Brain Surface Conformal Parameterization with Algebraic Functions

  • Yalin Wang
  • Xianfeng Gu
  • Tony F. Chan
  • Paul M. Thompson
  • Shing-Tung Yau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4191)


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 planar conformal parameterization methods, our algorithm does not introduce any singularity points. It also offers a method to explicitly match landmark curves between anatomical surfaces such as the cortex, and to compute conformal invariants for statistical comparisons of anatomy.


Conformal Invariant Cortical Surface Algebraic Function Brain Surface Central Sulcus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yalin Wang
    • 1
    • 2
  • Xianfeng Gu
    • 3
  • Tony F. Chan
    • 1
  • Paul M. Thompson
    • 2
  • Shing-Tung Yau
    • 4
  1. 1.Mathematics DepartmentUCLALos AngelesUSA
  2. 2.Lab. of Neuro ImagingUCLA School of MedicineLos AngelesUSA
  3. 3.Comp. Sci. DepartmentSUNY at Stony BrookStony BrookUSA
  4. 4.Department of MathematicsHarvard UniversityCambridgeUSA

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