A new continuous max-flow algorithm for multiphase image segmentation using super-level set functions

•New graph construction for multiphase segmentation according to the super level set representation.•Continuous max-flow algorithm overcomes some drawbacks of the discrete graph cut method.•Mathematical analysis for the proposed algorithms.

We propose a graph cut based global minimization method for image segmentation by representing the segmentation label function with a series of nested binary super-level set functions. This representation enables us to use K-1K-1 binary functions to partition any images into K phases. Both continuous and discretized formulations will be treated. For the discrete model, we propose a new graph cut algorithm which is faster than the existing graph cut methods to obtain the exact global solution. In the continuous case, we further improve the segmentation accuracy 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 algorithms are easy and stable. Experimental results show that our model is very competitive to some existing methods.