Low Dimensional Manifold Model for Image Processing

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

Information Theory Numerical Analysis and Scientific Computing mathscidoc:1709.19001

Distinguished Paper Award in 2018

SIAM Journal on Imaging Sciences
In this paper, we propose a novel low dimensional manifold model (LDMM) and apply it to some image processing problems. LDMM is based on the fact that the patch manifolds of many natural images have low dimensional structure. Based on this fact, the dimension of the patch manifold is used as a regularization to recover the image. The key step in LDMM is to solve a Laplace-Beltrami equation over a point cloud which is solved by the point integral method. The point integral method enforces the sample point constraints correctly and gives better results than the standard graph Laplacian. Numerical simulations in image denoising, inpainting and super-resolution problems show that LDMM is a powerful method in image processing.
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@inproceedings{stanleylow,
  title={Low Dimensional Manifold Model for Image Processing},
  author={Stanley Osher, Zuoqiang Shi, and Wei Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170925162250578360819},
  booktitle={SIAM Journal on Imaging Sciences},
}
Stanley Osher, Zuoqiang Shi, and Wei Zhu. Low Dimensional Manifold Model for Image Processing. In SIAM Journal on Imaging Sciences. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170925162250578360819.
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