Early vision: From computational structure to algorithms and parallel hardware

I review a new theoretical framework that from the computational nature of early vision leads to algorithms for solving them and suggests a specific class of appropriate hardware. The common computational structure of many early vision problems is that they are mathematically ill-posed in the sense of Hadamard. Standard regularization analysis can be used to solve them in terms of variational principles that enforce constraints derived from a physical analysis of the problem, see T. Poggio and V. Torre (Artificial Intelligence Lab. Memo No. 773, MIT, Cambridge, Mass., 1984). Studies of human perception may reveal whether some principles of a similar type are exploited by biological vision. It can also be shown that the corresponding variational principles are implemented in a natural way by analog networks, see T. Poggio and C. Koch (Artificial Intelligence Lab. Memo No. 783, MIT, Cambridge, Mass., 1984). Specific electrical and chemical networks for localizing edges and computing visual motion are derived. These results suggest that local circuits of neurons may exploit this unconventional model of computation.