Total Variation Regularization for Functions with Values in a Manifold

Jan Lellmann, Evgeny Strekalovskiy, Sabrina Koetter, Daniel Cremers

Research output: Chapter in Book/Report/Conference proceedingConference contribution

57 Scopus citations


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.
Original languageEnglish (US)
Title of host publication2013 IEEE International Conference on Computer Vision
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages8
ISBN (Print)9781479928408
StatePublished - Dec 2013
Externally publishedYes


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