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 Potts 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.