Total Variation Regularization for Functions with Values in a Manifold
KAUST Grant NumberKUK-I1-007-43
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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.
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.
SponsorsThis 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