Simchony, Chellappa, and Shao (1990) proposed a semi-direct method for computing area based optical flow. Their method is based on the iterative application of a direct Poisson solver. This method is restricted to Dirichlet boundary conditions, i.e., it is applicable only when velocity vectors at the boundary of the domain are known a priori. The authors show, both experimentally and through analysis, that the semi-direct method converges only for very large smoothness. At such levels of smoothness, the solution is obtained merely by filling in the known boundary values; the data from the image is almost totally ignored. Next, the authors consider the Concus and Golub method (1973), another semi-direct method, for computing optical flow. This method always converges, but the convergence is too slow to be of any practical value. The authors conclude that semi-direct methods are not suited for the computation of area based optical flow.>

T. Simchony et al. (1990) proposed a semidirect method for computing area-based optical flow, based on the iterative application of a direct Poisson solver. This method is restricted to Dirichlet boundary conditions, i.e. it is applicable only when velocity vectors at the boundary of the domain are known a priori. It is shown, both experimentally and through analysis, that the semidirect method converges only for a very high degree of smoothness. At such levels of smoothness, the solution is obtained merely by filling in the known boundary values; the data from the image is almost totally ignored. It is concluded that the semidirect method is not suited for the computation of area-based optical flow.>

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.>

Several analog networks have been proposed for solving the variational problems of early vision. The networks can be implemented in hardware using analog VLSI: thus, they can be used in real-time environments. The underlying mathematical formulations do not necessarily lead to a unique solution. The authors show how the nonuniqueness carries over to the analog networks. In particular, they study networks for contour-based optical flow, area-based optical flow, membrane surface reconstruction, and thin-plate surface reconstruction. An additional constraint, the minimum norm constraint, is proposed in the variational formulations of these problems. The minimum norm constraint ensures a unique solution. In analog networks, the constraint can be imposed simply by shunting each node to ground through an appropriate positive resistor. The minimum norm constraint also tends to force the solution to conform more with local measurements. This is in accord with a psychophysical study which has revealed the presence of such a tendency in the human visual system