Brain surface conformal parameterization with the Ricci flow

2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings

Volumn , Issue , 2007, Pages 1312-1315

  Wang, Yalin ^a,b   Gu, Xianfeng ^c   Chan, Tony F ^a   Thompson, Paul M ^b   Yau, Shing Tung ^d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c Stony Brook University   (United States)

^d HARVARD UNIVERSITY   (United States)

Author keywords

Biomedical imaging; Brain mapping; Ricci flow; Surface parameterization

Indexed keywords

ANATOMICAL MODELING; RICCI FLOW METHOD; YAMABE EQUATION;

CONSTRAINT THEORY; MEDICAL IMAGING; PARAMETERIZATION; SIGNAL PROCESSING; STATISTICAL METHODS; THREE DIMENSIONAL;

BRAIN;

EID: 36348971646     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISBI.2007.357101     Document Type: Conference Paper

References (16)

1. P. M. Thompson. J. N. Giedd, R. P. Woods, D. Mac Donald, A. C. Evans, and A. W. Toga. "Growth patterns in the developing human brain detected using continuum-mechanical tensor mapping," Nature, vol. 404. no. 6774, pp. 190-193, March 2000.
2. S. Osher and J. A. Sethian. "Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations." J. Comput. Phys., vol. 79, pp. 12-49, 1988.
3. Y. Wang, X. Gu, K. M. Hayashi, T. F. Chan, P. M. Thompson, and S.-T. Yau. "Brain surface parameterization using Riemann surface structure." in MICCAI, Palm Springs. CA. USA. 2005, vol. II, pp. 26-29.
4. Y. Wang, X. Gu, K. M. Hayashi, T. F. Chan. P. M. Thompson, and S.-T. Yau, "Surface parameterization using Riemann surface structure," in 10th IEEE ICCV, 2005, pp. 1061-1066.
5. E.L. Schwartz. A. Shaw, and E. Wolfson. "A numerical solution to the generalized mapmaker's problem: Flattening nonconvex polyhedral surfaces," IEEE TPAMI, vol. 11, no. 9, pp. 1005-1008. Sep. 1989.
6. B. Timsari and R. M. Leahy, "An optimization method for creating semi-isometric flat maps of the cerebral cortex," in Proceedings of SPIE. Medical Imaging. San Diego. CA, Feb. 2000.
7. H. A. Drury, D. C. Van Essen, C. H. Anderson, C. W. Lee, T. A. Coogan. and J. W. Lewis. "Computerized mappings of the cerebral cortex: A multiresolution flattening method and a surface-based coordinate system," J. Cognitive Neurosciences, vol. 8, pp. 1-28, 1996.
8. M. K. Hurdal and K. Stephenson, "Cortical cartography using the discrete conformai approach of circle packings," NeuroImage, vol. 23, pp. S119-S128, 2004.
9. S. Angenent, S. Haker, A. Tannenbaum, and R. Kikinis, "Conformal geometry and brain flattening," Med. Image Comput. Comput.-Assist. Intervention, pp. 271-278, Sep. 1999.
10. X. Gu, Y. Wang, T. F. Chati, P. M. Thompson, and S.-T. Yau, "Genus zero surface conformal mapping and its application to brain surface mapping," IEEE TMI, vol. 23, no. 8, pp. 949-958, Aug. 2004.
11. L. Ju. J. Stern. K. Rehm, K. Schaper, M. K. Hurdal, and D. Rottenberg, "Cortical surface flattening using least squares conformal mapping with minimal metric distortion," in IEEE ISBI. Arlington, VA, USA. 2004. pp. 77-80.
12. A. A. Joshi, R. M. Leahy, P. M. Thompson, and D. W. Shattuck, "Cortical surface parameterization by p-harmonic energy minimization." in IEEE ISBI, Arlington, VA, USA, 2004, pp. 428-431.
13. L. Ju, M. K. Hurdal, J. Stern. K. Rehm, K. Schaper, and D. Rottenberg. "Quantitative evaluation of three surface flattening methods," NeuroImage, vol. 28, no. 4, pp. 869-880, 2005.
14. B. Fischl. M. I. Sereno, and A. M. Dale. "Cortical surface-based analysis II: Inflation, flatteningm and a surface-based coordinate system," NeuroImage, vol. 9, pp. 179-194, 1999.
15. R. Schoen and S.-T. Yau. Lectures on Differential Geometry, International Press, 1994.
16. R. S. Hamilton, "The Ricci flow on surfaces." Contemp. Math., vol. 71, pp. 237-262, 1988.