Folding-Free Global Conformal Mapping for Genus-0 Surfaces by Harmonic Energy Minimization

Rongjie Lai Department of Mathematics, University of California, Irvine Zaiwen Wen Peking University Wotao Yin University of California, Los Angeles Xianfeng Gu Stony Brook University Ronald Lok Ming Lui The Chinese University of Hong Kong

Computational Geometry mathscidoc:1609.09023

Distinguished Paper Award in 2017

Journal of Scientific Computing, 58, (3), 705-725, 2014.3
Surface conformal maps between genus-0 surfaces play important roles in applied mathematics and engineering, with applications in medical image analysis and computer graphics. Previous work (Gu and Yau in Commun Inf Syst 2(2):121–146, 2002) introduces a variational approach, where global conformal parameterization of genus-0 surfaces was addressed through minimizing the harmonic energy, with two weaknesses: its gradient descent iteration is slow, and its solutions contain undesired parameterization foldings when the underlying surface has long sharp features. In this paper, we propose an algorithm that significantly accelerates the harmonic energy minimization and a method that iteratively removes foldings by taking advantages of the weighted Laplace–Beltrami eigen-projection. Experimental results show that the proposed approaches compute genus-0 surface harmonic maps much faster than the existing algorithm in Gu and Yau (Commun Inf Syst 2(2):121–146, 2002) and the new results contain no foldings.
Harmonic energy minimization, Conformal map, Optimization with orthogonality constraints, Weighted Laplace–Beltrami eigenfunctions
[ Download ] [ 2016-09-05 21:18:24 uploaded by lmlui ] [ 588 downloads ] [ 0 comments ] [ Cited by 6 ]
@inproceedings{rongjie2014folding-free,
  title={Folding-Free Global Conformal Mapping for Genus-0 Surfaces by Harmonic Energy Minimization},
  author={Rongjie Lai, Zaiwen Wen, Wotao Yin, Xianfeng Gu, and Ronald Lok Ming Lui},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160905211824364108635},
  booktitle={Journal of Scientific Computing},
  volume={58},
  number={3},
  pages={705-725},
  year={2014},
}
Rongjie Lai, Zaiwen Wen, Wotao Yin, Xianfeng Gu, and Ronald Lok Ming Lui. Folding-Free Global Conformal Mapping for Genus-0 Surfaces by Harmonic Energy Minimization. 2014. Vol. 58. In Journal of Scientific Computing. pp.705-725. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160905211824364108635.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved