A splitting algorithm for image segmentation on manifolds represented by the grid based particle method

Jun Liu Shing-Yu Leung

Information Theory mathscidoc:1912.43187

Journal of Scientific Computing, 56, (2), 243-266, 2013.8
We propose a numerical approach to solve variational problems on manifolds represented by the grid based particle method (GBPM) recently developed in Leung et al. (J. Comput. Phys. 230(7):25402561, 2011), Leung and Zhao (J. Comput. Phys. 228:77067728, 2009a, J. Comput. Phys. 228:29933024, 2009b, Commun. Comput. Phys. 8:758796, 2010). In particular, we propose a splitting algorithm for image segmentation on manifolds represented by unconnected sampling particles. To develop a fast minimization algorithm, we propose a new splitting method by generalizing the augmented Lagrangian method. To efficiently implement the resulting method, we incorporate with the local polynomial approximations of the manifold in the GBPM. The resulting method is flexible for segmentation on various manifolds including closed or open or even surfaces which are not orientable.
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@inproceedings{jun2013a,
  title={A splitting algorithm for image segmentation on manifolds represented by the grid based particle method},
  author={Jun Liu, and Shing-Yu Leung},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112824443560747},
  booktitle={Journal of Scientific Computing},
  volume={56},
  number={2},
  pages={243-266},
  year={2013},
}
Jun Liu, and Shing-Yu Leung. A splitting algorithm for image segmentation on manifolds represented by the grid based particle method. 2013. Vol. 56. In Journal of Scientific Computing. pp.243-266. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112824443560747.
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