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An algorithm for minimizing the Mumford-Shah functional
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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Cited by
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Chambolle, A., & Pock, T. (2011) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-010-0251-1 · Cited by 4,336
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Metadata
- Authors
- Pock, T., Cremers, D., Bischof, H., & Chambolle, A.
- Venue
- 2009 IEEE 12th International Conference on Computer Vision
- Publisher
- IEEE
- Published
- 2009-09
- Pages
- 1133-1140
- OpenAlex
- W2544610656
- Cited by
- 353
- References
- 0
- FWCI
- 14.18
- Type
- conference paper
- Language
- en
- Open access
- closed
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Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
