Fuzzy Relative Position Between Objects in Image Processing: New Definition and Properties Based on 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 in comparing an object to a fuzzy landscape representing the degree of satisfaction of a directional relationship to a reference object. We detail its formal properties, and show that it is flexible and fits the intuition. Moreover, it applies also in 3D, and for fuzzy objects issued from images. It can be used for structural pattern recognition in images under imprecision.

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