Global minimization for the Chan-Vese model

Prof Xue-Cheng Tai, Depart of Mathematics, University of Bergen, Norway
Abstract: We propose an exact global minimization framework for the Chan-Vese model with 4 regions in a convex variational setting. A global solution is guaranteed if the data term satisfies a mild condition. Theoretical and experimental arguments are given that such a condition will hold in practice for the most commonly used type of data terms. Otherwise, a truncation scheme is proposed which tends to produce global solutions in practice, should this not be the case. We also build up a convex relaxation for Pott's model with 4 regions, which is at least as tight as the tightest existing relaxation, but significantly simpler. Algorithms are proposed which are very efficient due to the simple formulations.