XPMaps and Topological Segmentation - a Unified Approach to Finite Topologies in the Plane

Ullrich Köthe

University of Hamburg, Department of Informatics, Technical Report FBI-HH-M-308/01, December 2001 (long version of above DGCI paper with proofs, 14 pages)

shorter version in:

in: A. Braquelaire, J.-O. Lachaud, A. Vialard (eds.): Proc. of 10th International Conference on Discrete Geometry for Computer Imagery (DGCI 2002), Lecture Notes in Computer Science 2301, pp. 22-33, Heidelberg: Springer, 2002 (note: this article is © Springer-Verlag)

Abstract

Finite topological spaces are now widely recognized as a valuable tool of image analysis. However, their practical application is complicated because there are so many different approaches. We show that there are close relationships between those approaches which motivate the introduction of XPMaps as a concept that subsumes the important characteristics of the other approaches. The notion of topological segmentations then extends this concept to a particular class of labelings of XPMaps. We show that the new notions lead to significant simplifications from both a theoretical and practical viewpoint.

Long version: PostScript (313 kb), PDF (1 Mb)
DGCI version: PostScript (237 kb), PDF (773 kb)

Back to Ullrich Köthe's publication page