Two-stage image segmentation based on nonconvex ℓ2−ℓp approximation and thresholding

Abstract Image segmentation is of great importance in image processing. In this paper, we propose a two-stage image segmentation strategy based on the nonconvex l 2 − l p approximation of the Mumford–Shah (MS) model, where we use the nonconvex l p ( 0 p 1 ) regularizer to approximate the Hausdorff measure and to extract more boundary information. In the first stage, we solve the nonconvex variant of the MS model efficiently via the split-Bregman algorithm. Moreover, we use a closed-form p -shrinkage operator to deal with the l p quasi-norm subproblem, which is easy to implement. The second stage is segmenting the u obtained in the first stage into different phases with thresholds determined by the K-means clustering method. We compare our method with several state-of-the-art methods both qualitatively and quantitatively to demonstrate the effectiveness and advantages of our strategy.