Brain surface conformal parameterization with algebraic functions

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

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish (US)
Title of host publicationMedical Image Computing and Computer-Assisted Intervention, MICCAI 2006 - 9th International Conference, Proceedings
Number of pages9
ISBN (Print)354044727X, 9783540447276
StatePublished - Jan 1 2006
Externally publishedYes
Event9th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2006 - Copenhagen, Denmark
Duration: Oct 1 2006Oct 6 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4191 LNCS - II
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2006

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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