Relaxed Primal-Dual Algorithm for Efficient Potts-Model-Based Image Segmentation

This paper applies the original dual algorithm under the relaxed condition to the graph cut problem based on the Potts model, aiming to improve the computational efficiency of the segmentation. According to the previous research results, it is indicated that the original dual algorithm indeed performs better than the previous algorithms in seeking the optimal solution. On this basis, the method in this paper, through the original dual algorithm with relaxation steps, speeds up the search for the optimal solution of the graph cut problem based on the Potts model. We provide details such as the theoretical proof under certain conditions and the specific iterative steps when applying this algorithm in practice. At the same time, we simulate the scenarios where this method is used with different relaxation factors in image segmentation, proving the effectiveness of the relaxation steps and providing guidance for finding the maximum relaxation factor that converges in the future.