Conformal slit mapping and its applications to brain surface parameterization.

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

Research output: Chapter in Book/Report/Conference proceedingChapter

20 Citations (Scopus)

Abstract

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. In this paper, we studied its application to brain surface parameterization. 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 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 publicationMedical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention
Pages585-593
Number of pages9
Volume11
EditionPt 1
StatePublished - 2008
Externally publishedYes

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Brain
Cerebral Cortex
Anatomy

ASJC Scopus subject areas

  • Medicine(all)

Cite this

Wang, Y., Gu, X., Chan, T. F., Thompson, P. M., & Yau, S. T. (2008). Conformal slit mapping and its applications to brain surface parameterization. In Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention (Pt 1 ed., Vol. 11, pp. 585-593)

Conformal slit mapping and its applications to brain surface parameterization. / Wang, Yalin; Gu, Xianfeng; Chan, Tony F.; Thompson, Paul M.; Yau, Shing Tung.

Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. Vol. 11 Pt 1. ed. 2008. p. 585-593.

Research output: Chapter in Book/Report/Conference proceedingChapter

Wang, Y, Gu, X, Chan, TF, Thompson, PM & Yau, ST 2008, Conformal slit mapping and its applications to brain surface parameterization. in Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. Pt 1 edn, vol. 11, pp. 585-593.
Wang Y, Gu X, Chan TF, Thompson PM, Yau ST. Conformal slit mapping and its applications to brain surface parameterization. In Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. Pt 1 ed. Vol. 11. 2008. p. 585-593
Wang, Yalin ; Gu, Xianfeng ; Chan, Tony F. ; Thompson, Paul M. ; Yau, Shing Tung. / Conformal slit mapping and its applications to brain surface parameterization. Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. Vol. 11 Pt 1. ed. 2008. pp. 585-593
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