Semi-automated derivation of conceptual neighborhood graphs of topological relations

Abstract

Conceptual neighborhood graphs are similarity-based schemata of spatial/temporal relations. This paper proposes a semi-automated method for deriving a conceptual neighborhood graph of topological relations, which shows all pairs of relations between which a smooth transformation can be performed. The method is applicable to various sets of topological relations distinguished by the 9+-intersection. The method first identifies possible primitive-level transitions, combines those primitive-level transitions, and removes invalid combinations that do not satisfy some necessary conditions. As a demonstration, we develop conceptual neighborhood graphs of topological region-region relations in ℝ2, , and ℝ3 , topological relations between a directed line and a region in ℝ2 , and Allen's interval relations. © 2009 Springer Berlin Heidelberg.