Comparison of multi-label graph cuts method and Monte Carlo simulation with block-spin transformation for the piecewise constant Mumford–Shah segmentation model

• We give a comparison of two methods for solving the Mumford–Shah segmentation model.
• We propose a hybrid method for solving the Mumford–Shah segmentation model.
• This hybrid method combines the advantages of the two methods, robustness and speed.
• We show that the hybrid method is efficient for a wide range of model parameters.

The Mumford–Shah segmentation model is an energy model widely applied in computer vision. Many attempts have been made to minimize the energy of the model. We focus on recently proposed two methods for solving multi-phase segmentation; the graph cuts method by Bae and Tai (2009) [16] and the Monte Carlo method by Watanabe et al. (2011) [21]. We compare the convergence of solutions, the values of obtained energy, the computational time, etc. Finally we propose a hybrid method combining the advantages of the Monte Carlo and the graph cuts. The hybrid method can find the global minimum energy solution efficiently without sensitivity of initial guess.