Encoding spatial images: A fuzzy set theory approach

As the use of fuzzy set theory continues to grow, there is an increased need for methodologies and formalisms to manipulate obtained fuzzy subsets. Concepts involving relative position of fuzzy patterns are acknowledged as being of high importance in many areas. In this paper, we present an approach based on the concept of dominance in fuzzy set theory for modelling relative positions among fuzzy subsets of a plane. In particular, we define the following spatial relations: to the left (right), in front of, behind, above, below, near, far from, and touching. This concept has been implemented to define spatial relationships among fuzzy subsets of the image plane. Spatial relationships based on fuzzy set theory, coupled with a fuzzy segmentation, should therefore yield realistic results in scene understanding.