Topological spatial relations based on components and dimensions of set intersections

Robert D. Franzosa; Max J. Egenhofer

doi:10.1117/12.142172

9 April 1993 Topological spatial relations based on components and dimensions of set intersections

Robert D. Franzosa, Max J. Egenhofer

Proceedings Volume 1832, Vision Geometry; (1993) https://doi.org/10.1117/12.142172
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States

Abstract

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.

Citation Download Citation

Robert D. Franzosa and Max J. Egenhofer "Topological spatial relations based on components and dimensions of set intersections", Proc. SPIE 1832, Vision Geometry, (9 April 1993); https://doi.org/10.1117/12.142172

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