Approximate Topological Relations

In spatial data models for various applications, such as geographical information systems (GISs), the importance of topological relations is widely recognized. Topology makes very general statements about the structure and the relations of spatial objects. A refinement of topology by means of other geometric aspects can help to bend the various models that have been developed for topological relations towards a more effective description of geographic space. The introduction of broad boundaries is a direction to define approximate topological relations between spatial objects. In this paper, approximate topological relations are destined to capture boundary uncertainty, variations over time, proximity measures, and vector-raster representations. Approximate topological relations are structured in conceptual neighborhood graphs that have a twofold interpretation: two neighboring relations are at topological distance 1 in terms of the nine-intersection model and can be obtained, one from the other, by an elementary continuous deformation.