Mandible shape modeling using the second eigenfunction of the Laplace-Beltrami operator

Progress in Biomedical Optics and Imaging - Proceedings of SPIE

Volumn 7962, Issue , 2011, Pages

  Seo, Seongho ^a   Chung, Moo K ^a,b,c   Whyms, Brian J ^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

centerline; heat kernel smoothing; Laplace Beltrami eigenfunction; mandible growth; morphometry

Indexed keywords

CENTERLINES; EIGEN FUNCTION; HEAT KERNEL SMOOTHING; MANDIBLE GROWTH; MORPHOMETRY;

COMPUTERIZED TOMOGRAPHY; IMAGE PROCESSING; IMAGING SYSTEMS; LAPLACE TRANSFORMS; MEDICAL IMAGING; THREE DIMENSIONAL;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 79958019980     PISSN: 16057422     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.877537     Document Type: Conference Paper

References (22)

1. Scammon, R. E., "The measurement of the body in childhood," in [The measurement of man], Harris, J. A., Jackson, C. M., Patterson, D. G., and Scammon, R. E., eds., 173-214, University of Minnesota Press, Minneapolis (1930).
2. Scott, J. H., [Dento-facial Development and Growth], Pergamon Press, Oxford (1976).
3. Smartt Jr., J. M., Low, D. W., and Bartlett, S. P., "The pediatric mandible: I. A primer on growth and development," Plast. Reconstr. Surg. 116, 14e-23e (July 2005).
4. Walker, G. F. and Kowalski, C. J., "On the growth of the mandible," American Journal of Physical Anthropology 36, 111-118 (January 1972).
5. Enlow, D. H. and Hans, M. G., [Essentials of Facial Growth], W.B. Saunders Company, Philadelphia (1996).
6. Cornea, N. D., Silver, D., and Min, P., "Curve-skeleton properties, applications, and algorithms," IEEE Transactions on Visualization and Computer Graphics 13(3), 530-548 (2007).
7. Lazarus, F. and Verroust, A., "Level set diagrams of polyhedral objects," in [Proceedings of the fifth ACM symposium on Solid modeling and applications], 130-140 (1999).
8. Xiao, Y., Siebert, P., and Werghi, N., "A discrete Reeb graph approach for the segmentation of human body scans," in [Fourth International Conference on 3-D Digital Imaging and Modeling], 378-385 (2003).
9. Attene, M., Biasotti, S., and Spagnuolo, M., "Shape understanding by contour-driven retiling," The Visual Computer 19(2), 127-138 (2003).
10. Shi, Y., Lai, R., Krishna, S., Sicotte, N., Dinov, I., and Toga, A. W., "Anisotropic Laplace-Beltrami eigenmaps: Bridging Reeb graphs and skeletons," in [Proceedings of Mathematical Methods in Biomedical Image Analysis (MMBIA)], 1-7 (2008).
11. Lévy, B., "Laplace-Beltrami Eigenfunctions: Towards an Algorithm that Understands Geometry," in [IEEE International Conference on Shape Modeling and Applications], 13 (2006).
12. Rosenberg, S., [The Laplacian on a Riemannian Manifold], Cambridge University Press (1997).
13. Chung, M. K., Statistical Morphometry in Neuroanatomy, PhD thesis, McGill University (2001).
14. Qiu, A., Bitouk, D., and 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, 1296-1306 (2006).
15. Seo, S., Chung, M., and Vorperian, H., "Heat kernel smothing using Laplace-Beltrami eigenfunctions," in [Medical Image Computing and Computer-Assisted Intervention - MICCAI 2010], Lecture Notes in Computer Science 6363, 505-512 (2010).
16. Hernandez, V., Roman, J. E., Tomas, A., and Vidal, V., "A survey of software for sparse eigenvalue problems," Tech. Rep. STR-6, Universidad Politécnica de Valencia (2006). Available at http://www.grycap.upv.es/ slepc.
17. Lehoucq, R., Sorensen, D., and Yang, C., [ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods], SIAM Publications, Philadelphia (1998).
18. Dong, S., Bremer, P.-T., Garland, M., Pascucci, V., and Hart, J. C., "Quadrangulating a mesh using Laplacian eigenvectors," Tech. Rep. UIUCDCS-R-2005-2583, Department of Computer Science, University of Illinois at Urbana-Champaign (June 2005).
19. Banuelos, R. and Burdzy, K., "On the Hot Spots Conjecture of J Rauch," Journal of Functional Analysis 164, 1-33 (1999).
20. Brechbühler, C., Gerig, G., and Kubler, O., "Parametrization of closed surfaces for 3-D shape description," Computer Vision and Image Understanding 61, 154-170 (1995).
21. Zhu, L. and Jiang, T., "Parameterization of 3D brain structures for statistical shape analysis," in [Medical Imaging 2004: Image Processing], Proc. SPIE 5370, 1254-1261 (2004).
22. Chung, M. K., Adluru, N., Lee, J. E., Lazar, M., Lainhart, J. E., and Alexander, A. L., "Cosine series representation of 3D curves and its application to white matter fiber bundles in diffusion tensor imaging," Statistics and Its Interface 3, 69-80 (2010).