Parallelizable Inpainting and Refinement of Diffeomorphisms using Beltrami Holomorphic Flow

Tsz Wai Wong University of California, Los Angeles Xianfeng Gu Stony Brook University Tony F. Chan The Hong Kong University of Science and Technology Ronald Lok Ming Lui The Chinese University of Hong Kong

Computational Geometry mathscidoc:1609.09030

Proceedings of the IEEE International Conference on Computer Vision, 2383-2390, 2011
In this paper, we propose novel algorithms for inpainting and refinement of diffeomorphisms. We first represent a diffeomorphism by its Beltrami coefficient. Then it is possible to refine and inpaint the diffeomorphism by processing this Beltrami coefficient. With the inpainted/refined Beltrami coefficient, we construct a new diffeomorphism using the exact Beltrami holomorphic flow algorithm proposed in this paper. We apply our algorithms on several practical applications, which include the inpainting of a highly distorted diffeomorphism, the inpainting of image sequences of deforming shapes, the super-resolution of diffeomorphisms and the global parameterization of cortical surfaces by combining local parameterizations. Experiments show that our algorithm can solve these problems with natural and smooth results. We demonstrate how our proposed method can be widely applied in areas from texture mapping to video processing, and from computer graphics to medical imaging.
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@inproceedings{tsz2011parallelizable,
  title={Parallelizable Inpainting and Refinement of Diffeomorphisms using Beltrami Holomorphic Flow},
  author={Tsz Wai Wong, Xianfeng Gu, Tony F. Chan, and Ronald Lok Ming Lui},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160906104701501640642},
  booktitle={Proceedings of the IEEE International Conference on Computer Vision},
  pages={2383-2390},
  year={2011},
}
Tsz Wai Wong, Xianfeng Gu, Tony F. Chan, and Ronald Lok Ming Lui. Parallelizable Inpainting and Refinement of Diffeomorphisms using Beltrami Holomorphic Flow. 2011. In Proceedings of the IEEE International Conference on Computer Vision. pp.2383-2390. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160906104701501640642.
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