Analog VLSI Circuits for the Perception of Visual Motion

3

Optimization Networks

The main computational task of the visual motion system, as outlined in the previous chapter (Figure 2.7), is optimization. Ideally, the system finds the optimal visual motion estimate with respect to the applied matching and flow models and the given visual information. This chapter introduces constraint satisfaction as a framework for formulating such optimization problems, and shows how to design recurrent networks that can establish appropriate solutions. Two simple examples serve to illustrate the methodology, and will be revisited in the context of computational network architectures described in later chapters.

3.1 Associative Memory and Optimization

Since the ground-breaking work of McCulloch and Pitts [1943] many different mathematical descriptions of computation in neural networks have been proposed. Amongst these, models of how neural networks can store and retrieve information were of major interest. Beginning in the early 1970s, the concept of associative content-addressable memory became popular. Network models of associative memory are able to learn different prototype patterns and, when presented with a new pattern, to associate it to the stored prototype that is most similar. While many key ideas of associative memory were developed much earlier [Cragg and Temperley 1955, Little and Shaw 1975, Grossberg 1978], it was John Hopfield who established a network model that was clearly defined and had a strong physical interpretation [Hopfield ...