Topological spatial relations based on components and dimensions of set intersections
Robert Franzosa, Max J. Egenhofer · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1993
The notion of topological spatial relations is introduced. It corresponds to the topological type of a pair of intersecting sets in a topological space. The previously introduced 4-intersection (boundary-boundary, interior-interior, boundary-interior, and interior-interior), a topological invariant of topological spatial relations, is further refined by considering the number of components and the dimension of each component in each intersection in the 4-intersection. Properties of these invariants are examined. We show how the topological spatial relations between two 2-disks in the plane can be classified using these invariants.