Brain surface conformal parameterization with the slit mapping

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

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

2 Scopus citations

Abstract

Brain surface conformal mapping has been studied intensively. In this paper, we propose a method that computes a conformal mapping from a multiply connected mesh to the so-called slit domain, which consists of a canonical rectangle or disk in which 3D curved landmarks on the original surfaces are mapped to concentric or parallel lines in the slit domain. After cutting along some landmark curve features on surface models of the cerebral cortex, we obtain multiple connected domains. By computing exact harmonic one-forms, closed harmonic one-forms, and holomorphic one-forms, we are able to build a circular slit mapping that conformally maps the surface to an annulus with some concentric arcs and a rectangle with some slits. The whole algorithm is based on solving linear systems so it is very stable. In the slit domain parameterization results, the feature curves are either mapped to straight lines or a concentric arcs. This representation is convenient for anatomical visualization, and may assist statistical comparisons of anatomy, surface-based registration and signal processing. Preliminary experimental results parameterizing various brain anatomical surfaces are presented.

Original languageEnglish (US)
Title of host publication2008 5th IEEE International Symposium on Biomedical Imaging
Subtitle of host publicationFrom Nano to Macro, Proceedings, ISBI
Pages448-451
Number of pages4
DOIs
StatePublished - Sep 10 2008
Externally publishedYes
Event2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI - Paris, France
Duration: May 14 2008May 17 2008

Publication series

Name2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Proceedings, ISBI

Other

Other2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI
CountryFrance
CityParis
Period5/14/085/17/08

Keywords

  • Biomedical imaging
  • Brain mapping
  • Slit mapping
  • Surface parameterization

ASJC Scopus subject areas

  • Biomedical Engineering

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  • Cite this

    Wang, Y., Gu, X., Chan, T. F., Thompson, P. M., & Yau, S. T. (2008). Brain surface conformal parameterization with the slit mapping. In 2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Proceedings, ISBI (pp. 448-451). [4541029] (2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Proceedings, ISBI). https://doi.org/10.1109/ISBI.2008.4541029