Difference between revisions of "Publications/boutry.17.dgci"

From LRDE

(Created page with "{{Publication | published = true | date = 2017-06-13 | authors = Nicolas Boutry, Laurent Najman, Thierry Géraud | title = Well-Composedness in Alexandrov spaces implies Digit...")
 
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author = <nowiki>{</nowiki>Nicolas Boutry and Laurent Najman and Thierry G\'eraud<nowiki>}</nowiki>,
  
author = <nowiki>{</nowiki>Nicolas Boutry and Laurent Najman and Thierry G\'eraud<nowiki>}</nowiki>,
 
title = <nowiki>{</nowiki>Well-Composedness in <nowiki>{</nowiki>A<nowiki>}</nowiki>lexandrov spaces implies Digital
  
title = <nowiki>{</nowiki>Well-Composedness in <nowiki>{</nowiki>A<nowiki>}</nowiki>lexandrov spaces implies Digital
−
Well-Composedness in $\mathbb<nowiki>{</nowiki>Z<nowiki>}</nowiki>^n$<nowiki>}</nowiki>,
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Well-Composedness in $Z^n$<nowiki>}</nowiki>,
 
booktitle = <nowiki>{</nowiki>Discrete Geometry for Computer Imagery -- Proceedings of
  
booktitle = <nowiki>{</nowiki>Discrete Geometry for Computer Imagery -- Proceedings of
 
the 20th IAPR International Conference on Discrete Geometry
  
the 20th IAPR International Conference on Discrete Geometry
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note = <nowiki>{</nowiki>To appear.<nowiki>}</nowiki>,
  
note = <nowiki>{</nowiki>To appear.<nowiki>}</nowiki>,
 
abstract = <nowiki>{</nowiki>In digital topology, it is well-known that, in 2D and in
  
abstract = <nowiki>{</nowiki>In digital topology, it is well-known that, in 2D and in
−
3D, a digital set $X \subseteq \mathbb<nowiki>{</nowiki>Z<nowiki>}</nowiki>^n$ is
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3D, a digital set $X \subseteq Z^n$ is \emph<nowiki>{</nowiki>digitally
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\emph<nowiki>{</nowiki>digitally well-composed (DWC)<nowiki>}</nowiki>, <nowiki>{</nowiki>\it i.e.<nowiki>}</nowiki>, does not
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well-composed (DWC)<nowiki>}</nowiki>, <nowiki>{</nowiki>\it i.e.<nowiki>}</nowiki>, does not contain any
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contain any critical configuration, if its immersion in the
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critical configuration, if its immersion in the Khalimsky
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Khalimsky grids $\mathbb<nowiki>{</nowiki>H<nowiki>}</nowiki>^<nowiki>{</nowiki>n<nowiki>}</nowiki>$ is \emph<nowiki>{</nowiki>well-composed in
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grids $H^n$ is \emph<nowiki>{</nowiki>well-composed in the sense of
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the sense of Alexandrov (AWC)<nowiki>}</nowiki>, <nowiki>{</nowiki>\it i.e.<nowiki>}</nowiki>, its boundary is
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Alexandrov (AWC)<nowiki>}</nowiki>, <nowiki>{</nowiki>\it i.e.<nowiki>}</nowiki>, its boundary is a disjoint
−
a disjoint union of discrete $(n-1)$-surfaces. We show that
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union of discrete $(n-1)$-surfaces. We show that this is
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this is still true in $n$-D, $n \geq 2$, which is of prime
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still true in $n$-D, $n \geq 2$, which is of prime
 
importance since today 4D signals are more and more frequent.<nowiki>}</nowiki>
  
importance since today 4D signals are more and more frequent.<nowiki>}</nowiki>
 
<nowiki>}</nowiki>
  
<nowiki>}</nowiki>

Revision as of 11:56, 19 June 2017

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
2017-06-13

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.}
}





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