Intrinsic brain surface conformal mapping using a variational method

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

doi:10.1117/12.534480

Intrinsic brain surface conformal mapping using a variational method

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

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

13 Scopus citations

Abstract

We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms with or without boundaries. For genus zero surfaces, our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. In this paper, we apply the algorithm to the cortical surface matching problem. We use a mesh structure to represent the brain surface. Further constraints are added to ensure that the conformal map is unique. Empirical tests on MRI data show that the mappings preserve angular relationships, are stable in MRIs acquired at different times, and are robust to differences in data triangulation, and resolution. Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility.

Original language	English (US)
Pages (from-to)	241-252
Number of pages	12
Journal	Proceedings of SPIE - The International Society for Optical Engineering
Volume	5370 I
DOIs	https://doi.org/10.1117/12.534480
State	Published - 2004
Externally published	Yes
Event	Progress in Biomedical Optics and Imaging - Medical Imaging 2004: Imaging Processing - San Diego, CA, United States Duration: Feb 16 2004 → Feb 19 2004

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Condensed Matter Physics
Computer Science Applications
Applied Mathematics
Electrical and Electronic Engineering

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@article{8cef67f3e8154dbcb40c80d10c9503ac,

title = "Intrinsic brain surface conformal mapping using a variational method",

abstract = "We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms with or without boundaries. For genus zero surfaces, our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. In this paper, we apply the algorithm to the cortical surface matching problem. We use a mesh structure to represent the brain surface. Further constraints are added to ensure that the conformal map is unique. Empirical tests on MRI data show that the mappings preserve angular relationships, are stable in MRIs acquired at different times, and are robust to differences in data triangulation, and resolution. Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility.",

author = "Yalin Wang and Xianfeng Gu and Chan, {Tony F.} and Thompson, {Paul M.} and Yau, {Shing Tung}",

year = "2004",

doi = "10.1117/12.534480",

language = "English (US)",

volume = "5370 I",

pages = "241--252",

journal = "Proceedings of SPIE - The International Society for Optical Engineering",

issn = "0277-786X",

publisher = "SPIE",

note = "Progress in Biomedical Optics and Imaging - Medical Imaging 2004: Imaging Processing ; Conference date: 16-02-2004 Through 19-02-2004",

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TY - JOUR

T1 - Intrinsic brain surface conformal mapping using a variational method

AU - Wang, Yalin

AU - Gu, Xianfeng

AU - Chan, Tony F.

AU - Thompson, Paul M.

AU - Yau, Shing Tung

PY - 2004

Y1 - 2004

N2 - We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms with or without boundaries. For genus zero surfaces, our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. In this paper, we apply the algorithm to the cortical surface matching problem. We use a mesh structure to represent the brain surface. Further constraints are added to ensure that the conformal map is unique. Empirical tests on MRI data show that the mappings preserve angular relationships, are stable in MRIs acquired at different times, and are robust to differences in data triangulation, and resolution. Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility.

AB - We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms with or without boundaries. For genus zero surfaces, our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. In this paper, we apply the algorithm to the cortical surface matching problem. We use a mesh structure to represent the brain surface. Further constraints are added to ensure that the conformal map is unique. Empirical tests on MRI data show that the mappings preserve angular relationships, are stable in MRIs acquired at different times, and are robust to differences in data triangulation, and resolution. Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility.

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U2 - 10.1117/12.534480

DO - 10.1117/12.534480

M3 - Conference article

AN - SCOPUS:5644266441

SN - 0277-786X

VL - 5370 I

SP - 241

EP - 252

JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

T2 - Progress in Biomedical Optics and Imaging - Medical Imaging 2004: Imaging Processing

Y2 - 16 February 2004 through 19 February 2004

ER -

Intrinsic brain surface conformal mapping using a variational method

Abstract

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