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.
|Title of host publication
|Handbook of Variational Methods for Nonlinear Geometric Data
|Philipp Grohs, Martin Holler, Andreas Weinmann
|Number of pages
|Place of Publication
|Springer International Publishing
|Published - 04.04.2020