# Topological Relations from Metric Refinements

Egenhofer, M. and M. Dube. Topological Relations from Metric Refinements. Proceedings of the 17th ACM SIGSPATIAL – International Conference on Advances in Geographic Information Systems, Seattle, WA. D. Agrawal, W. Aref, C. Lu, M. Mokbel, P. Scheuermann, C. Shahabi and O. Wolfson (eds.), November, 2009. pp. 158-167.

Abstract: Naive Geography’s premise “Topology matters, metric refines” calls for metric properties that provide opportunities for finer grained distinctions than the purely qualitative topological relations. This paper defines a comprehensive set of eleven metric refinements that apply to the eight coarse topological relations between two regions that the 9-intersection and the Region-Connection Calculus identify and develops the applicable value ranges for each metric refinement. It is shown that any topological relation between two regions can be derived uniquely from the conjunction of at most three such refinement specifications (i.e., pairs of metric refinements and applicable value ranges). The smallest set of refinement specifications that determine uniquely all eight relations resorts to six of the eleven metric refinements.