Well-Composedness in Alexandrov Spaces Implies Digital Well-Composedness in \(\mathbb {Z}^n\)

  • Nicolas Boutry
  • Laurent Najman
  • Thierry Géraud
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10502)


In digital topology, it is well-known that, in 2D and in 3D, a digital set \(X \subseteq \mathbb {Z} ^n\) is digitally well-composed (DWC), i.e., does not contain any critical configuration, if its immersion in the Khalimsky grids \(\mathbb {H}^{n} \) is well-composed in the sense of Alexandrov (AWC), i.e., its boundary is a disjoint union of discrete \((n-1)\)-surfaces. We show that this is still true in n-D, \(n \ge 2\), which is of prime importance since today 4D signals are more and more frequent.


Well-composed Discrete surfaces Alexandrov spaces Critical configurations Digital topology 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Nicolas Boutry
    • 1
    • 2
  • Laurent Najman
    • 2
  • Thierry Géraud
    • 1
  1. 1.EPITA Research and Development Laboratory (LRDE)Le Kremlin-BicêtreFrance
  2. 2.Université Paris-Est, LIGM, Équipe A3SI, ESIEEChamps-sur-MarneFrance

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