Hyperbolic harmonic mapping for surface registration

Rui Shi Wei Zeng Zhengyu Su Jian Jiang Hanna Damasio Zhonglin Lu Yalin Wang Shing-Tung Yau Xianfeng Gu

Computational Geometry mathscidoc:1912.43612

IEEE transactions on pattern analysis and machine intelligence, 39, (5), 965-980, 2016.5
Automatic computation of surface correspondence via harmonic map is an active research field in computer vision, computer graphics and computational geometry. It may help document and understand physical and biological phenomena and also has broad applications in biometrics, medical imaging and motion capture industries. Although numerous studies have been devoted to harmonic map research, limited progress has been made to compute a diffeomorphic harmonic map on general topology surfaces with landmark constraints. This work conquers this problem by changing the Riemannian metric on the target surface to a hyperbolic metric so that the harmonic mapping is guaranteed to be a diffeomorphism under landmark constraints. The computational algorithms are based on Ricci flow and nonlinear heat diffusion methods. The approach is general and robust. We employ our algorithm to study the
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@inproceedings{rui2016hyperbolic,
  title={Hyperbolic harmonic mapping for surface registration},
  author={Rui Shi, Wei Zeng, Zhengyu Su, Jian Jiang, Hanna Damasio, Zhonglin Lu, Yalin Wang, Shing-Tung Yau, and Xianfeng Gu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204426738024176},
  booktitle={IEEE transactions on pattern analysis and machine intelligence},
  volume={39},
  number={5},
  pages={965-980},
  year={2016},
}
Rui Shi, Wei Zeng, Zhengyu Su, Jian Jiang, Hanna Damasio, Zhonglin Lu, Yalin Wang, Shing-Tung Yau, and Xianfeng Gu. Hyperbolic harmonic mapping for surface registration. 2016. Vol. 39. In IEEE transactions on pattern analysis and machine intelligence. pp.965-980. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204426738024176.
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