Braids of Partitions
International audience In obtaining a tractable solution to the problem of extracting a minimal partition from hierarchy or tree by dynamic programming, we introduce the braids of partition and h-increasing energies, the former extending the solution space from a hierarchy to a larger set, the latte...
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ftanrparis:oai:HAL:hal-01134114v1 2024-09-15T18:13:42+00:00 Braids of Partitions Tresses de partitions Kiran, Bangalore Ravi Serra, Jean Centre de Robotique (CAOR) Mines Paris - PSL (École nationale supérieure des mines de Paris) Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL) 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) ANR-10-BLAN-0205,KIDICO,Intégration des connaissances pour la convolution discrète, la segmentation et la reconstruction d'informations dans les images digitales(2010) Rejkavik, Iceland 2015-05-27 https://hal.science/hal-01134114 https://hal.science/hal-01134114/document https://hal.science/hal-01134114/file/Braids_ISMM2015.pdf en eng HAL CCSD hal-01134114 https://hal.science/hal-01134114 https://hal.science/hal-01134114/document https://hal.science/hal-01134114/file/Braids_ISMM2015.pdf info:eu-repo/semantics/OpenAccess International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing https://hal.science/hal-01134114 International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, May 2015, Rejkavik, Iceland Lattice Optimization Hierarchies Dynamic Programming [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] info:eu-repo/semantics/conferenceObject Conference papers 2015 ftanrparis 2024-08-28T23:59:04Z International audience In obtaining a tractable solution to the problem of extracting a minimal partition from hierarchy or tree by dynamic programming, we introduce the braids of partition and h-increasing energies, the former extending the solution space from a hierarchy to a larger set, the latter describing the family of energies, for which one can obtain the solution by a dynamic programming. We also provide the singularity condition for the existence of unique solution, leading to the definition of the energetic lattice. The paper also identifies various possible braids in literature and how this structure relaxes the segmentation problem. Conference Object Iceland Portail HAL-ANR (Agence Nationale de la Recherche) |
institution |
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collection |
Portail HAL-ANR (Agence Nationale de la Recherche) |
op_collection_id |
ftanrparis |
language |
English |
topic |
Lattice Optimization Hierarchies Dynamic Programming [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] |
spellingShingle |
Lattice Optimization Hierarchies Dynamic Programming [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Kiran, Bangalore Ravi Serra, Jean Braids of Partitions |
topic_facet |
Lattice Optimization Hierarchies Dynamic Programming [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] |
description |
International audience In obtaining a tractable solution to the problem of extracting a minimal partition from hierarchy or tree by dynamic programming, we introduce the braids of partition and h-increasing energies, the former extending the solution space from a hierarchy to a larger set, the latter describing the family of energies, for which one can obtain the solution by a dynamic programming. We also provide the singularity condition for the existence of unique solution, leading to the definition of the energetic lattice. The paper also identifies various possible braids in literature and how this structure relaxes the segmentation problem. |
author2 |
Centre de Robotique (CAOR) Mines Paris - PSL (École nationale supérieure des mines de Paris) Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL) 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) ANR-10-BLAN-0205,KIDICO,Intégration des connaissances pour la convolution discrète, la segmentation et la reconstruction d'informations dans les images digitales(2010) |
format |
Conference Object |
author |
Kiran, Bangalore Ravi Serra, Jean |
author_facet |
Kiran, Bangalore Ravi Serra, Jean |
author_sort |
Kiran, Bangalore Ravi |
title |
Braids of Partitions |
title_short |
Braids of Partitions |
title_full |
Braids of Partitions |
title_fullStr |
Braids of Partitions |
title_full_unstemmed |
Braids of Partitions |
title_sort |
braids of partitions |
publisher |
HAL CCSD |
publishDate |
2015 |
url |
https://hal.science/hal-01134114 https://hal.science/hal-01134114/document https://hal.science/hal-01134114/file/Braids_ISMM2015.pdf |
op_coverage |
Rejkavik, Iceland |
genre |
Iceland |
genre_facet |
Iceland |
op_source |
International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing https://hal.science/hal-01134114 International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, May 2015, Rejkavik, Iceland |
op_relation |
hal-01134114 https://hal.science/hal-01134114 https://hal.science/hal-01134114/document https://hal.science/hal-01134114/file/Braids_ISMM2015.pdf |
op_rights |
info:eu-repo/semantics/OpenAccess |
_version_ |
1810451453358112768 |