Brain surface conformal parameterization

Y. Wang, Xianfeng Gu, Kiralee M. Hayashi, Tony F. Chan, Paul M. Thompson, Shing Tung Yau

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

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. We can then automatically partition the surface using a critical graph that connects zero points in the conformal structure on the surface. The trajectories of iso-parametric curves canonically partition a surface into patches. Each of these patches is either a topological disk or a cylinder and can be conformally mapped to a parallelogram by integrating a holomorphic 1-form defined on the surface. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable. To illustrate the technique, we computed conformai 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 subjects, even for branching structures such as the ventricles, which are otherwise difficult to parameterize. Compared with other variational approaches based on surface inflation, our technique works on surfaces with arbitrary complexity while guaranteeing minimal distortion in the parameterization. It also generates grids on surfaces for PDE-based signal processing.

Original languageEnglish (US)
Title of host publicationProceedings of the Eighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005
EditorsM.H. Hamza
Pages76-81
Number of pages6
StatePublished - Dec 1 2005
Externally publishedYes
EventEighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005 - Honolulu, HI, United States
Duration: Aug 15 2005Aug 17 2005

Publication series

NameProceedings of the Eighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005

Other

OtherEighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005
Country/TerritoryUnited States
CityHonolulu, HI
Period8/15/058/17/05

Keywords

  • Brain mapping
  • Conforaml net
  • Critical graph
  • Riemann surface structure

ASJC Scopus subject areas

  • Engineering(all)

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