Adaptive total variation based image segmentation with semi-proximal alternating minimization

Abstract To improve the image segmentation quality, it is important to adequately describe the local features of targets in images. In this paper, we develop a novel adaptive total variation based two-stage segmentation approach to restore and segment images under complex degradations. To find a smooth approximation solution in the first stage, we introduce an effective regularization term that combines an adaptive weighted matrix with the gradient operator. The adaptive weighted matrix gives different penalties in the axis directions to enhance the diffusion along the tangent direction of the edge. It can filter out the details far away from the edge and preserve the main structure of targets. For the convex objective function in the first stage, a semi-proximal alternating direction method of multipliers (sPADMM) with guaranteed convergence is successfully employed. We utilize the K-means method to select thresholds automatically and complete the segmentation by thresholding the image into different regions in the second stage. Extensive experimental comparisons between our method and some state-of-the-art methods including a deep learning approach are provided. All numerical results illustrate clearly that our method has better performance for different kinds of segmentation and restoration tasks.