Discrete scale axis representations for 3D geometry

ACM SIGGRAPH 2010 Papers, SIGGRAPH 2010

Volumn , Issue , 2010, Pages

  Miklos, Balint ^a   Giesen, Joachim ^b   Pauly, Mark ^c  

^a ETH ZURICH   (Switzerland)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^c EPFL   (Switzerland)

Author keywords

Geometry representations; Medial axis; Scale axis; Shape analysis; Stability

Indexed keywords

COMPUTER GRAPHICS; CONVERGENCE OF NUMERICAL METHODS; INTERACTIVE COMPUTER GRAPHICS; MATHEMATICAL TRANSFORMATIONS; THREE DIMENSIONAL COMPUTER GRAPHICS; TOPOLOGY;

GEOMETRIC SIMPLIFICATION; GEOMETRY REPRESENTATION; LEVELS OF ABSTRACTION; MATHEMATICAL FOUNDATIONS; MEDIAL AXIS; SCALE AXIS; SHAPE ANALYSIS; TOPOLOGICAL PROPERTIES;

GEOMETRY;

EID: 84891060314     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1778765.1778838     Document Type: Conference Paper

References (33)

1. ALLIEZ, P., COHEN-STEINER, D., YVINEC, M., AND DESBRUN, M. 2005. Variational tetrahedral meshing. ACM Trans. Graph. 24, 3, 617-625.
2. AMENTA, N., AND BERN, M. 1998. Surface reconstruction by Voronoi filtering. ACM Symposium on Computational Geometry.
3. AMENTA, N., AND KOLLURI, R. K. 2000. Accurate and Efficient Unions of Balls. In ACM Symposium on Computational Geometry, 119-128.
4. AMENTA, N., AND KOLLURI, R. K. 2001. The medial axis of a union of balls. Computational Geometry 20, 1-2, 25-37.
5. AMENTA, N., CHOI, S., AND KOLLURI, R. K. 2001. The power crust, unions of balls, and the medial axis transform. Computational Geometry 19, 2-3, 127-153.
6. ATTALI, D., AND MONTANVERT, A. 1996. Modeling noise for a better simplification of skeletons. In Proceedings of International Conference on Image Processing, 13-16.
7. ATTALI, D., BOISSONNAT, J.-D., EDELSBRUNNER, H., AND BOISSONNAT, J.-D. 2009. Stability and Computation of the Medial Axis - a State-of-the-Art Report. Math. Foundations of Scient. Visualization, Comp. Graphics, and Data Exploration.
8. BELYAEV, A., YOSHIZAWA, S., AND SEIDEL, H.-P. 2007. Skeleton-based Variational Mesh Deformations. Computer Graphics Forum 26, 3, 255-264.
9. BLUM, H. 1967. A Transformation for Extracting New Descriptors of Shape. Models for the Perception of Speech and Visual Form, 362-380.
10. BOISSONNAT, J.-D., AND OUDOT, S. 2005. Provably good sampling and meshing of surfaces. Graph. Models 67, 5, 405-451.
11. BRUCE, J. W., GIBLIN, P. J., AND GIBSON, C. 1985. Symmetry Sets. Proc. of the Royal Society of Edinburgh 101, A, 163-186.
12. CHAUSSARD, J., COUPRIE, M., AND TALBOT, H. 2009. A discrete lambda-medial axis. DGCI 5810, 421-433.
13. CHAZAL, F., AND LIEUTIER, A. 2005. The lambda-medial axis. Graph. Models 67, 304-331.
14. CHEN, X., GOLOVINSKIY, A., AND FUNKHOUSER, T. 2009. A benchmark for 3D mesh segmentation. ACM Transactions on Graphics (Proc. SIGGRAPH) 28, 3 (Aug.).
15. CHOI, H. I., CHOI, S. W., AND MOON, H. P. 1997. Mathematical Theory Of Medial Axis Transform. Pacific J. Math 181, 57-88.
16. CORNEA, N. D., SILVER, D., AND MIN, P. 2007. Curve-Skeleton Properties, Applications, and Algorithms. IEEE Transactions on Visualization and Computer Graphics 13, 3, 18.
17. CULVER, T., KEYSER, J., AND MANOCHA, D. 2004. Exact computation of the medial axis of a polyhedron. Computer Aided Geometric Design 21, 1, 65-98.
18. DEY, T. K., AND ZHAO, W. 2004. Approximate medial axis as a Voronoi subcomplex. Computer-Aided Design 36, 2, 195-202.
19. DEY, T. K., WOO, H., AND ZHAO, W. 2003. Approximate medial axis for CAD models. ACM Symposium on Solid and Physical Modeling.
20. FOSKEY, M., LIN, M. C., AND MANOCHA, D. 2003. Efficient computation of a simplified medial axis. ACM Symposium on Solid and Physical Modeling.
21. GIESEN, J., MIKLOS, B., PAULY, M., AND WORMSER, C. 2009. The scale axis transform. Annual Symposium on Computational Geometry, 106-115.
22. PIZER, S. M., SIDDIQI, K., SZEKELY, G., DAMON, J. N., AND ZUCKER, S. W. 2003. Multiscale Medial Loci and Their Properties. Int. J. Comput. Vision 55, 155-179.
23. PIZER, S., SIDDIQI, K., AND YUSHKEVICH, P. 2008. Medial Representations, vol. 37 of Computational Imaging and Vision. Springer Netherlands, Dordrecht.
24. PODOLAK, J., SHILANE, P., GOLOVINSKIY, A., RUSINKIEWICZ, S., AND FUNKHOUSER, T. 2006. A planar-reflective symmetry transform for 3D shapes. ACM Transactions on Graphics (Proc. SIGGRAPH) 25, 3, 549-559.
25. PRASAD, L. 1997. Morphological analysis of shapes. CNLS Newsletter 139, 1-18.
26. RUMPF, M., AND TELEA, A. 2002. A continuous skeletonization method based on level sets. In VISSYM'02: Proceedings of the symposium on Data Visualisation 2002, 151-ff.
27. SIDDIQI, K., BOUIX, S., TANNENBAUM, A., AND ZUCKER, S. W. 2002. Hamilton-Jacobi Skeletons. International Journal of Computer Vision 48, 3(July), 215-231.
28. STOLPNER, S., AND WHITESIDES, S. 2009. Medial Axis Approximation with Bounded Error. In International Symposium on Voronoi Diagrams in Science and Engineering.
29. STYNER, M., GERIG, G., JOSHI, S., AND PIZER, S. 2003. Automatic and Robust Computation of 3D Medial Models Incorporating Object Variability. Int. J. Comput. Vision 55, 2, 107-122.
30. SUD, A., FOSKEY, M., AND MANOCHA, D. 2005. Homotopypreserving medial axis simplification. In Proceedings of the 2005 ACM Symposium on Solid and Physical Modeling, 39-50.
31. SVENSSON, S. 2001. Reversible surface skeletons of 3d objects by iterative thinning of distance transforms. Digital and image geometry: advanced lectures, 400-411.
32. TAM, R., AND HEIDRICH, W. 2003. Shape Simplification Based on the Medial Axis Transform. In IEEE Visualization 2003.
33. WARD, A. D., AND HAMARNEH, G. 2009. The Groupwise Medial Axis Transform for Fuzzy Skeletonization and Pruning. IEEE Transactions on Pattern Analysis and Machine Intelligence 99.