Lifting methods for manifold-valued variational problems
arXiv:1908.03776
The paper reviews and extends lifting techniques that turn difficult manifold-valued variational problems, such as segmentation and optical flow, into convex formulations that can be solved globally using finite element discretizations.
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.
In press as part of a Springer Handbook