On Computing with Spatial Data

Abstract

Space plays a fundamental role in human cognition. In everyday situations, it is often viewed as a construct induced by spatial relationships, rather than as a container that exists independently of the objects located in it. A variety of formalisms naturally deal with space on the basis of relations between objects. Moreover, the need to handle imprecise and uncertain information when processing spatial data has long been recognized and fuzzy approaches have proven to be of great interest for spatial modeling and reasoning. For instance, spatial relationships often find good models in fuzzy relations, whether they are naturally loaded with ambiguity (like to the right of) or associated with crisp, mathematical definitions (like adjacency). Some models are designed for spatial reasoning, others are not. Some can handle fuzzy objects, while others can only handle crisp objects. Depending on the models, the considered objects are points, lines, surfaces or volumes. They have to be available in raster form, or in vector form. The object geometry is approximated by a simple entity (e.g., a rectangle) or is somehow encapsulated in the model. Other means, like histograms, or linguistic descriptions produced by fuzzy systems, can be used to carry spatial relationship information. The tutorial gives a comprehensive summary on the subject and presents applications to various fields (e.g., geographic information systems, human-machine communication, medical imaging). The intended audience includes professionals, researchers and developers interested in soft computing-based systems exploiting spatial data.