  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.
