ABSTRACT
The term "pattern theory" was introduced by Ulf Grenander in the 1970s (Grenander 76-81) as a name for a field of applied mathematics which gave a theoretical setting for a large number of related ideas, techniques and results from fields such as computer vision (D. Geman 90), speech recognition (Rabiner 90, 93), statistical pattern recognition (Ripley 96), neural nets (Hertz 91) and parts of artificial intelligence (Pearl 88).l As these research fields have grown explosively, it is helpful to understand the common themes which unite them. Pattern theory proposes that the types of stochastic models used in one field will crop up in all the others. The underlying idea is to find stochastic models which capture all the patterns which we see in nature, so that random samples from these models have the same 'look and feel' as the samples from the world itself. Then the detection of patterns in noisy and ambiguous samples can be achieved by the use of Bayes's rule, a method which can be described as 'analysis by synthesis'.
