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

Nicolas Boutry (1) , Laurent Najman (1) , Thierry Géraud (2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 LRDE - Laboratoire de Recherche et de Développement de l'EPITA

In digital topology, it is well-known that, in 2D and in 3D, a digital set X ⊆ Z n is digitally well-composed (DWC), i.e., does not contain any critical configuration, if its immersion in the Khalimsky grids 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 ≥ 2, which is of prime importance since today 4D signals are more and more frequent.

Mots clés: well-composed·discrete surfaces; Alexandrov spaces; critical configurations; digital topology

Domaines: Topologie géométrique [math.GT]; Mathématique discrète [cs.DM]; Traitement des images [eess.IV]

Nicolas Boutry, Laurent Najman, Thierry Géraud. Well-Composedness in Alexandrov Spaces Implies Digital Well-Composedness in $\mathbb {Z}^n$. 20th International Conference on Discrete Geometry for Computer Imagery (DGCI 2017), Sep 2017, Vienne, Austria. pp.225-237, ⟨10.1007/978-3-319-66272-5_19⟩. ⟨hal-01586418⟩