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dc.contributor.authorLellmann, Jan
dc.contributor.authorStrekalovskiy, Evgeny
dc.contributor.authorKoetter, Sabrina
dc.contributor.authorCremers, Daniel
dc.date.accessioned2016-02-28T06:34:53Z
dc.date.available2016-02-28T06:34:53Z
dc.date.issued2013-12
dc.identifier.citationLellmann J, Strekalovskiy E, Koetter S, Cremers D (2013) Total Variation Regularization for Functions with Values in a Manifold. 2013 IEEE International Conference on Computer Vision. Available: http://dx.doi.org/10.1109/ICCV.2013.366.
dc.identifier.doi10.1109/ICCV.2013.366
dc.identifier.urihttp://hdl.handle.net/10754/600041
dc.description.abstractWhile total variation is among the most popular regularizers for variational problems, its extension to functions with values in a manifold is an open problem. In this paper, we propose the first algorithm to solve such problems which applies to arbitrary Riemannian manifolds. The key idea is to reformulate the variational problem as a multilabel optimization problem with an infinite number of labels. This leads to a hard optimization problem which can be approximately solved using convex relaxation techniques. The framework can be easily adapted to different manifolds including spheres and three-dimensional rotations, and allows to obtain accurate solutions even with a relatively coarse discretization. With numerous examples we demonstrate that the proposed framework can be applied to variational models that incorporate chromaticity values, normal fields, or camera trajectories. © 2013 IEEE.
dc.description.sponsorshipThis publication is based on work sup-ported by Award No. KUK-I1-007-43, made by King Ab-dullah University of Science and Technology (KAUST),EPSRC first grant No. EP/J009539/1, Royal Society Inter-national Exchange Award No. IE110314, Leverhulme EarlyCareer Fellowship ECF-2013-436, and ERC Starting GrantConvexVision
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)
dc.subjectangular data
dc.subjectdenoising
dc.subjectmanifold
dc.subjectrotation group
dc.subjecttensor
dc.subjecttotal variation
dc.subjectvariational methods
dc.titleTotal Variation Regularization for Functions with Values in a Manifold
dc.typeConference Paper
dc.identifier.journal2013 IEEE International Conference on Computer Vision
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdom
dc.contributor.institutionTechnische Universitat Munchen, Munich, Germany
kaust.grant.numberKUK-I1-007-43


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