On the Qualitative Representation of Spatial Knowledge in 2D Space

Various relation-based systems, concerned with the qualitative representation and processing of spatial knowledge, have been developed in numerous application domains. In this paper we identify the common concepts underlying qualitative spatial knowledge representation, we compare the representational properties of the different systems and we outline the computational tasks involved in relation-based spatial information processing. The paper also describes symbolic spatial indexes, relation-based structures which combine several ideas in spatial knowledge representation. A symbolic spatial index is an array that preserves only a set of spatial relations among distinct objects in an image, called the modelling space; the index array discards information, such as shape and size of objects, and irrelevant spatial relations. The construction of a symbolic spatial index from an input image can be thought of as a transformation that keeps only a set of representative points needed for the definition of the relations of the modelling space. By keeping the relative arrangements of the representative points in symbolic spatial indexes and discarding all other points, we maintain enough information to answer queries regarding the spatial relations of the modelling space without the need to access the initial image or an object database. Symbolic spatial indexes can be used to solve problems involving route planning, composition of spatial relations and update operations.