Lifting Methods for Manifold-Valued Variational Problems

Thomas Vogt, Evgeny Strekalovskiy, Daniel Cremers, Jan Lellmann


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.
Original languageEnglish
Title of host publicationHandbook of Variational Methods for Nonlinear Geometric Data
EditorsPhilipp Grohs, Martin Holler, Andreas Weinmann
Number of pages25
Place of PublicationCham
PublisherSpringer International Publishing
Publication date04.04.2020
ISBN (Print)978-3-030-31350-0
ISBN (Electronic)978-3-030-31351-7
Publication statusPublished - 04.04.2020


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