Total variation regularization for functions with values in a manifold
Lellmann J, Strekalovskiy E, Koetter S, Cremers D (2013)
Publication Type: Conference contribution
Publication year: 2013
Publisher: Institute of Electrical and Electronics Engineers Inc.
Pages Range: 2944-2951
Conference Proceedings Title: Proceedings of the IEEE International Conference on Computer Vision
Event location: AUS
ISBN: 9781479928392
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.
Involved external institutions
Germany (DE)
United Kingdom (GB)How to cite
APA:
Lellmann, J., Strekalovskiy, E., Koetter, S., & Cremers, D. (2013). Total variation regularization for functions with values in a manifold. In Proceedings of the IEEE International Conference on Computer Vision (pp. 2944-2951). AUS: Institute of Electrical and Electronics Engineers Inc..
MLA:
Lellmann, Jan, et al. "Total variation regularization for functions with values in a manifold." Proceedings of the 2013 14th IEEE International Conference on Computer Vision, ICCV 2013, AUS Institute of Electrical and Electronics Engineers Inc., 2013. 2944-2951.
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