Difference between revisions of "Publications/boutry.15.ismm"
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| address = Reykjavik, Iceland |
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| publisher = Springer |
| publisher = Springer |
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+ | | editors = J A Benediktsson, J Chanussot, L Najman, H Talbot |
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+ | | pages = 561 to 572 |
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| project = Image |
| project = Image |
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| urllrde = 201503-ISMMb |
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address = <nowiki>{</nowiki>Reykjavik, Iceland<nowiki>}</nowiki>, |
address = <nowiki>{</nowiki>Reykjavik, Iceland<nowiki>}</nowiki>, |
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publisher = <nowiki>{</nowiki>Springer<nowiki>}</nowiki>, |
publisher = <nowiki>{</nowiki>Springer<nowiki>}</nowiki>, |
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− | + | editor = <nowiki>{</nowiki>J.A. Benediktsson and J. Chanussot and L. Najman and H. |
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+ | Talbot<nowiki>}</nowiki>, |
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+ | pages = <nowiki>{</nowiki>561--572<nowiki>}</nowiki>, |
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project = <nowiki>{</nowiki>Image<nowiki>}</nowiki>, |
project = <nowiki>{</nowiki>Image<nowiki>}</nowiki>, |
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abstract = <nowiki>{</nowiki>Latecki <nowiki>{</nowiki>\it et al.<nowiki>}</nowiki> introduced the notion of 2D and 3D |
abstract = <nowiki>{</nowiki>Latecki <nowiki>{</nowiki>\it et al.<nowiki>}</nowiki> introduced the notion of 2D and 3D |
Revision as of 16:20, 18 May 2015
- Authors
- Nicolas Boutry, Thierry Géraud, Laurent Najman
- Where
- Mathematical Morphology and Its Application to Signal and Image Processing -- Proceedings of the 12th International Symposium on Mathematical Morphology (ISMM)
- Place
- Reykjavik, Iceland
- Type
- inproceedings
- Publisher
- Springer
- Keywords
- Image
- Date
- 2015-04-07
Abstract
Latecki et al. introduced the notion of 2D and 3D well-composed images, i.e., a class of images free from the ``connectivities paradox of digital topology. Unfortunately natural and synthetic images are not a priori well-composed. In this paper we extend the notion of ``digital well-composedness to nD setsinteger-valued functions (gray-level images), and interval-valued maps. We also prove that the digital well-composedness implies the equivalence of connectivities of the level set components in nD. Contrasting with a previous result stating that it is not possible to obtain a discrete nD self-dual digitally well-composed function with a local interpolation, we then propose and prove a self-dual discrete (non-local) interpolation method whose result is always a digitally well-composed function. This method is based on a sub-part of a quasi-linear algorithm that computes the morphological tree of shapes.
Documents
Bibtex (lrde.bib)
@InProceedings{ boutry.15.ismm, author = {Nicolas Boutry and Thierry G\'eraud and Laurent Najman}, title = {How to Make {$n$D} Functions Digitally Well-Composed in a Self-Dual Way}, booktitle = {Mathematical Morphology and Its Application to Signal and Image Processing -- Proceedings of the 12th International Symposium on Mathematical Morphology (ISMM)}, year = {2015}, series = {Lecture Notes in Computer Science Series}, volume = {9082}, address = {Reykjavik, Iceland}, publisher = {Springer}, editor = {J.A. Benediktsson and J. Chanussot and L. Najman and H. Talbot}, pages = {561--572}, project = {Image}, abstract = {Latecki {\it et al.} introduced the notion of 2D and 3D well-composed images, {\it i.e.}, a class of images free from the ``connectivities paradox'' of digital topology. Unfortunately natural and synthetic images are not {\it a priori} well-composed. In this paper we extend the notion of ``digital well-composedness'' to $n$D sets, integer-valued functions (gray-level images), and interval-valued maps. We also prove that the digital well-composedness implies the equivalence of connectivities of the level set components in $n$D. Contrasting with a previous result stating that it is not possible to obtain a discrete $n$D self-dual digitally well-composed function with a local interpolation, we then propose and prove a self-dual discrete (non-local) interpolation method whose result is always a digitally well-composed function. This method is based on a sub-part of a quasi-linear algorithm that computes the morphological tree of shapes.} }