In this work we show how sublabel-accurate multilabeling approaches can be derived by approximating a classical label-continuous convex relaxation of nonconvex free-discontinuity problems. This insight allows to extend these sublabel-accurate approaches from total variation to general convex and nonconvex regularizations. Furthermore, it leads to a systematic approach to the discretization of continuous convex relaxations. We study the relationship to existing discretizations and to discrete-continuous MRFs. Finally, we apply the proposed approach to obtain a sublabel-accurate and convex solution to the vectorial Mumford-Shah functional and show in several experiments that it leads to more precise solutions using fewer labels.
@article{arxiv.1611.06987,
title = {Sublabel-Accurate Discretization of Nonconvex Free-Discontinuity Problems},
author = {Thomas Möllenhoff and Daniel Cremers},
journal= {arXiv preprint arXiv:1611.06987},
year = {2017}
}