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arXiv · 1908.03776

Lifting methods for manifold-valued variational problems

Thomas Vogt·Evgeny Strekalovskiy·Daniel Cremers·Jan Lellmann
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Abstract

Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higher-dimensional space. The lifted models can then be efficiently solved to a global optimum, which allows to find approximate global minimizers of the original problem. Recently, these techniques have also been applied to problems with values in a manifold. We provide a review of such methods in a refined framework based on a finite element discretization of the range, which extends the concept of sublabel-accurate lifting to manifolds. We also generalize existing methods for total variation regularization to support general convex regularization.

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Thomas Vogt, Evgeny Strekalovskiy, Daniel Cremers, Jan Lellmann. 2019-08-10. Lifting methods for manifold-valued variational problems. https://arxiv.org/abs/1908.03776

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