Difference between revisions of "Publications/boutry.19.jmiv"
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 title = How to Make nD Plain Maps AlexandrovWellComposed in a Selfdual Way 
 title = How to Make nD Plain Maps AlexandrovWellComposed in a Selfdual Way 

 journal = Journal of Mathematical Imaging and Vision 
 journal = Journal of Mathematical Imaging and Vision 

−   volume = 
+   volume = 61 
−   
+   number = 6 
+   pages = 849 to 873 

 lrdeprojects = Olena 
 lrdeprojects = Olena 

 abstract = In 2013, Najman and Géraud proved that by working on a wellcomposed discrete representation of a graylevel 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 noncubical case. We propose in this paper a way to compute a wellcomposed representation of any graylevel image defined on a discrete surface, which is a more general framework than the usual cubical grid. Furthermore, the proposed representation is selfdual 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 graylevel images of the works of Daragon et al. on discrete surfaces. 
 abstract = In 2013, Najman and Géraud proved that by working on a wellcomposed discrete representation of a graylevel 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 noncubical case. We propose in this paper a way to compute a wellcomposed representation of any graylevel image defined on a discrete surface, which is a more general framework than the usual cubical grid. Furthermore, the proposed representation is selfdual 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 graylevel images of the works of Daragon et al. on discrete surfaces. 

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in a Selfdual Way<nowiki>}</nowiki>, 
in a Selfdual Way<nowiki>}</nowiki>, 

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> 
+  volume = <nowiki>{</nowiki>61<nowiki>}</nowiki>, 
−  +  number = <nowiki>{</nowiki>6<nowiki>}</nowiki>, 

−  +  pages = <nowiki>{</nowiki>849873<nowiki>}</nowiki>, 

year = <nowiki>{</nowiki>2019<nowiki>}</nowiki>, 
year = <nowiki>{</nowiki>2019<nowiki>}</nowiki>, 

+  month = jul, 

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 

wellcomposed discrete representation of a graylevel 
wellcomposed discrete representation of a graylevel 
Latest revision as of 14:48, 17 October 2019
 Authors
 Nicolas Boutry, Thierry Géraud, Laurent Najman
 Journal
 Journal of Mathematical Imaging and Vision
 Type
 article
 Projects
 Olena
 Keywords
 Image
 Date
 20190204
Abstract
In 2013, Najman and Géraud proved that by working on a wellcomposed discrete representation of a graylevel 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 noncubical case. We propose in this paper a way to compute a wellcomposed representation of any graylevel image defined on a discrete surface, which is a more general framework than the usual cubical grid. Furthermore, the proposed representation is selfdual 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 graylevel 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}lexandrovWellComposed in a Selfdual Way}, journal = {Journal of Mathematical Imaging and Vision}, volume = {61}, number = {6}, pages = {849873}, year = {2019}, month = jul, abstract = {In 2013, Najman and G\'eraud proved that by working on a wellcomposed discrete representation of a graylevel 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 noncubical case. We propose in this paper a way to compute a wellcomposed representation of any graylevel image defined on a discrete surface, which is a more general framework than the usual cubical grid. Furthermore, the proposed representation is selfdual 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 graylevel images of the works of Daragon et al. on discrete surfaces.} }