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...
Main Authors: | , , |
---|---|
Other Authors: | , , , , , , , , |
Format: | Conference Object |
Language: | English |
Published: |
HAL CCSD
2015
|
Subjects: | |
Online Access: | https://hal.science/hal-01168723 https://hal.science/hal-01168723/document https://hal.science/hal-01168723/file/article.pdf https://doi.org/10.1007/978-3-319-18720-4_47 |
id |
ftecoleponts:oai:HAL:hal-01168723v1 |
---|---|
record_format |
openpolar |
spelling |
ftecoleponts:oai:HAL:hal-01168723v1 2024-09-15T18:13:58+00:00 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) Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout (BEZOUT) Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS) 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.science/hal-01168723 https://hal.science/hal-01168723/document https://hal.science/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.science/hal-01168723 https://hal.science/hal-01168723/document https://hal.science/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.science/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 ftecoleponts https://doi.org/10.1007/978-3-319-18720-4_47 2024-07-24T07:39:31Z 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 École des Ponts ParisTech: HAL 561 572 |
institution |
Open Polar |
collection |
École des Ponts ParisTech: HAL |
op_collection_id |
ftecoleponts |
language |
English |
topic |
[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
spellingShingle |
[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 |
topic_facet |
[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) Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout (BEZOUT) Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS) 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.science/hal-01168723 https://hal.science/hal-01168723/document https://hal.science/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.science/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.science/hal-01168723 https://hal.science/hal-01168723/document https://hal.science/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 |
container_start_page |
561 |
op_container_end_page |
572 |
_version_ |
1810451752547254272 |