This paper presents a theoretical synthesis of early computational vision based on variational principles, describes implementations using analog networks, and then states the limitations on the work presented. The paper first discusses a theoretical framework that covers a number of the variational methods previously developed independently for early vision problems. It is shown that many such methods (including computation of motion, shape from shading, surface interpolation, and stereo matching) are special cases of rigorous regularization theories for solving ill-posed (in the sense used by Hadamard in 1923) mathematical problems [1]. An example shows that the framework includes previous variational approaches to the computation of motion. Another example applies the variational approach to edge detection, providing results that are similar to those of commonly used edge detection filters.

The second part of the paper discusses how analog networks, which can directly solve variational problems, offer a computational model of early vision that is quite different from the digital computer model. An example using resistor networks to solve the optical flow computation is presented. Appropriate sets of chemical reactions can, in principle, simulate the electrical currents. The author believes that the style of computation represented by analog circuits is a very useful model for neural computations as well as a challenge for future VLSI circuit designs.

The conclusion discusses the limitations on variational solutions proposed so far. The current theory offers little help for the problem of integrating different sources of information or computing with symbolic representations. The integration of ideas in this paper is carefully documented by 70 references.