Reeb graph computation based on a minimal contouring

IEEE International Conference on Shape Modeling and Applications 2008, Proceedings, SMI

Volumn , Issue , 2008, Pages 73-82

  Patanè, Giuseppe ^a,b   Spagnuolo, Michela ^a   Falcidieno, Bianca ^a  

^a IMATI CNR

^b UNIVERSITY OF GENOA   (Italy)

Author keywords

Morse theory; Reeb graph; Shape analysis and abstraction

Indexed keywords

APPLICATIONS; DIFFRACTIVE OPTICAL ELEMENTS; FILE ORGANIZATION; FUNCTIONS;

MORSE THEORY; REEB GRAPH; REEB GRAPHS; SHAPE ANALYSIS AND ABSTRACTION;

GRAPH THEORY;

EID: 50949121351     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SMI.2008.4547953     Document Type: Conference Paper

References (38)

1. M. Attene, S. Biasotti, and M. Spagnuolo. Shape understanding by contour-driven retiling. The Visual Computer, 19(2-3):127-138, 2003.
2. T. Banchoff. Critical points and curvature for embedded polyhedra. Journal of Differential Geometry, 1:245-256, 1967.
3. S. Biasotti. Computational Topology Methods for Shape Modelling Applications. PhD thesis, Università degli Studi di Genova, May 2004.
4. S. Biasotti, S. Marini, M. Mortara, G. Patanè, M. Spagnuolo, and B. Falcidieno. 3D shape matching through topological structures. In DGCI, pages 194-203, 2003.
5. P.-T. Bremer, H. Edelsbrunner, B. Hamann, and V. Pascucci. A topological hierarchy for functions on triangulated surfaces. IEEE Transactions on Visualization and Computer Graphics, 10(4):385-396, 2004.
6. H. Carr, J. Snoeyink, and U. Axen. Computing contour trees in all dimensions. Comput. Geom. Theory Appl., 24(2):75-94, 2003.
7. Y.-J. Chiang, T. Lenz, X. Lu, and G. Rote. Simple and optimal output-sensitive construction of contour trees using monotone paths. Comput. Geom. Theory Appl., 30(2):165-195, 2005.
8. K. Cole-McLaughlin, H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci. Loops in Reeb graphs of 2-manifolds. Discrete Comput. Geom., 32(2):231-244, 2004.
9. M. Desbrun, M. Meyer, P. Schröder, and A. H. Barr. Implicit fairing of irregular meshes using diffusion and curvature flow. In ACM SIGGRAPH 1999, pages 317-324, 1999.
10. S. Dong, P.-T. Bremer, M. Garland, V. Pascucci, and J. C. Hart. Spectral surface quadrangulation. ACM SIGGRAPH 2006, pages 1057-1066, 2006.
11. A. Elad and R. Kimmel. On bending invariant signatures for surfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(10):1285-1295, 2003.
12. M. S. Floater and K. Hormann. Surface parameterization: a tutorial and survey. In Advances in Multiresolution for Geometric Modelling, pages 157-186. 2005.
13. A. Fomenko and T. L. Kunii. Topological Modelling for Visualization. Springer Verlag, 1997.
14. R. Gal and D. Cohen-Or. Salient geometric features for partial shape matching and similarity. ACM Transactions on Graphics, 25(1):130-150, 2006.
15. R. Gal, A. Shamir, and D. Cohen-Or. Pose-oblivious shape signature. IEEE Transactions on Visualization and Computer Graphics, 13(2):261-271, 2007.
16. M. Hilaga, Y. Shinagawa, T. Kohmura, and T. L. Kunii. Topology matching for fully automatic similarity estimation of 3D shapes. In ACM SIGGRAPH 2001, pages 203-212, 2001.
17. F. Lazarus and A. Verroust. Level set diagrams of polyhedral objects. In Proc. of the Symp. on Solid Modeling and Applications, pages 130-140. ACM, 1999.
18. B. T. Messmer and H. Bunke. A new algorithm for error-tolerant subgraph isomorphism detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(5):493-504, 1998.
19. J. Milnor. Morse Theory, volume 51 of Annals of mathematics studies. Princeton University Press, 1963.
20. M. Mortara and G. Patanè. Shape-covering for skeleton extraction. International Journal of Shape Modelling, 8(2):245-252, 2002.
21. M. Mortara, G. Patanè, M. Spagnuolo, B. Falcidieno, and J. Rossignac. Blowing bubbles for multi-scale analysis and decomposition of triangle meshes. Algorithmica, 38(1):227-248, 2004.
22. X. Ni, M. Garland, and J. C. Hart. Fair morse functions for extracting the topological structure of a surface mesh. In ACM SIGGRAPH 2004, pages 613-622, 2004.
23. V. Pascucci, K. Cole-McLaughlin, and G. Scorzelli. Multi-resolution computation and presentation of contour trees. In IASTED Conference on Visualization, Imaging, and Image Processing, pages 452-290, 2004.
24. V. Pascucci, G. Scorzelli, P.-T. Bremer, and A. Mascarenhas. Robust on-line computation of Reeb graphs: simplicity and speed. In ACM SIGGRAPH 2007, pages 58.1-58.9, 2007.
25. G. Patanè, M. Spagnuolo, and B. Falcidieno. Para-graph: graph-based parameterization of triangle meshes with arbitrary genus. Computer Graphics Forum, 23(4):783-797, 2004.
26. G. Patanè, M. Spagnuolo, and B. Falcidieno. Families of cut-graphs for bordered meshes with arbitrary genus. Graphical Models, 69(2):119-138, 2007.
27. G. Patanè, M. Spagnuolo, and B. Falcidieno. Topological generators and cut-graphs of arbitrary triangle meshes. In Proc. of Shape Modeling and Applications, pages 113-122, 2007.
28. U. Pinkall and K. Polthier. Computing discrete minimal surfaces and their conjugates. Experimental Mathematics, 2(1):15-36, 1993.
29. G. Reeb. Sur les points singuliers d'une forme de pfaff completement integrable ou d'une fonction numerique. In Comptes Rendu Acad. Sciences, pages 847-849. Sciences Park, 1946.
30. M. Reuter, F.-E. Wolter, and N. Peinecke. Laplace-Beltrami spectra as Shape-DNA of surfaces and solids. Computer-Aided Design, 38(4):342-366, 2006.
31. Y. Shinagawa, T. L. Kunii, and Y. L. Kergosian. Surface coding based on Morse theory. IEEE Computer Graphics and Applications, 11:66-78, 1991.
32. D. Steiner and A. Fischer. Cutting 3D freeform objects with genus-n into single boundary surfaces using topological graphs. In Proc. of the Symp. on Solid Modeling and Applications, pages 336-343, 2002.
33. S. Takahashi, Y. Shinagawa, and T. L. Kunii. A feature-based approach for smooth surfaces. In Proc. of the Symp. on Solid Modeling and Applications, pages 97-110. ACM, 1997.
34. B. Vallet and B. Levy. Manifold harmonics. To appear in EUROGRAPHICS, 2008.
35. M. van Kreveld, R. van Oostrum, C. Bajaj, V. Pascucci, and D. Schikore. Contour trees and small seed sets for isosurface traversal. In Proc. of the Symposium on Computational geometry, pages 212-220. ACM, 1997.
36. Z. Wood, H. Hoppe, M. Desbrun, and P. Schröder. Removing excess topology from isosurfaces. ACM Transactions on Graphics, 23(2):190-208, 2004.
37. T. Zaharia and F. J. Preteux. 3D-shape-based retrieval within the MPEG-7 framework. In Nonlinear Image Processing and Pattern Analysis, volume 4304, pages 133-145, 2001.
38. E. Zhang, K. Mischaikow, and G. Turk. Feature-based surface parameterization and texture mapping. ACM Transactions on Graphics, 24(1):1-27, 2005.