ML Anthology

An Algorithm for Minimizing the Mumford-Shah Functional

Thomas Pock, Daniel Cremers, Horst Bischof, Antonin Chambolle
ICCV 2009 pp. 1133-1140
doi:10.1109/ICCV.2009.5459348 /iccv/2009/pock2009iccv-algorithm/

Abstract

In this work we revisit the Mumford-Shah functional, one of the most studied variational approaches to image segmentation. The contribution of this paper is to propose an algorithm which allows to minimize a convex relaxation of the Mumford-Shah functional obtained by functional lifting. The algorithm is an efficient primal-dual projection algorithm for which we prove convergence. In contrast to existing algorithms for minimizing the full Mumford-Shah this is the first one which is based on a convex relaxation. As a consequence the computed solutions are independent of the initialization. Experimental results confirm that the proposed algorithm determines smooth approximations while preserving discontinuities of the underlying signal.

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Cite

Text

Pock et al. "An Algorithm for Minimizing the Mumford-Shah Functional." IEEE/CVF International Conference on Computer Vision, 2009. doi:10.1109/ICCV.2009.5459348

Markdown

[Pock et al. "An Algorithm for Minimizing the Mumford-Shah Functional." IEEE/CVF International Conference on Computer Vision, 2009.](https://mlanthology.org/iccv/2009/pock2009iccv-algorithm/) doi:10.1109/ICCV.2009.5459348

BibTeX

@inproceedings{pock2009iccv-algorithm,
  title     = {{An Algorithm for Minimizing the Mumford-Shah Functional}},
  author    = {Pock, Thomas and Cremers, Daniel and Bischof, Horst and Chambolle, Antonin},
  booktitle = {IEEE/CVF International Conference on Computer Vision},
  year      = {2009},
  pages     = {1133-1140},
  doi       = {10.1109/ICCV.2009.5459348},
  url       = {https://mlanthology.org/iccv/2009/pock2009iccv-algorithm/}
}