(untitled) (Advances in Applied Mathematics and Mechanics, 2022)
Image segmentation is a significant problem in image processing. In this paper, we propose a new two-stage scheme for segmentation based on the Fischer-Burmeister total variation (FBTV). The first stage of our method is to calculate a smooth solution from the FBTV Mumford-Shah model. Furthermore, we design a new difference of convex algorithm (DCA) with the semi-proximal alternating direction method of multipliers (sPADMM) iteration. In the second stage, we make use of the smooth solution and the K-means method to obtain the segmentation result. To simulate images more accurately, a useful operator is introduced, which enables the proposed model to segment not only the noisy or blurry images but the images with missing pixels well. Experiments demonstrate the proposed method produces more preferable results comparing with some state-of-the-art methods, especially on the images with missing pixels.