Improving 9-Intersection Model by Replacing the

9-intersection model is the most popular framework used for formalizing the spatial relations between two spatial objects A and B. It transforms the topological relationships between two simple spatial objects A and B into point-set topology problem in terms of the intersections of A’s boundary (A), interior (A) and exterior (A) with B’s boundary ( B), interior (B) and exterior (B). It was shown in the 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, including being difficult to distinguish different disjoint relations and relations between complex objects with holes, difficult or even impossible to compute the intersections with the two object’s complements(A∩B, A∩B, A∩B,A∩B and A∩B ) since the complements are infinitive. The authors suggested to re-define the exterior of spatial object by replacing the complement with its Voronoi region. A new Voronoi-based 9-intersection (VNI) was proposed and used for formalizing topological relations between spatial objects. By improving the 9-interscetion model, it is now possible to distinguish disjoint relations and to deal with objects with holes. It is also possible to compute the exterior-based intersections and manipulate spatial relations with the VNI. 1. Overview of the original 9-intersection model The spatial relations between spatial entities are known as important as the entities themselves. It is therefore very essential to know what possible spatial relationships are and how they can be determined. The 9-intersection model is the most popular mathematical framework for formalizing spatial relations and have been used for a number of applications in spatial query languages [Engenhofer,1991, Clementini et al. 1994, Mark et al. 1995]. It transforms the topological relationships between two simple spatial objects A and B into point-set topology problem. That is, the topological relations between two objects A and B are defined in terms of the intersections of A’s boundary (A), interior (A) and exterior (A) with B’s boundary ( B), interior (B) and exterior (B). By considering whether the contents of the 9-intersection is empty or non-empty, a number of binary topological relations could be identified [Egenhofer and Franzosa, 1991]. For instance, eight relations