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

Nicolas Boutry, Laurent Najman, Thierry Géraud

Abstract: 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.