An algorithm for minimizing the Mumford-Shah functional
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- 1 September 2009
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- No. 15505499,p. 1133-1140
- https://doi.org/10.1109/iccv.2009.5459348
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.Keywords
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