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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

12 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)
Title of host publication	Proceedings of SPIE - The International Society for Optical Engineering
Editors	J.M. Fitzpatrick, M. Sonka
Pages	241-252
Number of pages	12
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

Other

Other	Progress in Biomedical Optics and Imaging - Medical Imaging 2004: Imaging Processing
Country/Territory	United States
City	San Diego, CA
Period	2/16/04 → 2/19/04

ASJC Scopus subject areas

Electrical and Electronic Engineering
Condensed Matter Physics

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10.1117/12.534480

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Intrinsic brain surface conformal mapping using a variational method. / Wang, Yalin; Gu, Xianfeng; Chan, Tony F.; Thompson, Paul M.; Yau, Shing Tung.

Proceedings of SPIE - The International Society for Optical Engineering. ed. / J.M. Fitzpatrick; M. Sonka. Vol. 5370 I 2004. p. 241-252.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Wang, Y, Gu, X, Chan, TF, Thompson, PM & Yau, ST 2004, Intrinsic brain surface conformal mapping using a variational method. in JM Fitzpatrick & M Sonka (eds), Proceedings of SPIE - The International Society for Optical Engineering. vol. 5370 I, pp. 241-252, Progress in Biomedical Optics and Imaging - Medical Imaging 2004: Imaging Processing, San Diego, CA, United States, 2/16/04. https://doi.org/10.1117/12.534480

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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.",

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

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Intrinsic brain surface conformal mapping using a variational method

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