A variational formulation for physical noised image segmentation

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• 作者：Qiong Lou (1)
  Jia-lin Peng (2)
  De-xing Kong (3)
  
  1. Center of Mathematical Sciences ; Zhejiang University ; Hangzhou ; 310027 ; China
  2. The School of Computer Science and Technology ; Huaqiao University ; Xiamen ; 361021 ; China
  3. Department of Mathematics ; Zhejiang University ; Hangzhou ; 310027 ; China
  
• 关键词：65K10 ; 68U10 ; 49M30 ; image segmentation ; variational method ; image denoising ; primal ; dual hybrid gradient algorithm ; non ; Gaussian noise
• 刊名：Applied Mathematics - A Journal of Chinese Universities
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：30
• 期：1
• 页码：77-92
• 全文大小：1,385 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Applications of Mathematics
  Chinese Library of Science
  
• 出版者：Editorial Committee of Applied Mathematics - A Journal of Chinese Universities
• ISSN：1993-0445

文摘

Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others, these results show that our proposed model and algorithms are effective.