Spatial reasoning under imprecision using fuzzy set theory, formal logics and mathematical morphology

In spatial reasoning, in particular for applications in image understanding, structure recognition and computer vision, a lot of attention has to be paid to spatial relationships and to the imprecision attached to information and knowledge to be handled. Two main components are knowledge representation and reasoning. We show in this paper that the fuzzy set framework associated to the formalism provided by mathematical morphology and formal logics allows us to derive appropriate representations and reasoning tools.