On covariant derivatives and their applications to image regularization

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• dc.contributor.author Batard, Thomasca
• dc.contributor.author Bertalmío, Marceloca
• dc.date.accessioned 2016-06-10T08:50:32Z
• dc.date.available 2016-06-10T08:50:32Z
• dc.date.issued 2014ca
• dc.description.abstract We present a generalization of the Euclidean and Riemannian gradient operators to a vector bundle, a geometric structure generalizing the concept of manifold. One of the key ideas is to replace the standard differentiation of a function by the covariant differentiation of a section. Dealing with covariant derivatives satisfying the property of compatibility with vector bundle metrics, we construct generalizations of existing mathematical models for image regularization that involve the Euclidean gradient operator, namely the linear scale-space and the Rudin-Osher-Fatemi denoising model. For well-chosen covariant derivatives, we show that our denoising model outperforms stateof-the-art variational denoising methods of the same type both in terms of PSNR and Q-index [45].
• dc.description.sponsorship This work was supported by European Research Council, Starting Grant ref. 306337.
• dc.format.mimetype application/pdfca
• dc.identifier.citation Batard T, Bertalmío M. On covariant derivatives and their applications to image regularization. SIAM J Imaging Sci. 2014;7(4):2393-422. DOI: 10.1137/140954039ca
• dc.identifier.doi http://dx.doi.org/10.1137/140954039
• dc.identifier.issn 1936-4954ca
• dc.identifier.uri http://hdl.handle.net/10230/26897
• dc.language.iso engca
• dc.publisher SIAM (Society for Industrial and Applied Mathematics)ca
• dc.relation.ispartof SIAM Journal on Imaging Sciences. 2014;7(4):2393-422.
• dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/306337ca
• dc.rights © Society for Industrial and Applied Mathematicsca
• dc.rights.accessRights info:eu-repo/semantics/openAccessca
• dc.subject.keyword Denoising
• dc.subject.keyword Total variation
• dc.subject.keyword Scale-space
• dc.subject.keyword Generalized Laplacian
• dc.subject.keyword Riemannian manifold
• dc.subject.keyword Vector bundle
• dc.title On covariant derivatives and their applications to image regularizationca
• dc.type info:eu-repo/semantics/articleca
• dc.type.version info:eu-repo/semantics/acceptedVersionca