Representation of structural information in images using fuzzy set theory

In this paper, we show how fuzzy set theory can be used to represent structural information in images, in particular, relationships between imprecise objects, defined as spatial fuzzy sets. We distinguish two types of relationships: on the one hand, relationships that are well defined in the case of crisp objects (like adjacency or distance), and on the other hand, relationships that do not find any consensual definition even in the binary case (typically relative position between objects). We propose several ways to generalize relationships of the first class in order to incorporate imprecision attached to the objects. For the second class, we argue that fuzzy definitions are appropriate even when dealing with crisp objects, and we propose original definitions