A limit theorem for pattern synthesis in image processing (Q917157)

The author presents two mixed limit theorems for pattern synthesis, one for linear and one for cyclic connection graphs. He shows that for linear or cyclic graphs one can obtain limit theorems that do not essentially restrict the acceptor function \(A: G\times G\to {\mathbb{R}}_+\) where G is the generator space. The cyclic case is of interest for pattern synthesis in image processing where recent models of shape are based on connectors of this type. These theorems show that the form of the acceptor function is not of decisive importance for the existence of Gaussian limits of probability measures with imposed density. One concludes that the acceptor functions need not have any particular analytic form for Gaussian limits to exist, but only to satisfy some regularity conditions. I have particularly appreciated this paper for the interesting and suggestive theorems.