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

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• dc.contributor.author Bertalmío, Marceloca
• dc.contributor.author Batard, Thomasca
• dc.date.accessioned 2017-03-21T09:26:37Z
• dc.date.available 2017-03-21T09:26:37Z
• dc.date.issued 2016
• dc.description.abstract 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.
• dc.description.sponsorship 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.
• dc.format.mimetype application/pdfca
• dc.identifier.citation Batard T, Bertamío M. A class of nonlocal variational problems on a vector bundle for color image local contrast reduction/enhancement. Geometry, Imaging and Computing. 2015;2(3):187-236. DOI: 10.4310/GIC.2015.v2.n3.a2
• dc.identifier.doi http://dx.doi.org/10.4310/GIC.2015.v2.n3.a2
• dc.identifier.uri http://hdl.handle.net/10230/28268
• dc.language.iso eng
• dc.publisher International Press of Bostonca
• dc.relation.ispartof Geometry, Imaging and Computing. 2015;2(3):187-236.
• dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/306337
• dc.relation.projectID info:eu-repo/grantAgreement/ES/3PN/TIN2012-38112
• dc.rights © International Press of Boston, Inc.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Nonlocal variational model
• dc.subject.keyword Vector bundle
• dc.subject.keyword Covariant derivative
• dc.subject.keyword Image contrast reduction/enhancement
• dc.subject.keyword Primal-dual algorithm
• dc.title A class of nonlocal variational problems on a vector bundle for color image local contrast reduction/enhancementca
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion