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Brain surface parameterization using Riemann surface structure.

Yalin Wang1, Xianfeng Gu, Kiralee M Hayashi

  • 1Mathematics Department, UCLA, Los Angeles, CA 90095, USA. ylwang@math.ucla.edu

Medical Image Computing and Computer-Assisted Intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention
|May 12, 2006
PubMed
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This study introduces a novel method using holomorphic 1-forms for parameterizing complex anatomical surfaces. This technique offers stable, low-distortion mapping for brain structures like the cortex and ventricles.

Area of Science:

  • Computational geometry
  • Medical imaging analysis
  • Differential geometry

Background:

  • Parameterizing complex anatomical surfaces is challenging.
  • Existing methods like surface inflation struggle with intricate topologies.
  • A stable and generalizable parameterization method is needed for anatomical analysis.

Purpose of the Study:

  • To develop a general approach for parameterizing anatomical surfaces with complex topologies using holomorphic 1-forms.
  • To create intrinsic and stable surface subdivisions and parameterizations.
  • To enable statistical comparison and grid generation for neuroimaging data.

Main Methods:

  • Utilizing holomorphic 1-forms to leverage Riemann surface structures.
  • Inducing conformal structures to create curvilinear coordinate systems.

Related Experiment Videos

  • Partitioning surfaces into patches conformally mapped to parallelograms.

    • Main Results:

    • Demonstrated successful parameterization of brain anatomical surfaces (cortex, hippocampus, ventricles) from MRI scans.
    • Achieved consistent parameterizations across subjects, including challenging branching structures.
    • Showcased minimal distortion and stability compared to variational approaches.

    Conclusions:

    • The holomorphic 1-form approach provides a robust method for parameterizing complex anatomical surfaces.
    • This technique offers a stable, intrinsic, and low-distortion framework for neuroimaging analysis.
    • Enables statistical shape analysis and advanced signal processing on anatomical surfaces.