Brain surface conformal parameterization with algebraic functions

Yalin Wang Xianfeng Gu Tony F Chan Paul M Thompson Shing-Tung Yau

Computational Geometry mathscidoc:1912.43574

946-954, 2006.10
In medical imaging, parameterized 3D surface models are of great interest for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on algebraic functions. By solving the Yamabe equation with the Ricci flow method, we can conformally map a brain surface to a multi-hole disk. The resulting parameterizations do not have any singularities and are intrinsic and stable. To illustrate the technique, we computed parameterizations of several types of anatomical surfaces in MRI scans of the brain, including the hippocampi and the cerebral cortices with various landmark curves labeled. For the cerebral cortical surfaces, we show the parameterization results are consistent with selected landmark curves and can be matched to each other using constrained harmonic maps. Unlike previous
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@inproceedings{yalin2006brain,
  title={Brain surface conformal parameterization with algebraic functions},
  author={Yalin Wang, Xianfeng Gu, Tony F Chan, Paul M Thompson, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204144290974138},
  pages={946-954},
  year={2006},
}
Yalin Wang, Xianfeng Gu, Tony F Chan, Paul M Thompson, and Shing-Tung Yau. Brain surface conformal parameterization with algebraic functions. 2006. pp.946-954. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204144290974138.
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