About the equivalence between AWCness and DWCness
Résumé
In digital topology, it is well-known that, in 2D and in 3D, a set is digitally well-composed (DWC), that is, does not contain any critical configuration, iff its immersion in the Khalimsky grids is well-composed in the Alexandrov sense (AWC), that is, its topological boundary is a disjoint union of discrete surfaces. This report shows that this is still true in any finite dimension, which is of primary importance since today 4D signals are more and more frequent. A nice result of this proof is that we can now use DWC interpolation methods to produce AWC images. Note that the correctness of this proof is still not verified.
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