ML Anthology

A Convex Representation for the Vectorial Mumford-Shah Functional

Evgeny Strekalovskiy, Antonin Chambolle, Daniel Cremers
CVPR 2012 pp. 1712-1719
doi:10.1109/CVPR.2012.6247866 /cvpr/2012/strekalovskiy2012cvpr-convex/

Abstract

We propose the first tractable convex formulation of the vectorial Mumford-Shah functional which allows to compute high-quality solutions independent of the initialization. To this end, we generalize recently introduced convex formulations for scalar functionals to the vector-valued scenario in such a way that discontinuities in the different color channels preferably coincide. Furthermore, we propose an efficient solution which makes the overall optimization problem as tractable as in the scalar-valued case. Numerous experimental comparisons with the naive channel-wise approach, with the well-known Ambrosio-Tortorelli approximation, and with the classical total variation confirm the advantages of the proposed relaxation for contrast-preserving and edge-enhancing regularization.

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Cite

Text

Strekalovskiy et al. "A Convex Representation for the Vectorial Mumford-Shah Functional." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2012. doi:10.1109/CVPR.2012.6247866

Markdown

[Strekalovskiy et al. "A Convex Representation for the Vectorial Mumford-Shah Functional." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2012.](https://mlanthology.org/cvpr/2012/strekalovskiy2012cvpr-convex/) doi:10.1109/CVPR.2012.6247866

BibTeX

@inproceedings{strekalovskiy2012cvpr-convex,
  title     = {{A Convex Representation for the Vectorial Mumford-Shah Functional}},
  author    = {Strekalovskiy, Evgeny and Chambolle, Antonin and Cremers, Daniel},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {2012},
  pages     = {1712-1719},
  doi       = {10.1109/CVPR.2012.6247866},
  url       = {https://mlanthology.org/cvpr/2012/strekalovskiy2012cvpr-convex/}
}