Difference between revisions of "Publications/boutry.20.jmiv.1"
From LRDE
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| title = Topological Properties of the First Non-Local Digitally Well-Composed Interpolation on n-D Cubical Grids |
| title = Topological Properties of the First Non-Local Digitally Well-Composed Interpolation on n-D Cubical Grids |
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| journal = Journal of Mathematical Imaging and Vision |
| journal = Journal of Mathematical Imaging and Vision |
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− | | volume = |
+ | | volume = 62 |
| number = |
| number = |
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− | | pages = |
+ | | pages = 1256 to 1284 |
| lrdeprojects = Olena |
| lrdeprojects = Olena |
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| abstract = In discrete topology, we like digitally well-composed (shortly DWC) interpolations because they remove pinches in cubical images. Usual well-composed interpolations are local and sometimes self-dual (they treat in a same way dark and bright components in the image). In our case, we are particularly interested in <math>n</math>-D self-dual DWC interpolations to obtain a purely self-dual tree of shapes. However, it has been proved that we cannot have an <math>n</math>-D interpolation which is at the same time localself-dual, and well-composed. By removing the locality constraint, we have obtained an <math>n</math>-D interpolation with many properties in practice: it is self-dual, DWC, and in-between (this last property means that it preserves the contours). Since we did not published the proofs of these results before, we propose to provide in a first time the proofs of the two last properties here (DWCness and in-betweeness) and a sketch of the proof of self-duality (the complete proof of self-duality requires more material and will come later). Some theoretical and practical results are given. |
| abstract = In discrete topology, we like digitally well-composed (shortly DWC) interpolations because they remove pinches in cubical images. Usual well-composed interpolations are local and sometimes self-dual (they treat in a same way dark and bright components in the image). In our case, we are particularly interested in <math>n</math>-D self-dual DWC interpolations to obtain a purely self-dual tree of shapes. However, it has been proved that we cannot have an <math>n</math>-D interpolation which is at the same time localself-dual, and well-composed. By removing the locality constraint, we have obtained an <math>n</math>-D interpolation with many properties in practice: it is self-dual, DWC, and in-between (this last property means that it preserves the contours). Since we did not published the proofs of these results before, we propose to provide in a first time the proofs of the two last properties here (DWCness and in-betweeness) and a sketch of the proof of self-duality (the complete proof of self-duality requires more material and will come later). Some theoretical and practical results are given. |
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Well-Composed Interpolation on $n$-D Cubical Grids<nowiki>}</nowiki>, |
Well-Composed Interpolation on $n$-D Cubical Grids<nowiki>}</nowiki>, |
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journal = <nowiki>{</nowiki>Journal of Mathematical Imaging and Vision<nowiki>}</nowiki>, |
journal = <nowiki>{</nowiki>Journal of Mathematical Imaging and Vision<nowiki>}</nowiki>, |
||
− | volume = <nowiki>{</nowiki><nowiki>}</nowiki>, |
+ | volume = <nowiki>{</nowiki>62<nowiki>}</nowiki>, |
number = <nowiki>{</nowiki><nowiki>}</nowiki>, |
number = <nowiki>{</nowiki><nowiki>}</nowiki>, |
||
− | pages = <nowiki>{</nowiki><nowiki>}</nowiki>, |
+ | pages = <nowiki>{</nowiki>1256--1284<nowiki>}</nowiki>, |
month = sep, |
month = sep, |
||
year = <nowiki>{</nowiki>2020<nowiki>}</nowiki>, |
year = <nowiki>{</nowiki>2020<nowiki>}</nowiki>, |
Revision as of 08:25, 16 October 2020
- Authors
- Nicolas Boutry, Laurent Najman, Thierry Géraud
- Journal
- Journal of Mathematical Imaging and Vision
- Type
- article
- Projects
- Olena
- Keywords
- Image
- Date
- 2020-09-03
Abstract
In discrete topology, we like digitally well-composed (shortly DWC) interpolations because they remove pinches in cubical images. Usual well-composed interpolations are local and sometimes self-dual (they treat in a same way dark and bright components in the image). In our case, we are particularly interested in -D self-dual DWC interpolations to obtain a purely self-dual tree of shapes. However, it has been proved that we cannot have an -D interpolation which is at the same time localself-dual, and well-composed. By removing the locality constraint, we have obtained an -D interpolation with many properties in practice: it is self-dual, DWC, and in-between (this last property means that it preserves the contours). Since we did not published the proofs of these results before, we propose to provide in a first time the proofs of the two last properties here (DWCness and in-betweeness) and a sketch of the proof of self-duality (the complete proof of self-duality requires more material and will come later). Some theoretical and practical results are given.
Documents
Bibtex (lrde.bib)
@Article{ boutry.20.jmiv.1, author = {Nicolas Boutry and Laurent Najman and Thierry G\'eraud}, title = {Topological Properties of the First Non-Local Digitally Well-Composed Interpolation on $n$-D Cubical Grids}, journal = {Journal of Mathematical Imaging and Vision}, volume = {62}, number = {}, pages = {1256--1284}, month = sep, year = {2020}, abstract = {In discrete topology, we like digitally well-composed (shortly DWC) interpolations because they remove pinches in cubical images. Usual well-composed interpolations are local and sometimes self-dual (they treat in a same way dark and bright components in the image). In our case, we are particularly interested in $n$-D self-dual DWC interpolations to obtain a purely self-dual tree of shapes. However, it has been proved that we cannot have an $n$-D interpolation which is at the same time local, self-dual, and well-composed. By removing the locality constraint, we have obtained an $n$-D interpolation with many properties in practice: it is self-dual, DWC, and in-between (this last property means that it preserves the contours). Since we did not published the proofs of these results before, we propose to provide in a first time the proofs of the two last properties here (DWCness and in-betweeness) and a sketch of the proof of self-duality (the complete proof of self-duality requires more material and will come later). Some theoretical and practical results are given. } }