Modeling Topological Relations between Uncertain Spatial Regions in Geo-spatial Databases: Uncertain Intersection and Difference Topological Model

Topological relations have played important roles in spatial query, analysis and reasoning in Geographic Information Systems (GIS) and geospatial databases. The topological relations between crisp, uncertain and fuzzy spatial regions based upon the 9-intersections model have been identified. The research issue of topological relations, particularly, between spatial regions with uncertainties, has gained a lot of attention during the past two decades. However, the formal representation and calculation of the topological relations between uncertain regions is still an open issue and needs to be further developed. The paper provides a theoretical framework for modeling topological relations between uncertain spatial regions based upon a new uncertain topological model called the Uncertain Intersection and Difference (UID) Model. In order to derive all topological relations between two spatial regions with uncertainties, the spatial object of type Region (A) is decomposed in four components: the Interior, the Interior's Boundary, the Object's Boundary, and the Exterior's Boundary of A. By use of this definition of spatial region with uncertainties, new 4*4-Intersection and Uncertain Intersection and Difference (UID) models are proposed as a qualitative model for the identification of all topological relations between two spatial regions with uncertainties. These two new models are compared with other models studied in the literature. 152 binary topological relations can be identified by these two models. Then, the topological complexity and distance of the 152 relations will be study in details by using the UID model. Based upon this study of topological complexity and distance, a conceptual neighborhood graph for the 152 relations can be obtained. Examples are provided to illustrate the utility of these two models presented in this paper with results which can be applied for modeling GIS, geospatial databases and satellite image processing.