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 | |
| 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 | United States |
| City | San Diego, CA |
| Period | 2/16/04 → 2/19/04 |
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ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Condensed Matter Physics
Cite this
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
}
TY - GEN
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.
UR - http://www.scopus.com/inward/record.url?scp=5644266441&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=5644266441&partnerID=8YFLogxK
U2 - 10.1117/12.534480
DO - 10.1117/12.534480
M3 - Conference contribution
VL - 5370 I
SP - 241
EP - 252
BT - Proceedings of SPIE - The International Society for Optical Engineering
A2 - Fitzpatrick, J.M.
A2 - Sonka, M.
ER -