Genus zero surface conformal mapping and its application to brain surface mapping

Xianfeng Gu, Yalin Wang*, Tony F. Chan, Paul M. Thompson, Shing Tung Yau

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

465 Scopus citations


We developed a general method for global conformal parameterization based on the structure of the cohomology group of holomorphic one-forms for surfaces with or without boundaries (Gu and Yau, 2002), (Gu and Yau, 2003). For genus zero surfaces, our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. In this paper, we apply the algorithm to the cortical surface matching problem. We use a mesh structure to represent the brain surface. Further constraints are added to ensure that the conformal map is unique. Empirical tests on magnetic resonance imaging (MRI) data show that the mappings preserve angular relationships, are stable in MRIs acquired at different times, and are robust to differences in data triangulation, and resolution. Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility.

Original languageEnglish (US)
Pages (from-to)949-958
Number of pages10
JournalIEEE Transactions on Medical Imaging
Issue number8
StatePublished - Aug 2004
Externally publishedYes


  • Brain mapping
  • Conformal map
  • Landmark matching
  • Spherical harmonic transformation

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering


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