Generalized gradient on vector bundle – application to image denoising

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• dc.contributor.author Batard, Thomas
• dc.contributor.author Bertalmío, Marcelo
• dc.date.accessioned 2019-05-31T16:45:54Z
• dc.date.available 2019-05-31T16:45:54Z
• dc.date.issued 2013
• dc.description Comunicació presentada a: 4th International Conference, (SSVM 2013, celebrada del 2 al 6 de juny de 2013 a Leibnitz, Àustria.ca
• dc.description.abstract We introduce a gradient operator that generalizes the Euclidean and Riemannian gradients. This operator acts on sections of vector bundles and is determined by three geometric data: a Riemannian metric on the base manifold, a Riemannian metric and a covariant derivative on the vector bundle. Under the assumption that the covariant derivative is compatible with the metric of the vector bundle, we consider the problems of minimizing the L2 and L1 norms of the gradient. In the L2 case, the gradient descent for reaching the solutions is a heat equation of a differential operator of order two called connection Laplacian. We present an application to color image denoising by replacing the regularizing term in the Rudin-Osher-Fatemi (ROF) denoising model by the L1 norm of a generalized gradient associated with a well-chosen covariant derivative. Experiments are validated by computations of the PSNR and Q-index.en
• dc.format.mimetype application/pdf
• dc.identifier.citation Batard T, Bertalmío M. Generalized gradient on vector bundle – application to image denoising. In: Kuijper A, Bredies K, Pock T, Bischof H, editors. Scale space and variational methods in computer vision: 4th International Conference, (SSVM 2013); 2013 Jun 2-6; Leibnitz, Austria. Heidelberg: Springer Berlin; 2013. p. 12-23. (LNCS; no. 7893). DOI:10.1007/978-3-642-38267-3_2
• dc.identifier.doi http://dx.doi.org/10.1007/978-3-642-38267-3_2
• dc.identifier.issn 0302-9743
• dc.identifier.uri http://hdl.handle.net/10230/41681
• dc.language.iso eng
• dc.publisher Springer
• dc.relation.ispartof Kuijper A, Bredies K, Pock T, Bischof H, editors. Scale space and variational methods in computer vision: 4th International Conference, (SSVM 2013); 2013 Jun 2-6; Leibnitz, Austria. Heidelberg: Springer Berlin; 2013. p. 12-23. (LNCS; no. 7893).
• dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/306337
• dc.rights © Springer The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-38267-3_2
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Generalized gradienten
• dc.subject.keyword Riemannian manifolden
• dc.subject.keyword Vector bundleen
• dc.subject.keyword Total variationen
• dc.subject.keyword Color image denoisingen
• dc.subject.keyword Rudin-Osher-Fatemi modelen
• dc.title Generalized gradient on vector bundle – application to image denoising
• dc.type info:eu-repo/semantics/conferenceObject
• dc.type.version info:eu-repo/semantics/acceptedVersion