Sublabel-Accurate Discretization of Nonconvex Free-Discontinuity Problems

Thomas Mollenhoff, Daniel Cremers; Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2017, pp. 1183-1191


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.

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[pdf] [supp] [arXiv]
author = {Mollenhoff, Thomas and Cremers, Daniel},
title = {Sublabel-Accurate Discretization of Nonconvex Free-Discontinuity Problems},
booktitle = {Proceedings of the IEEE International Conference on Computer Vision (ICCV)},
month = {Oct},
year = {2017}