A class of nonlocal variational problems on a vector bundle for color image local contrast reduction/enhancement

We extend two existing variational models from the Euclidean space to a vector bundle over a Riemannian manifold. The Euclidean models, dedicated to regularize or enhance some color image features, are based on the concept of nonlocal gradient operator acting on a function of the Euclidean space. We...

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Detalles Bibliográficos
Autores: Bertalmío, Marcelo, Batard, Thomas
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10230/28268
Acceso en línea:http://hdl.handle.net/10230/28268
http://dx.doi.org/10.4310/GIC.2015.v2.n3.a2
Access Level:acceso abierto
Palabra clave:Nonlocal variational model
Vector bundle
Covariant derivative
Image contrast reduction/enhancement
Primal-dual algorithm
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spelling A class of nonlocal variational problems on a vector bundle for color image local contrast reduction/enhancementBertalmío, MarceloBatard, ThomasNonlocal variational modelVector bundleCovariant derivativeImage contrast reduction/enhancementPrimal-dual algorithmWe extend two existing variational models from the Euclidean space to a vector bundle over a Riemannian manifold. The Euclidean models, dedicated to regularize or enhance some color image features, are based on the concept of nonlocal gradient operator acting on a function of the Euclidean space. We then extend these models by generalizing this operator to a vector bundle over a Riemannian manifold with the help of the parallel transport map associated to some class of covariant derivatives. Through the dual formulations of the proposed models, we obtain the expressions of their solutions, which exhibit the functional spaces that describe the image features. Finally, for a well-chosen covariant derivative and its nonlocal extension, the proposed models perform local contrast modification (reduction or enhancement) and experiments show that they preserve more the aspect of the original image than the Euclidean models do while modifying equally its contrast.This work was supported by the European Research Council, Starting Grant ref. 306337, by the Spanish government, grant ref. TIN2012-38112, and by the Icrea Academia Award.International Press of Boston201720172016info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/28268http://dx.doi.org/10.4310/GIC.2015.v2.n3.a2reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésGeometry, Imaging and Computing. 2015;2(3):187-236.info:eu-repo/grantAgreement/EC/FP7/306337info:eu-repo/grantAgreement/ES/3PN/TIN2012-38112© International Press of Boston, Inc.info:eu-repo/semantics/openAccessoai:recercat.cat:10230/282682026-05-29T05:05:01Z
dc.title.none.fl_str_mv A class of nonlocal variational problems on a vector bundle for color image local contrast reduction/enhancement
title A class of nonlocal variational problems on a vector bundle for color image local contrast reduction/enhancement
spellingShingle A class of nonlocal variational problems on a vector bundle for color image local contrast reduction/enhancement
Bertalmío, Marcelo
Nonlocal variational model
Vector bundle
Covariant derivative
Image contrast reduction/enhancement
Primal-dual algorithm
title_short A class of nonlocal variational problems on a vector bundle for color image local contrast reduction/enhancement
title_full A class of nonlocal variational problems on a vector bundle for color image local contrast reduction/enhancement
title_fullStr A class of nonlocal variational problems on a vector bundle for color image local contrast reduction/enhancement
title_full_unstemmed A class of nonlocal variational problems on a vector bundle for color image local contrast reduction/enhancement
title_sort A class of nonlocal variational problems on a vector bundle for color image local contrast reduction/enhancement
dc.creator.none.fl_str_mv Bertalmío, Marcelo
Batard, Thomas
author Bertalmío, Marcelo
author_facet Bertalmío, Marcelo
Batard, Thomas
author_role author
author2 Batard, Thomas
author2_role author
dc.subject.none.fl_str_mv Nonlocal variational model
Vector bundle
Covariant derivative
Image contrast reduction/enhancement
Primal-dual algorithm
topic Nonlocal variational model
Vector bundle
Covariant derivative
Image contrast reduction/enhancement
Primal-dual algorithm
description We extend two existing variational models from the Euclidean space to a vector bundle over a Riemannian manifold. The Euclidean models, dedicated to regularize or enhance some color image features, are based on the concept of nonlocal gradient operator acting on a function of the Euclidean space. We then extend these models by generalizing this operator to a vector bundle over a Riemannian manifold with the help of the parallel transport map associated to some class of covariant derivatives. Through the dual formulations of the proposed models, we obtain the expressions of their solutions, which exhibit the functional spaces that describe the image features. Finally, for a well-chosen covariant derivative and its nonlocal extension, the proposed models perform local contrast modification (reduction or enhancement) and experiments show that they preserve more the aspect of the original image than the Euclidean models do while modifying equally its contrast.
publishDate 2016
dc.date.none.fl_str_mv 2016
2017
2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10230/28268
http://dx.doi.org/10.4310/GIC.2015.v2.n3.a2
url http://hdl.handle.net/10230/28268
http://dx.doi.org/10.4310/GIC.2015.v2.n3.a2
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Geometry, Imaging and Computing. 2015;2(3):187-236.
info:eu-repo/grantAgreement/EC/FP7/306337
info:eu-repo/grantAgreement/ES/3PN/TIN2012-38112
dc.rights.none.fl_str_mv © International Press of Boston, Inc.
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © International Press of Boston, Inc.
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv International Press of Boston
publisher.none.fl_str_mv International Press of Boston
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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