Lifting methods for manifold-valued variational problems

Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higherdimensional 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 sublabelaccurate lifting to manifolds.We also generalize existing methods for total variation regularization to support general convex regularization.