Application of Monte Carlo simulation with block-spin transformation based on the Mumford–Shah segmentation model to three-dimensional biomedical images

Abstract

In this paper, we present the iterative Monte Carlo method for solving Mumford–Shah segmentation model in the case of three-dimensional images with emphasis on multi-phase segmentation. The present method introduces iterative descent process to the preceding Monte Carlo method, proposed by our group, to improve convergence. The numerical simulations have shown that the present method overcomes the problem of the preceding Monte Carlo method that converges to local minima in some cases. The computational time of the present method can be shortened by introducing block-spin transformation procedure. We have also compared the result of the present method with the graph cuts method. The comparison has shown that the proposed method converges to almost the same solution of the graph cuts method in reasonably short time, and is superior in memory consumption, especially in the case of multi-phase segmentation. The comparison of the output pattern with the clinical experts’ annotation suggests that the Mumford–Shah segmentation model is suitable for a multi-phase image segmentation model of biomedical images. Because of the advantage of small memory consumption, the present Monte Carlo method with the block-spin transformation can be applied to a wide range of three-dimensional images. We make a remark that the block-spin transformation is also applicable to the graph cuts method, which leads to the saving of the computational time while maintaining lower-energy convergence.