Assembling a Learnable Mumford--Shah Type Model with Multigrid Technique for Image Segmentation

作     者：Meng, Junying Guo, Weihong Liu, Jun Yang, Mingrui 

作者机构：Beijing Normal Univ Sch Math Sci Lab Math & Complex Syst Minist Educ China Beijing 100875 Peoples R China Case Western Reserve Univ Dept Math Appl Math & Stat Cleveland OH 44106 USA Beijing Normal Univ Sch Math Sci Lab Math & Complex Syst Minist Educ China Beijing 100875 Peoples R China Cleveland Clin Lerner Res Inst Cleveland OH 44195 USA 

出 版 物：《SIAM JOURNAL ON IMAGING SCIENCES》 (SIAM J. Imaging Sci.)

年 卷 期：2024年第17卷第2期

页      面：1007-1039页

核心收录：

学科分类：1002[医学-临床医学] 070207[理学-光学] 07[理学] 08[工学] 0835[工学-软件工程] 0803[工学-光学工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：National Natural Science Foundation of China [12371527  42293272] 

主　　题：image segmentation deep neural network variational prior multigrid algorithm 

摘      要：The classical Mumford--Shah (MS) model has been successful in some medical image segmentation tasks, providing segmentation results with smooth boundaries of objects. However, the MS model, which operates at the pixel level of the images, faces challenges when dealing with medical images with low contrast or unclear edges. In this paper, we begin by using a feature extractor to capture high -dimensional deep features that contain more comprehensive semantic information than pixel -level data alone. Inspired by the MS model, we develop a variational model that incorporates threshold dynamics (TD) regularization for segmenting each feature. We obtain the final segmentation result for the original image by assembling segmentation results of all the features. This process results in MS-MGNet, a lightweight trainable segmentation network with a similar architecture to many encoder -decoder networks. The intermediate layers of MS-MGNet are designed by unrolling the numerical scheme based on the multigrid method for solving the variational model. We provide interpretability for the encoder -decoder architecture by elucidating the roles of each layer and offering explanations of the underlying mathematical models. By incorporating the TD regularizer, we integrate spatial priors from the variational models into the network architecture, resulting in better segmentation results with smoother edges and a certain robustness to noise. Compared to some relevant methods, experimental results on the selected data sets with low contrast or unclear edges show that the proposed method can achieve better segmentation performance with fewer parameters, even when trained on smaller data sets.