Lifting Methods for Manifold-Valued Variational Problems

Thomas Vogt (), Evgeny Strekalovskiy (), Daniel Cremers () and Jan Lellmann ()
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Thomas Vogt: University of Lübeck, Institute of Mathematics and Image Computing
Evgeny Strekalovskiy: Technical University Munich
Daniel Cremers: Technical University Munich
Jan Lellmann: University of Lübeck, Institute of Mathematics and Image Computing

Chapter Chapter 3 in Handbook of Variational Methods for Nonlinear Geometric Data, 2020, pp 95-119 from Springer

Abstract: 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.

Date: 2020
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DOI: 10.1007/978-3-030-31351-7_3

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