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Brain surface conformal parameterization using Riemann surface structure

Yalin Wang Lok Ming Lui Xianfeng Gu Kiralee M Hayashi Tony F Chan Arthur W Toga Paul M Thompson Shing-Tung Yau

Computational Geometry mathscidoc:1912.43515

IEEE transactions on medical imaging, 26, (6), 853-865, 2007.5
In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable (their solutions tend to be smooth functions and the boundary conditions of the Dirichlet problem can be enforced). Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3-D brain surface manifolds to modified PDEs on a two-dimensional parameter domain. Since the Jacobian matrix of a conformal parameterization is
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@inproceedings{yalin2007brain,
  title={Brain surface conformal parameterization using Riemann surface structure},
  author={Yalin Wang, Lok Ming Lui, Xianfeng Gu, Kiralee M Hayashi, Tony F Chan, Arthur W Toga, Paul M Thompson, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203737441602079},
  booktitle={IEEE transactions on medical imaging},
  volume={26},
  number={6},
  pages={853-865},
  year={2007},
}
Yalin Wang, Lok Ming Lui, Xianfeng Gu, Kiralee M Hayashi, Tony F Chan, Arthur W Toga, Paul M Thompson, and Shing-Tung Yau. Brain surface conformal parameterization using Riemann surface structure. 2007. Vol. 26. In IEEE transactions on medical imaging. pp.853-865. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203737441602079.
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