Difference between revisions of "Publications/boutry.19.jmiv"
From LRDE
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| title = How to Make n-D Plain Maps Alexandrov-Well-Composed in a Self-dual Way |
| title = How to Make n-D Plain Maps Alexandrov-Well-Composed in a Self-dual Way |
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| journal = Journal of Mathematical Imaging and Vision |
| journal = Journal of Mathematical Imaging and Vision |
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− | | volume = |
+ | | volume = 61 |
− | | |
+ | | number = 6 |
+ | | pages = 849 to 873 |
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| lrdeprojects = Olena |
| lrdeprojects = Olena |
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| abstract = In 2013, Najman and Géraud proved that by working on a well-composed discrete representation of a gray-level image, we can compute what is called its tree of shapes, a hierarchical representation of the shapes in this image. This way, we can proceed to morphological filtering and to image segmentation. However, the authors did not provide such a representation for the non-cubical case. We propose in this paper a way to compute a well-composed representation of any gray-level image defined on a discrete surface, which is a more general framework than the usual cubical grid. Furthermore, the proposed representation is self-dual in the sense that it treats bright and dark components in the image the same way. This paper can be seen as an extension to gray-level images of the works of Daragon et al. on discrete surfaces. |
| abstract = In 2013, Najman and Géraud proved that by working on a well-composed discrete representation of a gray-level image, we can compute what is called its tree of shapes, a hierarchical representation of the shapes in this image. This way, we can proceed to morphological filtering and to image segmentation. However, the authors did not provide such a representation for the non-cubical case. We propose in this paper a way to compute a well-composed representation of any gray-level image defined on a discrete surface, which is a more general framework than the usual cubical grid. Furthermore, the proposed representation is self-dual in the sense that it treats bright and dark components in the image the same way. This paper can be seen as an extension to gray-level images of the works of Daragon et al. on discrete surfaces. |
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in a Self-dual Way<nowiki>}</nowiki>, |
in a Self-dual Way<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>, |
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− | volume = <nowiki>{</nowiki> |
+ | volume = <nowiki>{</nowiki>61<nowiki>}</nowiki>, |
− | + | number = <nowiki>{</nowiki>6<nowiki>}</nowiki>, |
|
+ | pages = <nowiki>{</nowiki>849--873<nowiki>}</nowiki>, |
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year = <nowiki>{</nowiki>2019<nowiki>}</nowiki>, |
year = <nowiki>{</nowiki>2019<nowiki>}</nowiki>, |
||
abstract = <nowiki>{</nowiki>In 2013, Najman and G\'eraud proved that by working on a |
abstract = <nowiki>{</nowiki>In 2013, Najman and G\'eraud proved that by working on a |
Revision as of 13:17, 12 July 2019
- Authors
- Nicolas Boutry, Thierry Géraud, Laurent Najman
- Journal
- Journal of Mathematical Imaging and Vision
- Type
- article
- Projects
- Olena
- Keywords
- Image
- Date
- 2019-02-04
Abstract
In 2013, Najman and Géraud proved that by working on a well-composed discrete representation of a gray-level image, we can compute what is called its tree of shapes, a hierarchical representation of the shapes in this image. This way, we can proceed to morphological filtering and to image segmentation. However, the authors did not provide such a representation for the non-cubical case. We propose in this paper a way to compute a well-composed representation of any gray-level image defined on a discrete surface, which is a more general framework than the usual cubical grid. Furthermore, the proposed representation is self-dual in the sense that it treats bright and dark components in the image the same way. This paper can be seen as an extension to gray-level images of the works of Daragon et al. on discrete surfaces.
Documents
Bibtex (lrde.bib)
@Article{ boutry.19.jmiv, author = {Nicolas Boutry and Thierry G\'eraud and Laurent Najman}, title = {How to Make {$n$-D} Plain Maps {A}lexandrov-Well-Composed in a Self-dual Way}, journal = {Journal of Mathematical Imaging and Vision}, volume = {61}, number = {6}, pages = {849--873}, year = {2019}, abstract = {In 2013, Najman and G\'eraud proved that by working on a well-composed discrete representation of a gray-level image, we can compute what is called its tree of shapes, a hierarchical representation of the shapes in this image. This way, we can proceed to morphological filtering and to image segmentation. However, the authors did not provide such a representation for the non-cubical case. We propose in this paper a way to compute a well-composed representation of any gray-level image defined on a discrete surface, which is a more general framework than the usual cubical grid. Furthermore, the proposed representation is self-dual in the sense that it treats bright and dark components in the image the same way. This paper can be seen as an extension to gray-level images of the works of Daragon et al. on discrete surfaces.} }