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

Abstract : 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.
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Walter G. Kropatsch, Nicole M. Artner, Ines Janusch. 20th International Conference on Discrete Geometry for Computer Imagery (DGCI 2017), Sep 2017, Vienne, Austria. Lecture Notes in Computer Sciences, 10502, pp.225-237, 2017, Discrete Geometry for Computer Imagery 20th IAPR International Conference, DGCI 2017, Vienna, Austria, September 19 – 21, 2017, Proceedings. <10.1007/978-3-319-66272-5_19>
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https://hal.archives-ouvertes.fr/hal-01586418
Contributeur : Laurent Najman <>
Soumis le : mardi 12 septembre 2017 - 17:28:30
Dernière modification le : jeudi 14 septembre 2017 - 07:32:53

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Nicolas Boutry, Laurent Najman, Thierry Géraud. Well-Composedness in Alexandrov Spaces Implies Digital Well-Composedness in $\mathbb {Z}^n$. Walter G. Kropatsch, Nicole M. Artner, Ines Janusch. 20th International Conference on Discrete Geometry for Computer Imagery (DGCI 2017), Sep 2017, Vienne, Austria. Lecture Notes in Computer Sciences, 10502, pp.225-237, 2017, Discrete Geometry for Computer Imagery 20th IAPR International Conference, DGCI 2017, Vienna, Austria, September 19 – 21, 2017, Proceedings. <10.1007/978-3-319-66272-5_19>. <hal-01586418>

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