Refining topological relations between regions considering their shapes

Abstract

Topological relations are sometimes insufficient for differentiating spatial configurations of two objects with critical difference in their connection styles. In this paper, we present the projective 9 ∈+∈ -intersection model, which refines topological relations into projective binary relations by considering projective properties of the objects' shapes. This is indeed a reformulation of projective concepts of the Dimensional Model within the framework of the 9 ∈+∈ -intersection. Thirty projective binary relationsare established between two regions in R 2, one of which has a multi-order boundary (region ∈+∈mob). These relations are identified computationally by applying to all theoretical relations the existing constraints for topological region-region relations and seven new specific constraints. After defining the concept of continuous neighbours between two projective binary relations, a conceptual neighbourhood graph of the 30 projective region ∈+∈mob-region relations is developed. © 2008 Springer-Verlag Berlin Heidelberg.