Abstract: In recent years,the spectral clustering algorithm based on graph theory is a new tool to be applied to image segmentation．Essentially,image segmentation is to be converted into the optimization problem,and the minimum cut algorithm (Min-max cut) can fully meet the criteria of the clustering algorithm．In the process of implementation,optimization criteria into eigen system solves the problem．The implementation is computationally complex,and the required storage space and computing time complexity are increased as the image size increases．In the page,when Min-max cut algorithm is achieved,the weight matrices used in evaluating the graph cuts are based on the gray levels of an image,rather than the commonly used image pixels to determine the segmentation threshold．Experimental results show that the Min-max cut segmentation algorithm that this method achieves is simple,real-time,and has automatic segmentation and other superior segment ation performance．

Key words: Spectral clustering,Graph theory,Min-max cut algorithm,Image threshold segmentation