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

Authors

Nicolas Boutry, Laurent Najman, Thierry Géraud

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

2017-06-01

Abstract

In digital topology, it is well-known that, in 2D and in 3D, a digital set $X\subseteq Z^{n}$ is emphdigitally 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), 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.

Documents

• Paper

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},
  volume	= {10502},
  publisher	= {Springer},
  editor	= {W.G. Kropatsch and N.M. Artner and I. Janusch},
  pages		= {225--237},
  month		= sep,
  address	= {Vienna, Austria},
  doi		= {10.1007/978-3-319-66272-5_19},
  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.}
}