An Analog Model of Computation for the Ill-Posed Problems of Early Vision

A large gap exists at present between computational theories of vision and their possible implementation in neural hardware. The model of computation provided by the digital computer is clearly unsatisfactory for the neurobiologist, given the increasing evidence that neurons are complex devices, very different from simple digital switches. It is especially difficult to imagine how networks of neurons may solve the equations involved in vision algorithms in a way similar to digital computers. In this paper, we suggest an analog model of computation in electrical or chemical networks for a large class of vision problems, that map more easily into biological plausible mechanisms. Poggio and Torre (1984) have recently recognized that early vision problems such as motion analysis (Horn and Schunck, 1981; Hildreth, 1984a,b), edge detection (Torre and Poggio, 1984), surface interpolation (Grimson, 1981; Terzopoulos 1984), shape-from-shading (Ikeuchi and Horn, 1981) and stereomatching can be characterized as mathematically ill-posed problems in the sense of Hadamard (1923). Ill-posed problems can be "solved", according to regularization theories, by variational principles of a specific type. A natural way of implementing variational problems are electrical, chemical or neuronal networks. We present specific networks for solving several low-level vision problems, such as the computation of visual motion and edge detection