Weighted Nonlocal Laplacian on Interpolation from Sparse Data

Zuoqiang Shi Tsinghua University Stanley Osher University of California, Los Angeles Wei Zhu University of California, Los Angeles

Information Theory Numerical Analysis and Scientific Computing mathscidoc:1609.19002

Journal of Scientific Computing, 73, (2), 1164-1177, 2017
Inspired by the graph Laplacian and the point integral method, we introduce a novel weighted graph Laplacian method to compute a smooth interpolation function on a point cloud in high dimensional space. The numerical results in semi-supervised learning and image inpainting show that the weighted graph Laplacian is a reliable and efficient interpolation method. In addition, it is easy to implement and faster than graph Laplacian.
graph Laplacian; point cloud; weighted graph Laplacian; image inpainting
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@inproceedings{zuoqiang2017weighted,
  title={Weighted Nonlocal Laplacian on Interpolation from Sparse Data},
  author={Zuoqiang Shi, Stanley Osher, and Wei Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160902102623828209606},
  booktitle={Journal of Scientific Computing},
  volume={73},
  number={2},
  pages={1164-1177},
  year={2017},
}
Zuoqiang Shi, Stanley Osher, and Wei Zhu. Weighted Nonlocal Laplacian on Interpolation from Sparse Data. 2017. Vol. 73. In Journal of Scientific Computing. pp.1164-1177. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160902102623828209606.
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