Abstract
Inspired by the nonlocal methods in image processing and the point integral method, we introduce a novel weighted nonlocal Laplacian method to compute a continuous interpolation function on a point cloud in high dimensional space. The numerical results in semi-supervised learning and image inpainting show that the weighted nonlocal Laplacian is a reliable and efficient interpolation method. In addition, it is fast and easy to implement.
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This research was supported by DOE-SC0013838 and NSF DMS-1118971. Zuoqiang Shi was partially supported by NSFC Grants 11371220, 11671005.
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Shi, Z., Osher, S. & Zhu, W. Weighted Nonlocal Laplacian on Interpolation from Sparse Data. J Sci Comput 73, 1164–1177 (2017). https://doi.org/10.1007/s10915-017-0421-z
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DOI: https://doi.org/10.1007/s10915-017-0421-z