How to Make nD Functions Digitally Well-Composed in a Self-dual Way
International audience 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...
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ftccsdartic:oai:HAL:hal-01168723v1 2023-05-15T16:49:56+02:00 How to Make nD Functions Digitally Well-Composed in a Self-dual Way Boutry, Nicolas Géraud, Thierry Najman, Laurent Laboratoire d'Informatique Gaspard-Monge (LIGM) Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM) Laboratoire de Recherche et de Développement de l'EPITA (LRDE) Ecole Pour l'Informatique et les Techniques Avancées (EPITA) Benediktsson, J.A. Chanussot, J. Najman, L. Talbot, H. Reykjavik, Iceland 2015-05-27 https://hal.archives-ouvertes.fr/hal-01168723 https://hal.archives-ouvertes.fr/hal-01168723/document https://hal.archives-ouvertes.fr/hal-01168723/file/article.pdf https://doi.org/10.1007/978-3-319-18720-4_47 en eng HAL CCSD info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-18720-4_47 hal-01168723 https://hal.archives-ouvertes.fr/hal-01168723 https://hal.archives-ouvertes.fr/hal-01168723/document https://hal.archives-ouvertes.fr/hal-01168723/file/article.pdf doi:10.1007/978-3-319-18720-4_47 info:eu-repo/semantics/OpenAccess Mathematical Morphology and Its Applications to Signal and Image Processing https://hal.archives-ouvertes.fr/hal-01168723 Mathematical Morphology and Its Applications to Signal and Image Processing, Benediktsson, J.A.; Chanussot, J.; Najman, L.; Talbot, H., May 2015, Reykjavik, Iceland. pp.561-572, ⟨10.1007/978-3-319-18720-4_47⟩ http://www.springer.com/fr/book/9783319187198 [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] info:eu-repo/semantics/conferenceObject Conference papers 2015 ftccsdartic https://doi.org/10.1007/978-3-319-18720-4_47 2021-10-24T11:52:31Z International audience 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 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 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. Conference Object Iceland Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) 561 572 |
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Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
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English |
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[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
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[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] Boutry, Nicolas Géraud, Thierry Najman, Laurent How to Make nD Functions Digitally Well-Composed in a Self-dual Way |
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[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
description |
International audience 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 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 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. |
author2 |
Laboratoire d'Informatique Gaspard-Monge (LIGM) Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM) Laboratoire de Recherche et de Développement de l'EPITA (LRDE) Ecole Pour l'Informatique et les Techniques Avancées (EPITA) Benediktsson, J.A. Chanussot, J. Najman, L. Talbot, H. |
format |
Conference Object |
author |
Boutry, Nicolas Géraud, Thierry Najman, Laurent |
author_facet |
Boutry, Nicolas Géraud, Thierry Najman, Laurent |
author_sort |
Boutry, Nicolas |
title |
How to Make nD Functions Digitally Well-Composed in a Self-dual Way |
title_short |
How to Make nD Functions Digitally Well-Composed in a Self-dual Way |
title_full |
How to Make nD Functions Digitally Well-Composed in a Self-dual Way |
title_fullStr |
How to Make nD Functions Digitally Well-Composed in a Self-dual Way |
title_full_unstemmed |
How to Make nD Functions Digitally Well-Composed in a Self-dual Way |
title_sort |
how to make nd functions digitally well-composed in a self-dual way |
publisher |
HAL CCSD |
publishDate |
2015 |
url |
https://hal.archives-ouvertes.fr/hal-01168723 https://hal.archives-ouvertes.fr/hal-01168723/document https://hal.archives-ouvertes.fr/hal-01168723/file/article.pdf https://doi.org/10.1007/978-3-319-18720-4_47 |
op_coverage |
Reykjavik, Iceland |
genre |
Iceland |
genre_facet |
Iceland |
op_source |
Mathematical Morphology and Its Applications to Signal and Image Processing https://hal.archives-ouvertes.fr/hal-01168723 Mathematical Morphology and Its Applications to Signal and Image Processing, Benediktsson, J.A.; Chanussot, J.; Najman, L.; Talbot, H., May 2015, Reykjavik, Iceland. pp.561-572, ⟨10.1007/978-3-319-18720-4_47⟩ http://www.springer.com/fr/book/9783319187198 |
op_relation |
info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-18720-4_47 hal-01168723 https://hal.archives-ouvertes.fr/hal-01168723 https://hal.archives-ouvertes.fr/hal-01168723/document https://hal.archives-ouvertes.fr/hal-01168723/file/article.pdf doi:10.1007/978-3-319-18720-4_47 |
op_rights |
info:eu-repo/semantics/OpenAccess |
op_doi |
https://doi.org/10.1007/978-3-319-18720-4_47 |
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561 |
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