Difference between revisions of "Publications/boutry.15.ismm"
From LRDE
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| pages = 561 to 572 |
| pages = 561 to 572 |
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| lrdeprojects = Olena |
| lrdeprojects = Olena |
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− | | 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 |
+ | | 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 <math>n</math>D 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 <math>n</math>D. Contrasting with a previous result stating that it is not possible to obtain a discrete <math>n</math>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. |
| lrdepaper = http://www.lrde.epita.fr/dload/papers/boutry.15.ismm.pdf |
| lrdepaper = http://www.lrde.epita.fr/dload/papers/boutry.15.ismm.pdf |
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| lrdekeywords = Image |
| lrdekeywords = Image |
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| type = inproceedings |
| type = inproceedings |
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| id = boutry.15.ismm |
| id = boutry.15.ismm |
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+ | | identifier = doi:10.1007/978-3-319-18720-4_47 |
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| bibtex = |
| bibtex = |
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@InProceedings<nowiki>{</nowiki> boutry.15.ismm, |
@InProceedings<nowiki>{</nowiki> boutry.15.ismm, |
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Symposium on Mathematical Morphology (ISMM)<nowiki>}</nowiki>, |
Symposium on Mathematical Morphology (ISMM)<nowiki>}</nowiki>, |
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year = <nowiki>{</nowiki>2015<nowiki>}</nowiki>, |
year = <nowiki>{</nowiki>2015<nowiki>}</nowiki>, |
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+ | month = may, |
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series = <nowiki>{</nowiki>Lecture Notes in Computer Science Series<nowiki>}</nowiki>, |
series = <nowiki>{</nowiki>Lecture Notes in Computer Science Series<nowiki>}</nowiki>, |
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volume = <nowiki>{</nowiki>9082<nowiki>}</nowiki>, |
volume = <nowiki>{</nowiki>9082<nowiki>}</nowiki>, |
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Talbot<nowiki>}</nowiki>, |
Talbot<nowiki>}</nowiki>, |
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pages = <nowiki>{</nowiki>561--572<nowiki>}</nowiki>, |
pages = <nowiki>{</nowiki>561--572<nowiki>}</nowiki>, |
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+ | doi = <nowiki>{</nowiki>10.1007/978-3-319-18720-4_47<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 |
||
well-composed images, <nowiki>{</nowiki>\it i.e.<nowiki>}</nowiki>, a class of images free |
well-composed images, <nowiki>{</nowiki>\it i.e.<nowiki>}</nowiki>, a class of images free |
Latest revision as of 19:06, 7 April 2023
- 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
- Projects
- Olena
- 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 D 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 D. Contrasting with a previous result stating that it is not possible to obtain a discrete 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.
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}, month = may, 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}, doi = {10.1007/978-3-319-18720-4_47}, 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.} }