# Well-Composedness in Alexandrov spaces implies Digital Well-Composedness in Z^n

### From LRDE

- Authors
- Nicolas Boutry, Laurent Najman, Thierry Geraud
- Where
- Discrete Geometry for Computer Imagery -- Proceedings of the 20th IAPR International Conference on Discrete Geometry for Computer Imagery (DGCI)
- Place
- Vienna, Austria
- Type
- inproceedings
- Publisher
- Springer
- Projects
- Olena
- Keywords
- Image
- Date
- 2017-06-13

## 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 emphwell-composed in the sense of Alexandrov (AWC)

## Documents

## Bibtex (lrde.bib)

@InProceedings{ boutry.17.dgci, author = {Nicolas Boutry and Laurent Najman and Thierry G\'eraud}, title = {Well-Composedness in {A}lexandrov spaces implies Digital Well-Composedness in $Z^n$}, booktitle = {Discrete Geometry for Computer Imagery -- Proceedings of the 20th IAPR International Conference on Discrete Geometry for Computer Imagery (DGCI)}, year = {2017}, series = {Lecture Notes in Computer Science}, optvolume = {0}, publisher = {Springer}, editor = {W.G. Kropatsch and I. Janusch and N.M. Artner and D. Coeurjolly}, optpages = {}, month = {September}, address = {Vienna, Austria}, note = {To appear.}, abstract = {In digital topology, it is well-known that, in 2D and in 3D, a digital set $X \subseteq Z^n$ is \emph{digitally well-composed (DWC)}, {\it i.e.}, does not contain any critical configuration, if its immersion in the Khalimsky grids $H^n$ is \emph{well-composed in the sense of Alexandrov (AWC)}, {\it i.e.}, its boundary is a disjoint union of discrete $(n-1)$-surfaces. We show that this is still true in $n$-D, $n \geq 2$, which is of prime importance since today 4D signals are more and more frequent.} }