A Two-Stage Image Segmentation Method Using a Convex Variant of the Mumford-Shah Model and Thresholding
A Two-Stage Image Segmentation Method Using a Convex Variant of the Mumford-Shah Model and Thresholding
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DOI：
10.1137/120867068
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发表时间：
2013-01-01
影响因子：
2.1
通讯作者：
Zeng, Tieyong
中科院分区：
文献类型：
--
作者：
Cai, Xiaohao;Chan, Raymond;Zeng, Tieyong
Mumford-Shah模型是图像分割中最重要的模型之一，在过去的二十年中得到了广泛的研究。本文提出了一种基于Mumford-Shah模型的两阶段分割方法。我们的方法的第一阶段是找到一个光滑的解决方案g的Mumford-Shah模型的凸变量。一旦获得g，则在第二阶段中，通过将g阈值化为不同的相位来完成分割。阈值可以由用户给出，或者可以使用任何聚类方法自动获得。由于模型的凸性，g可以通过分裂Bregman算法或Chambolle-Pock方法等技术有效地求解。我们证明了我们的方法是收敛的，并且解g总是唯一的。在我们的方法中，在找到g之前不需要指定段的数量K（K = 2）。在第一阶段中找到g之后，我们可以通过选择（K-1）个阈值来获得任何K相分割，并且在第二阶段中，如果阈值被改变以揭示图像中的不同分割特征，则不需要重新计算g。实验结果表明，我们的两阶段的方法比许多标准的两阶段或多阶段分割方法非常一般的图像，包括反物质，管状，MRI，嘈杂，模糊的图像。
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.