Brain surface conformal parameterization with algebraic functions.

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

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 ... International Conference on Medical Image Computing and Computer-Assisted Intervention
Pages946-954
Number of pages9
Volume9
EditionPt 2
StatePublished - 2006
Externally publishedYes

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Brain
Anatomy
Diagnostic Imaging
Cerebral Cortex
Hippocampus
Magnetic Resonance Imaging

ASJC Scopus subject areas

  • Medicine(all)

Cite this

Wang, Y., Gu, X., Chan, T. F., Thompson, P. M., & Yau, S. T. (2006). Brain surface conformal parameterization with algebraic functions. In Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention (Pt 2 ed., Vol. 9, pp. 946-954)

Brain surface conformal parameterization with algebraic functions. / 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. 9 Pt 2. ed. 2006. p. 946-954.

Research output: Chapter in Book/Report/Conference proceedingChapter

Wang, Y, Gu, X, Chan, TF, Thompson, PM & Yau, ST 2006, Brain surface conformal parameterization with algebraic functions. in Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. Pt 2 edn, vol. 9, pp. 946-954.
Wang Y, Gu X, Chan TF, Thompson PM, Yau ST. Brain surface conformal parameterization with algebraic functions. In Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. Pt 2 ed. Vol. 9. 2006. p. 946-954
Wang, Yalin ; Gu, Xianfeng ; Chan, Tony F. ; Thompson, Paul M. ; Yau, Shing Tung. / Brain surface conformal parameterization with algebraic functions. Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. Vol. 9 Pt 2. ed. 2006. pp. 946-954
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