While the total variation is among the most popular regularizers for variational problems, its extension to functions with values in a manifold is an open problem. We propose an algorithm based on a convex relaxation method for solving such problems for arbitrary Riemannian manifolds. The framework can be adapted to different manifolds including spheres and three-dimensional rotations, and allows to obtain more accurate solutions than labelling methods. We show several applications including variational processing of chromaticity values, normal fields, and camera trajectories.
- http://www.damtp.cam.ac.uk/user/jl707/_media/lellmann_et_al_iccv2013.pdf - Preprint
- http://www.damtp.cam.ac.uk/user/jl707/software/start - MFOPT library for solving manifold-constrained variational problems