Encoding cortical surface by spherical harmonics

Statistica Sinica

Volumn 18, Issue 4, 2008, Pages 1269-1291

  Chung, Moo K ^a,c   Hartley, Richard ^b   Dalton, Kim M ^a,d   Davidson, Richard J ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

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

^d UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Asymmetry analysis; Cortical surface; Diffusion; Heat kernel; Spherical harmonics

Indexed keywords

EID: 60349116853     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (42)

1. Andrade, A., Kherif, F., Mangin, J., Worsley, K., Paradis, A., Simon, O., Dehaene, S., Le Bihan, D. and Poline, J.-B. (2001). Detection of fmri activation using cortical surface mapping. Human Brain Mapping 12, 79-93.
2. Ashburner, J. and Friston, K. (2000). Voxel-based morphometry - the methods. NeuroImage 11, 805-821.
3. Barrick, T., Mackay, C., Prima, S., maes, F., Vandermeulen, D., Crow, T. and Roberts, N. (2005). Automatic analysis of cerebral asymmetry: an exploratory study of the relationship between brain torgue and planum temporale asymmetry. NeuroImage 24, 678-691.
4. Barta, P., Miller, M. and Qiu, A. (2005). A stochastic model for studying the laminar structure of cortex from mri. IEEE Trans. Medical Imaging 24, 728-742.
5. Bernal-Rusiel, J., Atienza, M. and Centero, J. (2008). Detection of focal changes in human cortical thickness: Spherical wavelets versus gaussian smoothing. NeuroImage 41, 1278-1292.
6. Cachia, A., Mangin, J.-F., Riviere, D., Kherif, F., Boddaert, N., Andrade, A., Papadopoulos- Orfanos, D., Poline, J.-B., Bloch, I., Zilbovicius, M., Sonigo, P., Brunelle, F. and Regis, J. (2003). A primal sketch of the cortex mean curvature: a morphogenesis based approach to study the variability of the folding patterns. IEEE Transactions on Medical Imaging 22, 754-765.
7. Chaudhuri, P. and Marron, J. S. (2000). Scale space view of curve estimation. The Annals of Statistics 28, 408-428.
8. Chung, M., Dalton, K. M., L. S., Evans, A. and Davidson, R. (2007). Weighted fourier representation and its application to quantifying the amount of gray matter. IEEE Trans. Medical Imaging 26, 566-581.
9. Chung, M., Robbins, S., Dalton, K.M., D. R. A. A. and Evans, A. (2005). Cortical thickness analysis in autism with heat kernel smoothing. NeuroImage 25, 1256-1265.
10. Chung, M., Worsley, K., Robbins, S., Paus, T., Taylor, J., Giedd, J., Rapoport, J. and Evans, A. (2003). Deformation-based surface morphometry applied to gray matter deformation. Neurolmage 18, 198-213.
11. Collins, D., Neelin, P., Peters, T. and Evans, A. (1994). Automatic 3d intersubject registration of mr volumetric data in standardized Talairach space. J. Comput. Assisted Tomogr. 18, 192-205.
12. Courant, R. and Hilbert, D. (1953). Methods of Mathematical Physics: Volume II. Interscience, New York, english edition.
13. Dalton, K., Nacewicz, B., Johnstone, T., Schaefer, H., Gernsbacher, M., Goldsmith, H., Alexander, A. and Davidson, R. (2005). Gaze fixation and the neural circuitry of face processing in autism. Nature Neuroscience 8, 519-526.
14. Davatzikos, C. (1997). Spatial transformation and registration of brain images using elastically deformable models. Comput. Vis. Image Underst. 66, 207-222.
15. Davatzikos, C. and Bryan, R. (1995). Using a deformable surface model to obtain a shape representation of the cortex. Proceedings of the IEEE International Conference on Computer Vision 9, 2122-2127.
16. Fischl, B., Sereno, M., Tootell, R. and Dale, A. (1999). High-resolution intersubject averaging and a coordinate system for the cortical surface. Hum. Brain Mapping 8, 272-284.
17. Gaser, C., Luders, E., Thompson, P., Lee, A., Dutton, R., Geaga, J., Hayashi, K., Bellugi, U., Galaburda, A., Korenberg, J., Mills, D., Toga, A. and Reiss, A. (2006). Increased local gyrification mapped in Williams syndrome. Neurolmage 33, 46-54.
18. Gelb, A. (1997). The resolution of the Gibbs phenomenon for spherical harmonics. Math. Comp. 66, 699-717.
19. Gerig, G., Styner, M., Jones, D., Weinberger, D. and Lieberman, J. (2001). Shape analysis of brain ventricles using spharm. In MMBIA, 171-178.
20. Gu, X., Wang, Y., Chan, T., Thompson, T. and Yau, S. (2004). Genus zero surface conformal mapping and its application to brain surface mapping. IEEE Trans. Medical Imaging 23, 1-10.
21. Hagler Jr., D. J., S. A. S. M. (2006). Smoothing and cluster thresholding for cortical surfacebased group analysis of fmri data. Neurolmage 33, 1093-1103.
22. Han, J., Kim, J., Chung, C. and Park, K. (2007). Evaluation of smoothing in an iterative lp-norm minimization algorithm for surface-based source localization of meg. Physics in Medicine and Biology 52, 4791-4803.
23. Jo, H., Lee, J.-M., Kim, J.-H., Shin, Y.-W., Kim, I.-Y., Kwon, J. and Kim, S. (2007). Spatial accuracy of fmri activation influenced by volume- and surface-based spatial smoothing techniques. Neurolmage 34, 550-564.
24. Kennedy, D., O'Craven, K., Ticho, B., Goldstein, A., Makris, N. and Henson, J. (1999). Structural and functional brain asymmetries in human situs inversus totalis. Neurology 53, 1260-1265.
25. Kollakian, K. (1996). Performance analysis of automatic techniques for tissue classification in magnetic resonance images of the human brain. Technical Report Master's thesis, Concordia University, Montreal, Quebec, Canada.
26. Luders, E., Thompson, P.M., Narr, K., Toga, A., Jancke, L. and Gaser, C. (2006). A curvaturebased approach to estimate local gyrification on the cortical surface. Neurolmage 29, 1224-1230.
27. MacDonald, J., Kabani, N., Avis, D. and Evans, A. (2000). Automated 3-D extraction of inner and outer surfaces of cerebral cortex from mri. Neurolmage 12, 340-356.
28. Mallat, S. and Zhang, Z. (1993). Matching pursuits with time-frequency dictionaries. IEEE Trans. Signal Processing 41, 3397-3415.
29. Miller, M., Banerjee, A., Christensen, G., Joshi, S., Khaneja, N., Grenander, U. and Matejic, L. (1997). Statistical methods in computational anatomy. Statist. Meth. Medical Res. 6, 267-299.
30. Robbins, S. (2003). Anatomical standardization of the human brain in euclidean 3-space and on the cortical 2-manifold. Technical Report PhD thesis, School of Computer Science, McGill University, Montreal, Quebec, Canada.
31. Rosenberg, S. (1997). The Laplacian on a Riemannian Manifold. Cambridge University Press.
32. Rudin, W. (1991). Functional Analysis. McGraw-Hill.
33. Shen, L. and Chung, M. (2006). Large-scale modeling of parametric surfaces using spherical harmonics. In Third International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT), 294-301.
34. Shen, L., Ford, J., Makedon, F. and Saykin, A. (2004). Surface-based approach for classification of 3d neuroanatomical structures. Intelligent Data Analysis 8, 519-542.
35. Shen, L., Saykin, A., Chung, M., Huang, H., Ford, J., Makedon, F., McHugh, T. and Rhodes, C. (2006). Morphometric analysis of genetic variation in hippocampal shape in mild cognitive impairment: Role of an il-6 promoter polymorphism. In Life Science Society Computational Systems Bioinformatics Conference.
36. Sled, J., Zijdenbos, A. and Evans, A. (1988). A nonparametric method for automatic correction of intensity nonuniformity in mri data. IEEE Trans. Medical Imaging 17, 87-97.
37. Thompson, P. and Toga, A. (1996). A surface-based technique for warping 3-dimensional images of the brain. IEEE Trans. Medical Imaging 15.
38. Wahba, G. (1990). Spline Models for Observational Data. SIAM.
39. Wang, F.-Y. (1997). Sharp explict lower bounds of heat kernels. Ann. Probab. 24, 1995-2006.
40. Worsley, K., Marrett, S., Neelin, P., Vandal, A., Friston, K. and Evans, A. (1996). A unified statistical approach for determining significant signals in images of cerebral activation. Human Brain Mapping 4, 58-73.
41. Worsley, K., Taylor, J., Tomaiuolo, F. and Lerch, J. (2004). Unified univariate and multivariate random field theory. Neurolmage 23, S189-195.
42. Zhu, H., Ibrahim, J., Tang, N., Rowe, D., Hao, X., Bansal, R. and Peterson, B. (2007). A statistical analysis of brain morphology using wild bootstrapping. IEEE Trans. Medical Imaging 26, 954-966.