An algorithm for minimizing the Mumford-Shah functional

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.

• Type: Journal
• Year: 2009
• Where: ICCV
• Authors: Thomas Pock, Daniel Cremers, Horst Bischof, Antonin Chambolle
• Keywords: Algorithm, Computer Vision, Convex Relaxation, ICCV 2009, Primal-dual Projection Algorithm