TY - JOUR T1 - Non-Convex and Convex Coupling Image Segmentation via TGpV Regularization and Thresholding AU - Wu , Tingting AU - Shao , Jinbo JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 849 EP - 878 PY - 2020 DA - 2020/04 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0199 UR - https://global-sci.org/intro/article_detail/aamm/16427.html KW - Two-stage strategy, non-convex and convex coupling, total generalized $p$-variation (TGpV), alternating direction method of multipliers (ADMM), clustering methods. AB -

In this paper, we propose a non-convex and convex coupling variational model for image segmentation. We design the non-convex and convex regularization terms based on total generalized p-variation (TGpV) regularizer to preserve the boundary of segmented parts and detect the structure in the image. Our method has two stages. The first stage is to approximate the Mumford-Shah model. The second stage is to segment the smoothed $u$ into different phases by using a thresholding strategy. We develop a scheme based on the alternating direction method of multipliers (ADMM) algorithm,  generalized $p$-shrinkage operation and K-means clustering method to carry out our method. We perform numerical experiments on many kinds of images such as real Bacteria image, Tubular magnetic resonance angiography (MRA) image, magnetic resonance (MR) images, anti-mass images, artificial images, noisy or blurred images. Some comparisons are arranged to show the effectiveness and advantages of our method.