Vague Topological Predicates for Crisp Regions through Metric Refinements

Abstract

Topological relationships between spatial objects have been a focus of research on spatial data handling and reasoning for a long time. Especially as predicates they support the design of suitable query languages for data retrieval and analysis in spatial databases and geographical information systems. Whereas research on this topic has always been dominated by qualitative methods and by an emphasis of a strict separation of topological and metric, that is, quantitative, properties, this paper investigates their possible coexistence and cooperation. Metric details can be exploited to refine topological relationships and to make important semantic distinctions that enhance the expressiveness of spatial query languages. The metric refinements introduced in this paper have the feature of being topologically invariant under a ne transformations. Since the combination of a topological predicate with a metric refinement leads to a single unified quantitative measure, this measure has to be interpreted and mapped to a lexical item. This leads to vague topological predicates, and we demonstrate how these predicates can be integrated into a spatial query language.