Vision, analog networks, and the minimum norm constraint

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