Computer Simulations of Pattern Recognition as a Dynamical Process of a Synergetic System

Abstract

In this paper we want to present computer simulations of an algorithm of pattern recognition and associative memory, which was introduced by Haken [1] at the International Symposium at Schloß Elmau, Bavaria in 1987. This was the first specific formulation of a synergetic system that exhibited the analogy between pattern formation and pattern recognition that Haken suggested in 1979 [2]. The crucial point is that the ability of a system to form patterns is strongly related to its ability to recognize patterns or to act as an associative memory. While these basic ideas are discussed in the article of Haken (cf. these proceedings), we shall focus our attention on explicit simulations, and on a discussion of possible generalizations of this approach [3,4]. We shall proceed as follows: In Section 2 we introduce the mathematical assumptions that are nessecary, and show how an associative memory can be realized by a synergetic system [5,6]. In Section 3 we shall reduce the degrees of freedom of the system by introducing order parameters describing the interaction between the macroscopic states of the system. Then in the Sections 4 and 5 generalizations of our approach are discussed. We show that the approach can be formulated in a translationally invariant form which will lead us to the ability to decompose complex patterns or scenes [7]. In Section 5, a further generalization with respect to rotation and scaling is introduced, by use of the complex logarithmic map which also exists in the visual systems of mammals [8,9] as the connection between the retina and the visual cortex.