Heat kernel smoothing using Laplace-Beltrami eigenfunctions

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6363 LNCS, Issue PART 3, 2010, Pages 505-512

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

[No Author keywords available]

Indexed keywords

BELTRAMI; COMPUTATIONAL ANATOMY; EIGEN FUNCTION; HEAT KERNEL; ISOTROPIC DIFFUSION; KERNEL SMOOTHING TECHNIQUES; LINEAR COMBINATIONS; NOVEL SURFACES; NUMERICAL INSTABILITY; SERIES EXPANSION; SOURCE CODES;

EIGENVALUES AND EIGENFUNCTIONS; LAPLACE EQUATION; LAPLACE TRANSFORMS; MATHEMATICAL OPERATORS; MEDICAL COMPUTING; MEDICAL IMAGING;

GREEN'S FUNCTION;

ALGORITHM; ARTICLE; COMPUTER ASSISTED DIAGNOSIS; COMPUTER ASSISTED TOMOGRAPHY; HUMAN; IMAGE QUALITY; MANDIBLE; METHODOLOGY; RADIOGRAPHY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; TOOTH RADIOGRAPHY;

ALGORITHMS; HUMANS; MANDIBLE; RADIOGRAPHIC IMAGE ENHANCEMENT; RADIOGRAPHIC IMAGE INTERPRETATION, COMPUTER-ASSISTED; RADIOGRAPHY, DENTAL; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; TOMOGRAPHY, X-RAY COMPUTED;

EID: 84878971802     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-15711-0_63     Document Type: Conference Paper

References (14)

1. Andrade, A., Kherif, F., Mangin, J., Worsley, K.J., Paradis, A., Simon, O., Dehaene, S., Le Bihan, D., Poline, J.-B.: Detection of fmri activation using cortical surface mapping. Human Brain Mapping 12, 79-93 (2001) (Pubitemid 32120706)
2. Chung, M.K., Dalton, K.M., Shen, L., Evans, A.C., Davidson, R.J.: Weighted Fourier representation and its application to quantifying the amount of gray matter. IEEE Transactions on Medical Imaging 26, 566-581 (2007) (Pubitemid 46527336)
3. Chung, M.K., Robbins, S., Dalton, K.M., Davidson, R.J., Alexander, A.L., Evans, A.C.: Cortical thickness analysis in autism with heat kernel smoothing. NeuroImage 25, 1256-1265 (2005) (Pubitemid 40591666)
4. Chung, M.K., Taylor, J.: Diffusion smoothing on brain surface via finite element method. In: Proceedings of IEEE International Symposium on Biomedical Imaging, ISBI (2004)
5. Hagler Jr., A.P., Saygin, D.J., Sereno, M.I.: Smoothing and cluster thresholding for cortical surface-based group analysis of FMRI data. NeuroImage 33, 1093-1103 (2006)
6. Han, X., Jovicich, J., Salat, D., van der Kouwe, A., Quinn, B., Czanner, S., Busa, E., Pacheco, J., Albert, M., Killiany, R., et al.: Reliability of MRI-derived measurements of human cerebral cortical thickness: the effects of field strength, scanner upgrade and manufacturer. Neuroimage 32, 180-194 (2006)
7. Hernandez, V., Roman, J.E., Tomas, A., Vidal, V.: A survey of software for sparse eigenvalue problems. Technical Report STR-6, Universidad Politécnica de Valencia (2006), http://www.grycap.upv.es/slepc
8. Joshi, A.A., Shattuck, D.W., Thompson, P.M., Leahy, R.M.: A parameterization-based numerical method for isotropic and anisotropic diffusion smoothing on non- flat surfaces. IEEE Transactions on Image Processing 18(6), 1358-1365 (2009)
9. Lehoucq, R.B., Sorensen, D.C., Yang, C.: ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM Publications, Philadelphia (1998)
10. Lévy, B.: Laplace-Beltrami Eigenfunctions: Towards an Algorithm that Understands Geometry. In: IEEE International Conference on Shape Modeling and Applications, p. 13. IEEE, Los Alamitos (2006)
11. Qiu, A., Bitouk, D., Miller, M.I.: Smooth functional and structural maps on the neocortex via orthonormal bases of the laplace-beltrami operator. IEEE Transactions on Medical Imaging 25, 1296-1396 (2006)
12. Rosenberg, S.: The Laplacian on a Riemannian Manifold. Cambridge University Press, Cambridge (1997)
13. Spira, A., Kimmel, R., Sochen, N.: A short-time Beltrami kernel for smoothing images and manifolds. IEEE Transactions on Image Processing 16, 1628-1636 (2007) (Pubitemid 46796058)
14. Tasdizen, T., Whitaker, R., Burchard, P., Osher, S.: Geometric surface smoothing via anisotropic diffusion of normals. In: Geometric Modeling and Processing, pp. 687-693 (2006)