Multi-level Topological Relations of the Spatial Reasoning System RCC-8

Queries in geospatial databases, such as geographic information systems (GIS), image databases, are often based upon the relations among spatial objects. Spatial relations are the basis of many queries that GIS perform such as the topological relations. The general description of region-region topological relations in details is still an unsolved issue although much effort has been done. The eight basic topological relations between two spatial regions are written without any details in the classical form of the spatial reasoning system RCC-8: DC, EC, EQ, PO, TPP, TPPi, NTPP and NTPPi. In some applications, there are needs to describe in details these relations. In order to extract all the necessary details at all levels and to differentiate between relations of the same kind, multi-level topological relations of RCC-8 are introduced by using two concepts: the separation number and the types of spatial elements (Points and Lines) of the boundary-boundary intersection spatial set (BBISS). These two concepts are very important to detail these relations. In our study, the major contribution is multi-level topological relations of RCC-8. We focus our work on the four relations EC, PO, TPP and TPPi which can be detailed at two additional levels. First, these four relations are written and described in general detailed forms by the concept of separation number. Secondly, the same relations are expressed in other general forms by the concept of types of spatial elements. Finally, examples are provided to illustrate the determination of these relations presented in this paper.