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Brain surface parameterization using riemann surface structure

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

Computational Geometry mathscidoc:1912.43567

657-665, 2005.10
We develop a general approach that uses holomorphic 1-forms to parameterize anatomical surfaces with complex (possibly branching) topology. Rather than evolve the surface geometry to a plane or sphere, we instead use the fact that all orientable surfaces are Riemann surfaces and admit conformal structures, which induce special curvilinear coordinate systems on the surfaces. Based on Riemann surface structure, we can then canonically partition the surface into patches. Each of these patches can be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable. To illustrate the technique, we computed conformal structures for several types of anatomical surfaces in MRI scans of the brain, including the cortex, hippocampus, and lateral ventricles. We found that the resulting parameterizations were consistent across
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@inproceedings{yalin2005brain,
  title={Brain surface parameterization using riemann surface structure},
  author={Yalin Wang, Xianfeng Gu, Kiralee M Hayashi, Tony F Chan, Paul M Thompson, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204107344271131},
  pages={657-665},
  year={2005},
}
Yalin Wang, Xianfeng Gu, Kiralee M Hayashi, Tony F Chan, Paul M Thompson, and Shing-Tung Yau. Brain surface parameterization using riemann surface structure. 2005. pp.657-665. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204107344271131.
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