Digital topologies revisited: An approach based on the topological point-neighbourhood

  • Pavel Ptak
  • Helmut Kofler
  • Walter Kropatsch
Topology
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1347)

Abstract

Adopting the point-neighbourhood definition of topology, which we think may in some cases help acquire a very good insight of digital topologies, we unify the proof technique of the results on 4-connectedness and on 8-connectedness in ℤ2. We also show that there is no topology compatible with 6-connectedness. We shortly comment on potential further use of this approach.

Key words

Image processing digital topology adjacency path-connectedness and topological connectedness in ℤ2 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Pavel Ptak
    • 1
  • Helmut Kofler
    • 2
  • Walter Kropatsch
    • 2
  1. 1.Faculty of Electrical EngineeringCenter for Machine Perception CMP — Czech Technical UniversityPraha 2Czech Republic
  2. 2.Pattern Recognition and Image Proc. Group — PRIPVienna University of TechnologyViennaAustria

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