Fuzzy relative position between objects in image processing: a morphological approach

In order to cope with the ambiguity of spatial relative position concepts, we propose a new definition of the relative position between two objects in a fuzzy set framework. This definition is based on a morphological and fuzzy pattern-matching approach, and consists of comparing an object to a fuzzy landscape representing the degree of satisfaction of a directional relationship to a reference object. It has good formal properties, it is flexible, it fits the intuition, and it can be used for structural pattern recognition under imprecision. Moreover, it also applies in 3D and for fuzzy objects issued from images.