A variational shape optimization approach for image segmentation with a Mumford-Shah functional

Autores
Do?an, Günay; Morin, Pedro; Nochetto, Ricardo Horacio
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We introduce a novel computational method for a Mumford-Shah functional, which decomposes a given image into smooth regions separated by closed curves. Casting this as a shape optimization problem, we develop a gradient descent approach at the continuous level that yields nonlinear PDE flows. We propose time discretizations that linearize the problem and space discretization by continuous piecewise linear finite elements. The method incorporates topological changes, such as splitting and merging for detection of multiple objects, space-time adaptivity, and a coarse-tofine approach to process large images efficiently. We present several simulations that illustrate the performance of the method and investigate the model sensitivity to various parameters.
Fil: Do?an, Günay. University of Pennsylvania; Estados Unidos
Fil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Nochetto, Ricardo Horacio. University of Maryland; Estados Unidos
Materia
FINITE ELEMENT METHOD
IMAGE SEGMENTATION
MUMFORD-SHAH
SHAPE OPTIMIZATION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/84059
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/84059
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A variational shape optimization approach for image segmentation with a Mumford-Shah functionalDo?an, GünayMorin, PedroNochetto, Ricardo HoracioFINITE ELEMENT METHODIMAGE SEGMENTATIONMUMFORD-SHAHSHAPE OPTIMIZATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We introduce a novel computational method for a Mumford-Shah functional, which decomposes a given image into smooth regions separated by closed curves. Casting this as a shape optimization problem, we develop a gradient descent approach at the continuous level that yields nonlinear PDE flows. We propose time discretizations that linearize the problem and space discretization by continuous piecewise linear finite elements. The method incorporates topological changes, such as splitting and merging for detection of multiple objects, space-time adaptivity, and a coarse-tofine approach to process large images efficiently. We present several simulations that illustrate the performance of the method and investigate the model sensitivity to various parameters.Fil: Do?an, Günay. University of Pennsylvania; Estados UnidosFil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Nochetto, Ricardo Horacio. University of Maryland; Estados UnidosSociety for Industrial and Applied Mathematics2008-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84059Do?an, Günay; Morin, Pedro; Nochetto, Ricardo Horacio; A variational shape optimization approach for image segmentation with a Mumford-Shah functional; Society for Industrial and Applied Mathematics; SIAM Journal on Scientific Computing; 30; 6; 12-2008; 3028-30491064-8275CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1137/070692066info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:52:34Zoai:ri.conicet.gov.ar:11336/84059instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:52:34.991CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A variational shape optimization approach for image segmentation with a Mumford-Shah functional
title A variational shape optimization approach for image segmentation with a Mumford-Shah functional
spellingShingle A variational shape optimization approach for image segmentation with a Mumford-Shah functional
Do?an, Günay
FINITE ELEMENT METHOD
IMAGE SEGMENTATION
MUMFORD-SHAH
SHAPE OPTIMIZATION
title_short A variational shape optimization approach for image segmentation with a Mumford-Shah functional
title_full A variational shape optimization approach for image segmentation with a Mumford-Shah functional
title_fullStr A variational shape optimization approach for image segmentation with a Mumford-Shah functional
title_full_unstemmed A variational shape optimization approach for image segmentation with a Mumford-Shah functional
title_sort A variational shape optimization approach for image segmentation with a Mumford-Shah functional
dc.creator.none.fl_str_mv Do?an, Günay
Morin, Pedro
Nochetto, Ricardo Horacio
author Do?an, Günay
author_facet Do?an, Günay
Morin, Pedro
Nochetto, Ricardo Horacio
author_role author
author2 Morin, Pedro
Nochetto, Ricardo Horacio
author2_role author
author
dc.subject.none.fl_str_mv FINITE ELEMENT METHOD
IMAGE SEGMENTATION
MUMFORD-SHAH
SHAPE OPTIMIZATION
topic FINITE ELEMENT METHOD
IMAGE SEGMENTATION
MUMFORD-SHAH
SHAPE OPTIMIZATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We introduce a novel computational method for a Mumford-Shah functional, which decomposes a given image into smooth regions separated by closed curves. Casting this as a shape optimization problem, we develop a gradient descent approach at the continuous level that yields nonlinear PDE flows. We propose time discretizations that linearize the problem and space discretization by continuous piecewise linear finite elements. The method incorporates topological changes, such as splitting and merging for detection of multiple objects, space-time adaptivity, and a coarse-tofine approach to process large images efficiently. We present several simulations that illustrate the performance of the method and investigate the model sensitivity to various parameters.
Fil: Do?an, Günay. University of Pennsylvania; Estados Unidos
Fil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Nochetto, Ricardo Horacio. University of Maryland; Estados Unidos
description We introduce a novel computational method for a Mumford-Shah functional, which decomposes a given image into smooth regions separated by closed curves. Casting this as a shape optimization problem, we develop a gradient descent approach at the continuous level that yields nonlinear PDE flows. We propose time discretizations that linearize the problem and space discretization by continuous piecewise linear finite elements. The method incorporates topological changes, such as splitting and merging for detection of multiple objects, space-time adaptivity, and a coarse-tofine approach to process large images efficiently. We present several simulations that illustrate the performance of the method and investigate the model sensitivity to various parameters.
publishDate 2008
dc.date.none.fl_str_mv 2008-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/84059
Do?an, Günay; Morin, Pedro; Nochetto, Ricardo Horacio; A variational shape optimization approach for image segmentation with a Mumford-Shah functional; Society for Industrial and Applied Mathematics; SIAM Journal on Scientific Computing; 30; 6; 12-2008; 3028-3049
1064-8275
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84059
identifier_str_mv Do?an, Günay; Morin, Pedro; Nochetto, Ricardo Horacio; A variational shape optimization approach for image segmentation with a Mumford-Shah functional; Society for Industrial and Applied Mathematics; SIAM Journal on Scientific Computing; 30; 6; 12-2008; 3028-3049
1064-8275
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1137/070692066
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844613611926847488
score 13.070432

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