Anisotropic laplace-beltrami elgenmaps: Bridging reeb graphs and skeletons

2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops

Volumn , Issue , 2008, Pages

  Shi, Yonggang ^a   Lai, Rongjie ^b   Krishna, Sheila ^a   Sicotte, Nancy ^a   Dinov, Ivo ^a   Toga, Arthur W ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; ARTIFICIAL INTELLIGENCE; COMPUTER VISION; FEATURE EXTRACTION; FUNCTION EVALUATION; GRAPH THEORY; IMAGE PROCESSING; LAPLACE TRANSFORMS; PATTERN RECOGNITION; TOPOLOGY;

ANISOTROPIC LAPLACE; CORPUS CALLOSUM; EIGENFUNCTIONS; INTRINSIC GEOMETRY; LAPLACE-BELTRAMI OPERATORS; NEUROANATOMICAL STRUCTURES; REEB GRAPHS; SURFACE GEOMETRIES; WEIGHT FUNCTIONS;

COMPUTATIONAL GEOMETRY;

EID: 51849154987     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CVPRW.2008.4563018     Document Type: Conference Paper

References (22)

1. S. Biasotti. B. Falcidieno, and M. Spagnuolo. Extended reeb graphs for surface understanding and description. In Proc. DGCI'001, pages 185-197, 2000.
2. H. Blum and R. Nagel. Shape description using weighted symmetric axis features. Pattern Recognition, 10(3):167-180, 1978.
3. S. Bouix, J. C. Pruessner, D. L. Collins, and K. Siddiqi. Hippocampal shape analysis using medial surfaces. Neuro Image, 25(4):1077-1089, 2005.
4. T. Cootes, C. Taylor, D. Cooper, and J. Graham. Active shape models-thcir training and application. Computer Vision and Image Understanding, 61 (1):38-59. 1995.
5. P. Golland, W. Crimson, and R. Kikinis. Statistical shape analysis using fixed topology skeletons: Corpus callosum study. In Proc. IPMI, pages 382-387, 1999.
6. M. Hilaga, Y. Shinagawa, T. Kohmura, and T. L. Kunii. Topology matching for fully automatic similarity estimation of 3d shapes. In Proc. SIGGRAPH'01, pages 203-212, 2001.
7. J. Jost. Riemannian Geometry and Geometric Analysis. Springer, 3rd edition, 2001.
8. R. Kimmel and J. A. Scthian. Computing geodesic paths on manifolds. Proc. Nail. haul. Sci. USA, 95(15):8431-8435, 1998.
9. M. Niethammer. M. Reuler, F.-E. Wolter, S. Bouix. N. P. M.-S. Koo, and M. Shenton. Global medical shape analysis using the Laplace-Beltrami spectrum. In Proc. MICCAI, volume 1, pages 850-857, 2007.
10. R. L. Ognicwicz and O. Kblcr. Hierarchic voronoi skeletons. Pattern Recognition, 28(3):343-359, 1995.
11. S. M. Pizcr, D. S. Fritsch, P. A. Yushkcvich, V. E. Johnson, and H. L. Chaney. Segmentation, registration, and measurement of shape variation via image object shape. IEEE Trans. Med. Imag., 18(10):851-865. 1999.
12. A. Qiu, D. Bitouk, and M. I. Miller. Smooth functional and structural maps on the ncocortcx via orthonormal bases of the laplace-Beltrami operator. IEEE Trans. Med. Imag., 25(10):1296-1306, 2006.
13. G. Reeb. Sur les points singuliers d'une forme de Pfaff completement integrable ou d'une fonction nemérique. Comptes Rendus Acad. Sciences, 222:847-849, 1946.
14. M. Reuter, F. Wolter, and N. Peinecke. Laplace-Beltrami spectra as Shapc-DNA of surfaces and solids. Computer-Aided Design, 38:342-366, 2006.
15. J. R. Shewchuk. Dclaunay refinement algorithms for triangular mesh generation. Compul. Geom. Theory & Applications, 22(1-3):21-74, 2002.
16. Y. Shi, P. Thompson, I. Dinov, and A. Toga. Hamilton-Jacobi skeleton on cortical surfaces. IEEE Trans. Med. Imag., 27(5):664-673, 2008.
17. Y. Shinagawa and T. L. Kunii. Constructing a Reeb graph automatically from cross sections. IEEE Computer Graphics & Applications, 11 (6):44-51. 1991.
18. K. Siddiqi, S. Bouix, A. Tannebaum, and S. Zuker. Hamilton-Jacobi skeletons. Int'l Journal of Computer Vision, 48(3):215-231, 2002.
19. M. Styner, G. Gerig, J. Lieberman, D. Jones, and D. Weinberger. Statistical shape analysis of neuroanatomical structures based on medial models. Med. Image. Anal., 7(3):207-220, 2003.
20. P. M. Thompson, K. M. Hayashi, G. I. de Zubicaray, A. L. Janke, S. E. Rose, J. Semple, M. S. Hong, D. H. Herman, D. Gravano, D. M. Doddrell, and A. W. Toga. Mapping hippocampal and ventricular change in Alzheimer disease. Neuro Image, 22(4):1754-1766. 2004.
21. M. van Kreveld, R. van Oostrum, C. Bajaj, V. Pascucci, and D. Schikore. Contour trees and small seed sets for isosurface traversal. In Proc. 13th Anna. ACM Sympos. Comput. Geom., pages 212-220, 1997.
22. P. A. Yushkevich, H. Zhang, and J. C. Gee. Continuous medial representation for anatomical structures. IEEE Trans. Med. Imag., 25(12):1547-1564. 2006.