Well-Composedness in Alexandrov Spaces Implies Digital Well-Composedness in $\mathbb {Z}^n$
Boutry, Nicolas ; Najman, Laurent ; Géraud, Thierry
HAL, hal-01586418 / Harvested from HAL
Text on HAL
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.
Publié le : 2017-09-19
Classification:  well-composed·discrete surfaces,  Alexandrov spaces,  critical configurations ,  digital topology,  [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT],  [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],  [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] 
@article{hal-01586418,
     author = {Boutry, Nicolas and Najman, Laurent and G\'eraud, Thierry},
     title = {Well-Composedness in Alexandrov Spaces Implies Digital Well-Composedness in $\mathbb {Z}^n$},
     journal = {HAL},
     volume = {2017},
     number = {0},
     year = {2017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01586418}
}

Boutry, Nicolas; Najman, Laurent; Géraud, Thierry. Well-Composedness in Alexandrov Spaces Implies Digital Well-Composedness in $\mathbb {Z}^n$. HAL, Tome 2017 (2017) no. 0, . http://gdmltest.u-ga.fr/item/hal-01586418/