Total Variation Regularization for Functions with Values in a Manifold

Handle URI:
http://hdl.handle.net/10754/600041
Title:
Total Variation Regularization for Functions with Values in a Manifold
Authors:
Lellmann, Jan; Strekalovskiy, Evgeny; Koetter, Sabrina; Cremers, Daniel
Abstract:
While 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.
Citation:
Lellmann 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.
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
2013 IEEE International Conference on Computer Vision
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
Dec-2013
DOI:
10.1109/ICCV.2013.366
Type:
Conference Paper
Sponsors:
This 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
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Full metadata record

DC FieldValue Language
dc.contributor.authorLellmann, Janen
dc.contributor.authorStrekalovskiy, Evgenyen
dc.contributor.authorKoetter, Sabrinaen
dc.contributor.authorCremers, Danielen
dc.date.accessioned2016-02-28T06:34:53Zen
dc.date.available2016-02-28T06:34:53Zen
dc.date.issued2013-12en
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.en
dc.identifier.doi10.1109/ICCV.2013.366en
dc.identifier.urihttp://hdl.handle.net/10754/600041en
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.en
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 GrantConvexVisionen
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.subjectangular dataen
dc.subjectdenoisingen
dc.subjectmanifolden
dc.subjectrotation groupen
dc.subjecttensoren
dc.subjecttotal variationen
dc.subjectvariational methodsen
dc.titleTotal Variation Regularization for Functions with Values in a Manifolden
dc.typeConference Paperen
dc.identifier.journal2013 IEEE International Conference on Computer Visionen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
dc.contributor.institutionTechnische Universitat Munchen, Munich, Germanyen
kaust.grant.numberKUK-I1-007-43en
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