Well-Composedness in Alexandrov Spaces Implies Digital Well-Composedness in Zn

In digital topology, it is well-known that, in 2D and in 3D, a digital set X ⊆ Z is digitally well-composed (DWC), i.e., does not contain any critical configuration, if its immersion in the Khalimsky grids H 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.