A Two-Stage Image Segmentation Method Using a Convex Variant of the Mumford-Shah Model and Thresholding

被引:155
作者
Cai, Xiaohao [1 ]
Chan, Raymond [1 ]
Zeng, Tieyong [2 ]
机构
[1] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
[2] Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China
来源
SIAM JOURNAL ON IMAGING SCIENCES | 2013年 / 6卷 / 01期
关键词
image segmentation; Mumford-Shah model; split-Bregman; total variation; APPROXIMATION; ALGORITHMS;
D O I
10.1137/120867068
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
The Mumford-Shah model is one of the most important image segmentation models and has been studied extensively in the last twenty years. In this paper, we propose a two-stage segmentation method based on the Mumford-Shah model. The first stage of our method is to find a smooth solution g to a convex variant of the Mumford-Shah model. Once g is obtained, then in the second stage the segmentation is done by thresholding g into different phases. The thresholds can be given by the users or can be obtained automatically using any clustering methods. Because of the convexity of the model, g can be solved efficiently by techniques like the split-Bregman algorithm or the Chambolle-Pock method. We prove that our method is convergent and that the solution g is always unique. In our method, there is no need to specify the number of segments K (K = 2) before finding g. We can obtain any K-phase segmentations by choosing (K-1) thresholds after g is found in the first stage, and in the second stage there is no need to recompute g if the thresholds are changed to reveal different segmentation features in the image. Experimental results show that our two-stage method performs better than many standard two-phase or multiphase segmentation methods for very general images, including antimass, tubular, MRI, noisy, and blurry images.
引用
收藏
页码:368 / 390
页数:23
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