Constrained Optimization on Hierarchies and Braids of Partitions
International audience This theoretical paper provides a basis for the optimality of scale-sets by Guigues [6] and the optimal pruning of binary partition trees by Salembier-Garrido [11]. They extract constrained-optimal cuts from a hierarchy of partitions. Firstly, this paper extends their results...
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ftminesparistech:oai:HAL:hal-01134115v1 2024-06-09T07:47:09+00:00 Constrained Optimization on Hierarchies and Braids of Partitions L'optimisation contrainte sur des hiérarchies et tresses de partitions Serra, Jean Kiran, Bangalore Ravi 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) 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) 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-01134115 https://hal.science/hal-01134115/document https://hal.science/hal-01134115/file/ConstrainedOptBraids_ISMM2015.pdf en eng HAL CCSD hal-01134115 https://hal.science/hal-01134115 https://hal.science/hal-01134115/document https://hal.science/hal-01134115/file/ConstrainedOptBraids_ISMM2015.pdf info:eu-repo/semantics/OpenAccess International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing https://hal.science/hal-01134115 International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, May 2015, Rejkavik, Iceland Hierarchies Lagrange Lattice Optimization [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 ftminesparistech 2024-05-16T12:24:35Z International audience This theoretical paper provides a basis for the optimality of scale-sets by Guigues [6] and the optimal pruning of binary partition trees by Salembier-Garrido [11]. They extract constrained-optimal cuts from a hierarchy of partitions. Firstly, this paper extends their results to a larger family of partitions, namely the braid [9]. Secondly, the paper shows the dependence of valid constraint function values and multiplier values in a Lagrangian optimization framework. Lastly, but most importantly, it also proposes the energetic order and energetic lattice based solutions for the constraint optimization problem. This approach operates on a partition based constraint thus ensuring the existence of a valid multiplier and constraint value. Conference Object Iceland MINES ParisTech: Open Archive (HAL) Garrido ENVELOPE(-57.067,-57.067,-63.500,-63.500) Lagrange ENVELOPE(-62.597,-62.597,-64.529,-64.529) |
institution |
Open Polar |
collection |
MINES ParisTech: Open Archive (HAL) |
op_collection_id |
ftminesparistech |
language |
English |
topic |
Hierarchies Lagrange Lattice Optimization [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] |
spellingShingle |
Hierarchies Lagrange Lattice Optimization [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Serra, Jean Kiran, Bangalore Ravi Constrained Optimization on Hierarchies and Braids of Partitions |
topic_facet |
Hierarchies Lagrange Lattice Optimization [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] |
description |
International audience This theoretical paper provides a basis for the optimality of scale-sets by Guigues [6] and the optimal pruning of binary partition trees by Salembier-Garrido [11]. They extract constrained-optimal cuts from a hierarchy of partitions. Firstly, this paper extends their results to a larger family of partitions, namely the braid [9]. Secondly, the paper shows the dependence of valid constraint function values and multiplier values in a Lagrangian optimization framework. Lastly, but most importantly, it also proposes the energetic order and energetic lattice based solutions for the constraint optimization problem. This approach operates on a partition based constraint thus ensuring the existence of a valid multiplier and constraint value. |
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) 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) 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 |
Serra, Jean Kiran, Bangalore Ravi |
author_facet |
Serra, Jean Kiran, Bangalore Ravi |
author_sort |
Serra, Jean |
title |
Constrained Optimization on Hierarchies and Braids of Partitions |
title_short |
Constrained Optimization on Hierarchies and Braids of Partitions |
title_full |
Constrained Optimization on Hierarchies and Braids of Partitions |
title_fullStr |
Constrained Optimization on Hierarchies and Braids of Partitions |
title_full_unstemmed |
Constrained Optimization on Hierarchies and Braids of Partitions |
title_sort |
constrained optimization on hierarchies and braids of partitions |
publisher |
HAL CCSD |
publishDate |
2015 |
url |
https://hal.science/hal-01134115 https://hal.science/hal-01134115/document https://hal.science/hal-01134115/file/ConstrainedOptBraids_ISMM2015.pdf |
op_coverage |
Rejkavik, Iceland |
long_lat |
ENVELOPE(-57.067,-57.067,-63.500,-63.500) ENVELOPE(-62.597,-62.597,-64.529,-64.529) |
geographic |
Garrido Lagrange |
geographic_facet |
Garrido Lagrange |
genre |
Iceland |
genre_facet |
Iceland |
op_source |
International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing https://hal.science/hal-01134115 International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, May 2015, Rejkavik, Iceland |
op_relation |
hal-01134115 https://hal.science/hal-01134115 https://hal.science/hal-01134115/document https://hal.science/hal-01134115/file/ConstrainedOptBraids_ISMM2015.pdf |
op_rights |
info:eu-repo/semantics/OpenAccess |
_version_ |
1801378087099695104 |