Sublabel-Accurate Discretization of Nonconvex Free-Discontinuity Problems
Abstract
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.
Cite
Text
Mollenhoff and Cremers. "Sublabel-Accurate Discretization of Nonconvex Free-Discontinuity Problems." International Conference on Computer Vision, 2017. doi:10.1109/ICCV.2017.134Markdown
[Mollenhoff and Cremers. "Sublabel-Accurate Discretization of Nonconvex Free-Discontinuity Problems." International Conference on Computer Vision, 2017.](https://mlanthology.org/iccv/2017/mollenhoff2017iccv-sublabelaccurate/) doi:10.1109/ICCV.2017.134BibTeX
@inproceedings{mollenhoff2017iccv-sublabelaccurate,
title = {{Sublabel-Accurate Discretization of Nonconvex Free-Discontinuity Problems}},
author = {Mollenhoff, Thomas and Cremers, Daniel},
booktitle = {International Conference on Computer Vision},
year = {2017},
doi = {10.1109/ICCV.2017.134},
url = {https://mlanthology.org/iccv/2017/mollenhoff2017iccv-sublabelaccurate/}
}