stability In A Class Of Lateral Inhibition Networks Coupled Through Resistive Grids , 1989, Neural Computation.

[5]  Tomaso A. Poggio,et al.  Motion Field and Optical Flow: Qualitative Properties , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Timothy A. Grogan,et al.  Depth From Stereo: Variational Theory And A Hybrid Analog-Digital Network , 1989, Photonics West - Lasers and Applications in Science and Engineering.

[7]  Jin Luo,et al.  Computing motion using analog and binary resistive networks , 1988, Computer.

[8]  Christof Koch,et al.  Simple analog and hybrid networks for surface interpolation , 1987 .

[9]  Norberto M. Grzywacz,et al.  A computational theory for the perception of coherent visual motion , 1988, Nature.

[10]  David Lee,et al.  Computational Aspects Of Determining Optical Flow , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[11]  Berthold K. P. Horn,et al.  Determining Optical Flow , 1981, Other Conferences.

[12]  T. Poggio,et al.  III-Posed problems early vision: from computational theory to analogue networks , 1985, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[13]  C Koch,et al.  Analog "neuronal" networks in early vision. , 1986, Proceedings of the National Academy of Sciences of the United States of America.