A Model for Representing Topological Relations Between Simple Concave Regions

Abstract

At present, qualitative spatial reasoning has become the hot issues in many research fields. The most popular models of spatial topological relations are Region Connection Calculus (RCC) and 9-intersection model. However, there are few contributions on topological relations of concave regions in which the representative model is Cohn's RCC23. There are some limitations of RCC23 especially in practical applications due to its less expressiveness. In order to construct a more expressive model of topological relations between concave regions, this paper completed the following works: 9-intersection matrix is extended to 16-intersection matrix, and RCC23 is refined to RCC62 based on 16intersection matrix. More relations can be distinguished in RCC62, which is more expressive than RCC23. In order to further reason about relations in RCC62, the Conceptual Neighborhood Graph (CNG) and the Closest Topological Relation Graph (CTRG) of RCC62 are given.

A Formal Representation of the Semantics of Structural Geological Models

“…Chen et al [37] proposed V9I by replacing the exterior of 9IM with the Voronoi region of the entity. Ouyang et al [38] divided the outside of a concave area into two parts and the inside and outside of the convex shell and expanded the 9IM to 16IM. Further 61 relations are possible between 0-, 1-, 2-, and 3dimensional entities in three-dimensional space [36].…”

A survey of qualitative spatial representations

“…Dividing the exterior of a concave region into two parts, the inside and outside of the convex hull, the 9IM is extended to 16IM (Ouyang et al, 2009a), which is a refinement of RCC23 (Cohn, 1995) a calculus discriminating the topological relations between concave regions. For examples, three new relations can be identified between the regions on the spherical surface (Egenhofer, 2005).…”

“…However, the predicate to detect whether two concavities i 1 and i 2 in the convex hull of region x lie on the same side of x, SameSide (i 1 , i 2 , x) in Cohn (1995) does not always give the correct answer. This problem is solved in Ouyang et al (2009a) by an improved SameSide* predicate definition and an algorithm based on detecting concave concavities and transforming them to convex concavities, which are amenable to the revised SameSide predicate definition. The convex hull is a et al, 2004: 1103) powerful primitive and it has been shown that any pair of bounded, regular regions in 2D space can be distinguished by the three primitives: external connection, proper part of and being convex, if and only if they are not related by an affine transformation (Davis et al, 1999).…”

Surrounds in partitions

“…RCC-8 allows for holed regions, but captures the resulting relations in holes like the relations outside a holed region. With the addition of more axioms, further distinctions are possible, however [4,6,19,34]. The 9-intersection, on the other hand, specifies the types of objects to which it applies and derives from the objects' topological properties what relations are distinguishable.…”