On the relation between probabilistic inference and fuzzy sets in visual scene analysis

Abstract

Strict probabilistic inference is a difficult and costly procedure, and generally unfeasible in practice for interesting cases. It requires knowledge, storage, and computational handling of usually very complicated probability-density functions of the data. Independence assumptions commonly made to alleviate these problems are often wrong and may lead to unsatisfactory results. By contrast, working with fuzzy sets in data space is simple, while the underlying assumptions have remained largely obscure. Here I derive from probabilistic principles a fuzzy-set-type formulation of visual scene interpretation. The argument is focused on making explicit the conditions for reasoning with fuzzy sets and how their membership function should be constructed. It turns out that the conditions may be fulfilled to a good approximation in some cases of visual scene analysis.