Improving 9-intersection model by replacing the complement with Voronoi region

Abstract

intersection model is the most popular framework used for formalizing the spatial relations between two spatial objects A and B. It transforms the topological relation- ships between two simple spatial Objects A and B into point-set topology problem in terms of the intersections of A’s boundary ( A), interior (A0) and exterior (A - ) with B’s bound- ary ( B), interior (B0) and exterior (B - ). It is shown in this paper that there exist some limitations of the original 9-intersection model due to its definition of an object’s exterior as its complement,and it is difficult to distinguish different disjoint relations and relations be- tween complex objects with holes, difficult or even impossible to compute the intersections with the two object’s complements ( A B -, A0 B -, A - B, A - B0 and A - B - )since the complements are infinitive. The authors suggest to re-define the exterior of spa- tial object by replacing the complement with its Voronoi region. A new Voronoi-based 9-in- tersection (VNI) is proposed and used for formalizing topological relations between spatial objects. By improving the 9-interscetion model, it is now possible to distinguish disjoint rela- tions and to deal with objects with holes. Also it is possible to compute the exterior-based in- tersections and manipulate spatial relations with the VNI.