Laplace-Beltrami eigenfunction expansion of cortical manifolds

Proceedings - International Symposium on Biomedical Imaging

Volumn , Issue , 2011, Pages 372-375

  Seo, Seongho ^a   Chung, Moo K ^a,b,c  

^a Seoul National University   (South Korea)

^b UNIVERSITY OF WISCONSIN SCHOOL OF MEDICINE AND PUBLIC HEALTH   (United States)

^c UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Amygdala; cortical surface; Fourier representation; Laplace Beltrami eigenfunctions; spherical harmonics

Indexed keywords

AMYGDALA; CORTICAL SURFACES; EIGEN FUNCTION; FOURIER; SPHERICAL HARMONICS;

HARMONIC ANALYSIS; LAPLACE TRANSFORMS; MEDICAL IMAGING;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 80055040667     PISSN: 19457928     EISSN: 19458452     Source Type: Conference Proceeding    
DOI: 10.1109/ISBI.2011.5872426     Document Type: Conference Paper

References (16)

1. C. Brechbühler, G. Gerig, and O. Kubler, "Parametrization of closed surfaces for 3-D shape description," Comput. Vis. Image Und., vol. 61, pp. 154-170, 1995.
2. A. Kelemen, G. Szekely, and G. Gerig, "Elastic modelbased segmentation of 3-d neuroradiological data sets," IEEE Trans. Med. Imag., vol. 18, pp. 828-839, 1999.
3. X. Gu, Y.L. Wang, T.F. Chan, T.M. Thompson, and S.T. Yau, "Genus zero surface conformal mapping and its application to brain surface mapping," IEEE Trans. Med. Imag., vol. 23, pp. 1-10, 2004.
4. L. Shen, J. Ford, F. Makedon, and A. Saykin, "A surface-based approach for classification of 3D neu-roanatomical structures," Intell. Data Anal, vol. 8, pp. 519-542, 2004.
5. M. Styner, I. Oguz, S. Xu, C. Brechbuhler, D. Pantazis, J. Levitt, M. Shenton, and G. Gerig, "Framework for the statistical shape analysis of brain structures using spharm-pdm," in Insight Journal, Special Edition on the Open Science Workshop at MICCAI, 2006, http://hdl.handle.net/1926/215.
6. M. K. Chung, K. M. Dalton, L. Shen, A. C. Evans, and R. J. Davidson, "Weighted Fourier representation and its application to quantifying the amount of gray matter," IEEE Trans. Med. Imag., vol. 26, pp. 566-581, 2007.
7. G. Gerig, M. Styner, D. Jones, D. Weinberger, and J. Lieberman, "Shape analysis of brain ventricles using spharm," in MMBIA, 2001, pp. 171-178.
8. R. A. Yotter, P. M. Thompson, I. Nenadic, and C. Gaser, "Estimating local surface complexity maps using spherical harmonic reconstructions," in MICCAI, 2010, vol. 6362 of Lecture Notes in Computer Science, pp. 169-176.
9. J.D. MacDonald, N. Kabani, D. Avis, and A.C. Evans, "Automated 3-D extraction of inner and outer surfaces of cerebral cortex from mri," NeuroImage, vol. 12, pp. 340-356, 2000.
10. M. K. Chung, A. Qiu, B. M. Nacewicz, K. M. Dalton, S. Pollak, and R. J. Davidson, "Tiling manifolds with orthonormal basis," in MICCAI Workshop on Mathematical Foundations of Computational Anatomy, 2008.
11. B. Lévy, "Laplace-Beltrami Eigenfunctions: Towards an Algorithm that Understands Geometry," in IEEE International Conference on Shape Modeling and Applications, 2006, p. 13.
12. S. Seo, M. K. Chung, and H. K. Vorperian, "Heat kernel smoothing using Laplace-Beltrami eigenfunctions," in MICCAI, 2010, vol. 6363 of Lecture Notes in Computer Science, pp. 505-512.
13. R. Courant and D. Hilbert., Methods of Mathematical Physics, Volume I., Interscience, New York, 1953.
14. A. Qiu, D. Bitouk, and M. I. Miller, "Smooth functional and structural maps on the neocortex via orthonormal bases of the Laplace-Beltrami operator," IEEE Trans. Med. Imag., vol. 25, pp. 1296-1306, 2006.
15. M. Reuter, F.-E. Wolter, M. Shenton, and M. Niethammer, "Laplace-Beltrami eigenvalues and topological features of eigenfunctions for statistical shape analysis," Computer-Aided Design, vol. 41, no. 10, pp. 739-755, 2009.
16. Y. Shi, R. Lai, J.H. Morra, I. Dinov, P.M. Thompson, and A.W. Toga, "Robust surface reconstruction via Laplace-Beltrami eigen-projection and boundary deformation," IEEE Trans. Med. Imag., vol. 29, no. 12, pp. 2009-2022, 2010.