A generic convexification and graph cut method for multiphase image segmentation

We propose a unified graph cut based global minimization method for multiphase image segmentation by convexifying the non-convex image segmentation cost functionals. As examples, we shall apply this method to the non-convex multiphase Chan-Vese (CV) model and piecewise constant level set method (PCLSM). Both continuous and discretized formulations will be treated. For the discrete models, we propose a unified graph cut algorithm to implement the CV and PCLSM models, which extends the result of Bae and Tai [1] to any phases CV model. Moreover, in the continuous case, we further improve the model to be convex without any conditions using a number of techniques that are unique to the continuous segmentation models. With the convex relaxation and the dual method, the related continuous dual model is convex and we can mathematically show that the global minimization can be achieved. The corresponding continuous max-flow algorithm is easy and stable. Experimental results show that our model is very efficient.