Brain surface conformal parameterization with the Ricci flow

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

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

11 Scopus citations

Abstract

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. By solving the Yamabe equation with the Ricci flow method, we can conformally parameterize a brain surface via a mapping 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 cortical surfaces in MRI scans of the brain. We also show the parameterization results are consistent with constraints imposed on the mappings of selected landmark curves, and the resulting surfaces can be matched to each other using constrained harmonic maps. Unlike previous planar conformal parameterization methods, our algorithm does not introduce any singularity points.

Original languageEnglish (US)
Title of host publication2007 4th IEEE International Symposium on Biomedical Imaging
Subtitle of host publicationFrom Nano to Macro - Proceedings
Pages1312-1315
Number of pages4
DOIs
StatePublished - Nov 27 2007
Externally publishedYes
Event2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro; ISBI'07 - Arlington, VA, United States
Duration: Apr 12 2007Apr 15 2007

Publication series

Name2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings

Other

Other2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro; ISBI'07
CountryUnited States
CityArlington, VA
Period4/12/074/15/07

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Keywords

  • Biomedical imaging
  • Brain mapping
  • Ricci flow
  • Surface parameterization

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Medicine(all)

Cite this

Wang, Y., Gu, X., Chan, T. F., Thompson, P. M., & Yau, S. T. (2007). Brain surface conformal parameterization with the Ricci flow. In 2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings (pp. 1312-1315). [4193535] (2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings). https://doi.org/10.1109/ISBI.2007.357101