An algorithm for minimizing the Mumford-Shah functional

Thomas Pock, Daniel Cremers, Horst Bischof, Antonin Chambolle

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

246 Scopus citations


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.

Original languageEnglish
Title of host publication2009 IEEE 12th International Conference on Computer Vision, ICCV 2009
Number of pages8
StatePublished - 2009
Externally publishedYes
Event12th International Conference on Computer Vision, ICCV 2009 - Kyoto, Japan
Duration: 29 Sep 20092 Oct 2009

Publication series

NameProceedings of the IEEE International Conference on Computer Vision


Conference12th International Conference on Computer Vision, ICCV 2009


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