Representing spatial relations (Part II) : the geometrical approach

The representation and analysis of spatial relations is a tough problem in AI and Cognitive Science and is hence heavily discussed in the literature. Our general approach to this problem is to use a two-level representation where the relations may either be defined on a logical/propositional level or in terms of a three dimensional model of co-ordinates. Here we occupy ourselves with an approach to analyze spatial relations on the depictional level, i.e. on a representation of spatial scenes by space co-ordinates. First we describe a representation formalism for spatial objects, based on boundary representations. Coming from that, we introduce a method for testing the applicability of spatial relations between two or more objects. The degree of applicability of a spatial relation results from the deviation of the object to be located from an "ideal position" which is specified by the reference object(s) and various influences by spatial properties of the regarded objects like size or shape, where the deviation results from trigonometrical computations