Total variation for cyclic structures: Convex relaxation and efficient minimization

We introduce a novel type of total variation regularizer, TV
_S1
, for cyclic structures such as angles or hue values. The method handles the periodicity of values in a simple and consistent way and is invariant to value shifts. The regularizer is integrated in a recent functional lifting framework which allows for arbitrary nonconvex data terms. Results are superior and more natural than with the simple total variation without special care about wrapping interval end points. In addition we propose an equivalent formulation which can be minimized with the same time and memory efficiency as the standard total variation.