Difference between revisions of "Publications/najman.13.ismm"

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(Created page with "{{Publication | date = 2013-01-01 | authors = Laurent Najman, Thierry Géraud | title = Discrete set-valued continuity and interpolation | booktitle = Mathematical Morphology ...")
 
 
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{{Publication
  
{{Publication
−
| date = 2013-01-01
 +
| published = true
  +
| date = 2013-03-14
 
| authors = Laurent Najman, Thierry Géraud
  
| authors = Laurent Najman, Thierry Géraud
 
| title = Discrete set-valued continuity and interpolation
  
| title = Discrete set-valued continuity and interpolation
−
| booktitle = Mathematical Morphology and Its Application to Signal and Image Processing -- Proceedings of the 11th International Symposium on Mathematical Morphology (ISMM)
 +
| booktitle = Mathematical Morphology and Its Application to Signal and Image Processing – Proceedings of the 11th International Symposium on Mathematical Morphology (ISMM)
 
| editors = C L Luengo Hendriks, G Borgefors, R Strand
  
| editors = C L Luengo Hendriks, G Borgefors, R Strand
 
| volume = 7883
  
| volume = 7883
 
| series = Lecture Notes in Computer Science Series
  
| series = Lecture Notes in Computer Science Series
−
| address = Heidelberg
 +
| address = Uppsala, Sweden
 
| publisher = Springer
  
| publisher = Springer
 
| pages = 37 to 48
  
| pages = 37 to 48
−
| project = Image
 +
| lrdeprojects = Olena
−
| urllrde = 201305-ISMMb
  
 
| abstract = The main question of this paper is to retrieve some continuity properties on (discrete) T0-Alexandroff spaces. One possible application, which will guide us, is the construction of the so-called "tree of shapes" (intuitively, the tree of level lines). This tree, which should allow to process maxima and minima in the same wayfaces quite a number of theoretical difficulties that we propose to solve using set-valued analysis in a purely discrete setting. We also propose a way to interpret any function defined on a grid as a "continuous" function thanks to an interpolation scheme. The continuity properties are essential to obtain a quasi-linear algorithm for computing the tree of shapes in any dimension, which is exposed in a companion paper.
  
| abstract = The main question of this paper is to retrieve some continuity properties on (discrete) T0-Alexandroff spaces. One possible application, which will guide us, is the construction of the so-called "tree of shapes" (intuitively, the tree of level lines). This tree, which should allow to process maxima and minima in the same wayfaces quite a number of theoretical difficulties that we propose to solve using set-valued analysis in a purely discrete setting. We also propose a way to interpret any function defined on a grid as a "continuous" function thanks to an interpolation scheme. The continuity properties are essential to obtain a quasi-linear algorithm for computing the tree of shapes in any dimension, which is exposed in a companion paper.
  +
| lrdekeywords = Image
  +
| lrdepaper = https://www.lrde.epita.fr/dload/papers/najman.13.ismm.pdf
  +
| lrdenewsdate = 2013-03-14
 
| type = inproceedings
  
| type = inproceedings
 
| id = najman.13.ismm
  
| id = najman.13.ismm
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Image Processing -- Proceedings of the 11th International
  
Image Processing -- Proceedings of the 11th International
 
Symposium on Mathematical Morphology (ISMM)<nowiki>}</nowiki>,
  
Symposium on Mathematical Morphology (ISMM)<nowiki>}</nowiki>,
−
year = <nowiki>{</nowiki>2013<nowiki>}</nowiki>,
 +
year = 2013,
 
editor = <nowiki>{</nowiki>C.L. Luengo Hendriks and G. Borgefors and R. Strand<nowiki>}</nowiki>,
  
editor = <nowiki>{</nowiki>C.L. Luengo Hendriks and G. Borgefors and R. Strand<nowiki>}</nowiki>,
−
volume = <nowiki>{</nowiki>7883<nowiki>}</nowiki>,
 +
volume = 7883,
 
series = <nowiki>{</nowiki>Lecture Notes in Computer Science Series<nowiki>}</nowiki>,
  
series = <nowiki>{</nowiki>Lecture Notes in Computer Science Series<nowiki>}</nowiki>,
−
address = <nowiki>{</nowiki>Heidelberg<nowiki>}</nowiki>,
 +
address = <nowiki>{</nowiki>Uppsala, Sweden<nowiki>}</nowiki>,
 
publisher = <nowiki>{</nowiki>Springer<nowiki>}</nowiki>,
  
publisher = <nowiki>{</nowiki>Springer<nowiki>}</nowiki>,
 
pages = <nowiki>{</nowiki>37--48<nowiki>}</nowiki>,
  
pages = <nowiki>{</nowiki>37--48<nowiki>}</nowiki>,
−
project = <nowiki>{</nowiki>Image<nowiki>}</nowiki>,
  
 
abstract = <nowiki>{</nowiki>The main question of this paper is to retrieve some
  
abstract = <nowiki>{</nowiki>The main question of this paper is to retrieve some
 
continuity properties on (discrete) T0-Alexandroff spaces.
  
continuity properties on (discrete) T0-Alexandroff spaces.

Latest revision as of 16:21, 5 January 2018

Authors
Laurent Najman, Thierry Géraud
Where
Mathematical Morphology and Its Application to Signal and Image Processing – Proceedings of the 11th International Symposium on Mathematical Morphology (ISMM)
Place
Uppsala, Sweden
Type
inproceedings
Publisher
Springer
Projects
Olena
Keywords
Image
Date
2013-03-14

Abstract

The main question of this paper is to retrieve some continuity properties on (discrete) T0-Alexandroff spaces. One possible application, which will guide us, is the construction of the so-called "tree of shapes" (intuitively, the tree of level lines). This tree, which should allow to process maxima and minima in the same wayfaces quite a number of theoretical difficulties that we propose to solve using set-valued analysis in a purely discrete setting. We also propose a way to interpret any function defined on a grid as a "continuous" function thanks to an interpolation scheme. The continuity properties are essential to obtain a quasi-linear algorithm for computing the tree of shapes in any dimension, which is exposed in a companion paper.

Documents

Bibtex (lrde.bib)

@InProceedings{	  najman.13.ismm,
  author	= {Laurent Najman and Thierry G\'eraud},
  title		= {Discrete set-valued continuity and interpolation},
  booktitle	= {Mathematical Morphology and Its Application to Signal and
		  Image Processing -- Proceedings of the 11th International
		  Symposium on Mathematical Morphology (ISMM)},
  year		= 2013,
  editor	= {C.L. Luengo Hendriks and G. Borgefors and R. Strand},
  volume	= 7883,
  series	= {Lecture Notes in Computer Science Series},
  address	= {Uppsala, Sweden},
  publisher	= {Springer},
  pages		= {37--48},
  abstract	= {The main question of this paper is to retrieve some
		  continuity properties on (discrete) T0-Alexandroff spaces.
		  One possible application, which will guide us, is the
		  construction of the so-called "tree of shapes"
		  (intuitively, the tree of level lines). This tree, which
		  should allow to process maxima and minima in the same way,
		  faces quite a number of theoretical difficulties that we
		  propose to solve using set-valued analysis in a purely
		  discrete setting. We also propose a way to interpret any
		  function defined on a grid as a "continuous" function
		  thanks to an interpolation scheme. The continuity
		  properties are essential to obtain a quasi-linear algorithm
		  for computing the tree of shapes in any dimension, which is
		  exposed in a companion paper.}
}





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