Difference between revisions of "Publications/boutry.18.is"
From LRDE
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| title = Weakly Well-Composed Cell Complexes over nD Pictures |
| title = Weakly Well-Composed Cell Complexes over nD Pictures |
||
| journal = Information Sciences |
| journal = Information Sciences |
||
| − | | volume = |
+ | | volume = 499 |
| − | | pages = |
+ | | pages = 62 to 83 |
| lrdeprojects = Olena |
| lrdeprojects = Olena |
||
| − | | abstract = In previous work we proposed a combinatorial algorithm to “locally repair” the cubical complex Q(I) that is canonically associated with a given 3D picture I. The algorithm constructs a 3D polyhedral complex P(I) which is homotopy equivalent to Q(I) and whose boundary surface is a 2D manifold. A polyhedral complex satisfying these properties is called well-composed. In the present paper we extend these results to higher dimensions. We prove that for a given n-dimensional picture the obtained cell complex is well-composed in a weaker sense but is still homotopy equivalent to the initial cubical complex. |
+ | | abstract = In previous work we proposed a combinatorial algorithm to “locally repair” the cubical complex <math>Q(I)</math> that is canonically associated with a given 3D picture I. The algorithm constructs a 3D polyhedral complex <math>P(I)</math> which is homotopy equivalent to <math>Q(I)</math> and whose boundary surface is a 2D manifold. A polyhedral complex satisfying these properties is called well-composed. In the present paper we extend these results to higher dimensions. We prove that for a given <math>n</math>-dimensional picture the obtained cell complex is well-composed in a weaker sense but is still homotopy equivalent to the initial cubical complex. |
| lrdepaper = http://www.lrde.epita.fr/dload/papers/boutry.18.is.pdf |
| lrdepaper = http://www.lrde.epita.fr/dload/papers/boutry.18.is.pdf |
||
| lrdekeywords = Image |
| lrdekeywords = Image |
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| Line 20: | Line 20: | ||
title = <nowiki>{</nowiki>Weakly Well-Composed Cell Complexes over <nowiki>{</nowiki>$n$D<nowiki>}</nowiki> Pictures<nowiki>}</nowiki>, |
title = <nowiki>{</nowiki>Weakly Well-Composed Cell Complexes over <nowiki>{</nowiki>$n$D<nowiki>}</nowiki> Pictures<nowiki>}</nowiki>, |
||
journal = <nowiki>{</nowiki>Information Sciences<nowiki>}</nowiki>, |
journal = <nowiki>{</nowiki>Information Sciences<nowiki>}</nowiki>, |
||
| − | volume = <nowiki>{</nowiki> |
+ | volume = <nowiki>{</nowiki>499<nowiki>}</nowiki>, |
| − | pages = <nowiki>{</nowiki> |
+ | pages = <nowiki>{</nowiki>62--83<nowiki>}</nowiki>, |
| − | month = |
+ | month = oct, |
| − | year = <nowiki>{</nowiki> |
+ | year = <nowiki>{</nowiki>2019<nowiki>}</nowiki>, |
abstract = <nowiki>{</nowiki>In previous work we proposed a combinatorial algorithm to |
abstract = <nowiki>{</nowiki>In previous work we proposed a combinatorial algorithm to |
||
| − | ``locally repair'' the cubical complex Q(I) that is |
+ | ``locally repair'' the cubical complex $Q(I)$ that is |
canonically associated with a given 3D picture I. The |
canonically associated with a given 3D picture I. The |
||
| − | algorithm constructs a 3D polyhedral complex P(I) which |
+ | algorithm constructs a 3D polyhedral complex $P(I)$ which |
| − | homotopy equivalent to Q(I) and whose boundary surface |
+ | is homotopy equivalent to $Q(I)$ and whose boundary surface |
| − | 2D manifold. A polyhedral complex satisfying these |
+ | is a 2D manifold. A polyhedral complex satisfying these |
| − | properties is called well-composed. In the present |
+ | properties is called <nowiki>{</nowiki>\it well-composed<nowiki>}</nowiki>. In the present |
| − | extend these results to higher dimensions. We |
+ | paper we extend these results to higher dimensions. We |
| − | for a given n-dimensional picture the obtained |
+ | prove that for a given $n$-dimensional picture the obtained |
| − | is well-composed in a weaker sense but is |
+ | cell complex is well-composed in a weaker sense but is |
| − | equivalent to the initial cubical complex.<nowiki>}</nowiki> |
+ | still homotopy equivalent to the initial cubical complex.<nowiki>}</nowiki> |
<nowiki>}</nowiki> |
<nowiki>}</nowiki> |
||
Revision as of 11:21, 3 March 2020
- Authors
- Nicolas Boutry, Rocio Gonzalez-Diaz, Maria-Jose Jimenez
- Journal
- Information Sciences
- Type
- article
- Projects
- Olena
- Keywords
- Image
- Date
- 2018-07-04
Abstract
In previous work we proposed a combinatorial algorithm to “locally repair” the cubical complex that is canonically associated with a given 3D picture I. The algorithm constructs a 3D polyhedral complex which is homotopy equivalent to and whose boundary surface is a 2D manifold. A polyhedral complex satisfying these properties is called well-composed. In the present paper we extend these results to higher dimensions. We prove that for a given -dimensional picture the obtained cell complex is well-composed in a weaker sense but is still homotopy equivalent to the initial cubical complex.
Documents
Bibtex (lrde.bib)
@Article{ boutry.18.is,
author = {Nicolas Boutry and Rocio Gonzalez-Diaz and Maria-Jose
Jimenez},
title = {Weakly Well-Composed Cell Complexes over {$n$D} Pictures},
journal = {Information Sciences},
volume = {499},
pages = {62--83},
month = oct,
year = {2019},
abstract = {In previous work we proposed a combinatorial algorithm to
``locally repair'' the cubical complex $Q(I)$ that is
canonically associated with a given 3D picture I. The
algorithm constructs a 3D polyhedral complex $P(I)$ which
is homotopy equivalent to $Q(I)$ and whose boundary surface
is a 2D manifold. A polyhedral complex satisfying these
properties is called {\it well-composed}. In the present
paper we extend these results to higher dimensions. We
prove that for a given $n$-dimensional picture the obtained
cell complex is well-composed in a weaker sense but is
still homotopy equivalent to the initial cubical complex.}
}