Abstract

One of the best definitions of early vision is that it is inverse optics — a set of computational problems that both machines and biological organisms have to solve. While in classical optics the problem is to determine the images of physical objects, vision is confronted with the inverse problem of recovering three-dimensional shape from the light distribution in the image. Most processes of early vision such as stereomatching, computation of motion and all the “structure from" processes can be regarded as solutions to inverse problems. This common characteristic of early vision can be formalized: most early vision problems are “ill-posed problems" in the sense of Hadamard. In this article we will first review a new framework suggested by Poggio and Torre (1984). They suggested that the mathematical theory developed for regularizing ill-posed problems leads in a natural way to the solution of early vision problems in terms of variational principles of a certain class. They argued that this is a new theoretical framework for some of the variational solutions already obtained in the analysis of early vision processes. They also showed how several other problems in early vision can be approached and solved. Thus the computational, ill-posed nature of early vision problems dictates a specific class of algorithms for solving them, based on variational principles of a certain class. It is natural to consider next which classes of parallel hardware may efficiently implement regularization algorithms. We are especially interested in implementations that are suggestive for biology. I will thus review a model of computation proposed by Poggio and Koch (1984) that maps easily into biologically plausible mechanisms. They showed that a natural way of implementing variational principles of the regularization type is to use electrical, chemical or neuronal networks. They also showed how to derive specific networks for solving several low-level vision problems, such as the computation of visual motion and edge detection.

© 1985 Optical Society of America