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Nonlocal variational image segmentation models on graphs using the Split Bregman

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Abstract

Variational functionals such as Mumford-Shah and Chan-Vese methods have a major impact on various areas of image processing. After over 10 years of investigation, they are still in widespread use today. These formulations optimize contours by evolution through gradient descent, which is known for its overdependence on initialization and the tendency to produce undesirable local minima. In this paper, we propose an image segmentation model in a variational nonlocal means framework based on a weighted graph. The advantages of this model are twofold. First, the convexity global minimum (optimum) information is taken into account to achieve better segmentation results. Second, the proposed global convex energy functionals combine nonlocal regularization and local intensity fitting terms. The nonlocal total variational regularization term based on the graph is able to preserve the detailed structure of target objects. At the same time, the modified local binary fitting term introduced in the model as the local fitting term can efficiently deal with intensity inhomogeneity in images. Finally, we apply the Split Bregman method to minimize the proposed energy functional efficiently. The proposed model has been applied to segmentation of real medical and remote sensing images. Compared with other methods, the proposed model is superior in terms of both accuracy and efficient.

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Acknowledgments

This work was supported by the national natural science foundation of China (Grant nos. 61103130, 61271435, 61370138, U1301251); National Program on Key Basic Research Projects (973 programs) (Grant nos. 2010CB731804-1, 2011CB706901-4); Beijing Municipal Natural Science Foundation under Grant (No. 4141003); The Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions (No. IDHT20130225). The Project of Construction of Innovative Teams and Teacher Career Development for Universities and Colleges Under Beijing Municipality (no. CIT&TCD20130513).

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Authors and Affiliations

  1. University of Chinese Academy of Sciences, Beijing, 100049, China

    Ke Lu, Qian Wang, Daru Pan & Weiguo Pan

  2. Beijing Key Laboratory of Information Service Engineering, Beijing Union University, Beijing, 100101, China

    Ning He

  3. South China Normal University, Guangzhou, 510631, China

    Daru Pan

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  1. Ke Lu
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  2. Qian Wang
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Correspondence to Ke Lu.

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Lu, K., Wang, Q., He, N. et al. Nonlocal variational image segmentation models on graphs using the Split Bregman. Multimedia Systems 21, 289–299 (2015). https://doi.org/10.1007/s00530-013-0351-z

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