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

  • Ullrich Köthe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2301)


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.


Topological Space Cell Complex Open Star Node Split Plane Division 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Ullrich Köthe
    • 1
  1. 1.Cognitive Systems GroupUniversity of HamburgHamburg

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