Efficient Implementation Techniques for Topological Predicates on Complex Spatial Objects: The Evaluation Phase

Topological predicates like overlap, inside, meet, and disjoint uniquely characterize the relative position between objects in space. They have been the subject of extensive interdisciplinary research. Spatial database systems and geographical information systems have shown a special interest in them since they enable the support of suitable query languages for spatial data retrieval and analysis. A look into the literature reveals that the research efforts so far have mainly dealt with the conceptual design of and the reasoning with these predicates while the development of efficient and robust implementation methods for them has been largely neglected. Especially the recent design of topological predicates for different combinations of complex spatial data types has resulted in a large increase of their numbers and stressed the importance of their efficient implementation. The goal of this article is to develop efficient implementation techniques of topological predicates for all combinations of the complex spatial data types point2D, line2D, and region2D within the framework of the spatial algebra SPAL2D. Our solution consists of two phases. In the exploration phase described in previous work of the authors, for a given scene of two spatial objects, all topological events are registered in so-called topological feature vectors. These vectors serve as input for the evaluation phase which is the focus of this article and which analyzes the topological events and determines the Boolean result of a topological predicate or the kind of topological predicate by a formally defined method called 9-intersection matrix characterization. Besides this very general evaluation method, the article presents an optimized method for predicate verification, called matrix thinning, and an optimized method for predicate determination, called minimum cost decision tree. Our evaluation methods also turn out to be able to compute dimension-refined topological predicates. ∗This work was partially supported by the National Science Foundation (NSF) under grant number NSF-CAREER-IIS-0347574.