Brain surface parameterization using riemann surface structure

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

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

17 Scopus citations


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. Based on Riemann surface structure, we can then canonically partition the surface into patches. Each of these patches can be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable. To illustrate the technique, we computed conformal 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 offers a way to explicitly match landmark curves in anatomical surfaces such as the cortex, providing a surface-based framework to compare anatomy statistically and to generate grids on surfaces for PDE-based signal processing.

Original languageEnglish
Title of host publicationMedical Image Computing and Computer-Assisted Intervention - MICCAI 2005 - 8th International Conference, Proceedings
PublisherSpringer Verlag
Number of pages9
ISBN (Print)3540293264, 9783540293262
StatePublished - 2005
Externally publishedYes
Event8th International Conference on Medical Image Computing and Computer-Assisted Intervention - MICCAI 2005 - Palm Springs, CA, United States
Duration: 26 Oct 200529 Oct 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3750 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference8th International Conference on Medical Image Computing and Computer-Assisted Intervention - MICCAI 2005
Country/TerritoryUnited States
CityPalm Springs, CA


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