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Brain surface conformal parameterization with the Ricci flow

Yalin Wang Jie Shi Xiaotian Yin Xianfeng Gu Tony F Chan Shing-Tung Yau Arthur W Toga Paul M Thompson

Differential Geometry mathscidoc:1912.43526

IEEE transactions on medical imaging, 31, (2), 251-264, 2011.9
In brain mapping research, parameterized 3-D surface models are of great interest for statistical comparisons of anatomy, surface-based registration, and signal processing. Here, we introduce the theories of continuous and discrete surface Ricci flow, which can create Riemannian metrics on surfaces with arbitrary topologies with user-defined Gaussian curvatures. The resulting conformal parameterizations have no singularities and they are intrinsic and stable. First, we convert a cortical surface model into a multiple boundary surface by cutting along selected anatomical landmark curves. Secondly, we conformally parameterize each cortical surface to a parameter domain with a user-designed Gaussian curvature arrangement. In the parameter domain, a shape index based on conformal invariants is computed, and inter-subject cortical surface matching is performed by solving a constrained harmonic map. We
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@inproceedings{yalin2011brain,
  title={Brain surface conformal parameterization with the Ricci flow},
  author={Yalin Wang, Jie Shi, Xiaotian Yin, Xianfeng Gu, Tony F Chan, Shing-Tung Yau, Arthur W Toga, and Paul M Thompson},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203823530499090},
  booktitle={IEEE transactions on medical imaging},
  volume={31},
  number={2},
  pages={251-264},
  year={2011},
}
Yalin Wang, Jie Shi, Xiaotian Yin, Xianfeng Gu, Tony F Chan, Shing-Tung Yau, Arthur W Toga, and Paul M Thompson. Brain surface conformal parameterization with the Ricci flow. 2011. Vol. 31. In IEEE transactions on medical imaging. pp.251-264. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203823530499090.
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