Controlled-topology filtering

Proceedings SPM 2006 - ACM Symposium on Solid and Physical Modeling

Volumn 2006, Issue , 2006, Pages 53-62

  Gingold, Yotam I ^a   Zorin, Denis ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Computational topology; Critical points; Filtering; Isosurfaces

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; COMPUTER SIMULATION; FEATURE EXTRACTION; FILTRATION; TOPOLOGY;

COMPUTATIONAL TOPOLOGY; CRITICAL POINTS; EXTRACTION ALGORITHMS; ISOSURFACES;

SURFACE STRUCTURE;

EID: 33745954719     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1128888.1128895     Document Type: Conference Paper

References (40)

1. ANDÚJAR, C., BRUNET, P., AND AYALA, D. 2002. Topology-reducing surface simplification using a discrete solid representation. ACM Trans. Graph. 21, 1, 88-105.
2. BAJAJ, C., AND SCHIKORE, D. 1998. Topology preserving data simplification with error bounds. Journal on Computers and Graphics vol. 22, 1, 3-12.
3. BREMER, P.-T., PASCUCCI, V., EDELSBRUNNER, H., AND HAMANN, B. 2004. A topological hierarchy for functions on triangulated surfaces. IEEE Trans. Vis. Comput. Graphics 10, 385-396.
4. CARR, H., SNOEYINK, J., AND AXEN, U. 2000. Computing contour trees in all dimensions. In Symposium on Discrete Algorithms, 918-926.
5. CARR, H., SNOEYINK, J., AND VAN DE PANNE, M. 2004. Simplifying flexible isosurfaces using local geometric measures. In IEEE Visualization 2004, 497-504.
6. CURLESS, B., AND LEVOY, M. 1996. A volumetric method for building complex models from range images. In Proceedings of SIGGRAPH 96, Computer Graphics Proceedings, Annual Conference Series, 303-312.
7. DAMON, J. 1995. Local Morse theory for solutions to the heat equation and Gaussian blurring. J. Differential Equations 115, 2, 368-401.
8. DE LEEUW, W., AND VAN LIBRE, R. 1999. Collapsing flow topology using area metrics. In VIS '99: Proceedings of the conference on Visualization '99, IEEE Computer Society Press, Los Alamitos, CA, USA, 349-354.
9. DEMMEL, J. W., EISENSTAT, S. C., GILBERT, J. R., LI, X. S., AND LIU, J. W. H. 1999. A supernodal approach to sparse partial pivoting. SIAM J. Matrix Analysis and Applications 20, 3, 720-755.
10. DIEWALD, U., PREUER, T., AND RUMPF, M. 2000. Anisotropic diffusion in vector field visualization on Euclidean domains and surfaces. IEEE Transactions on Visualization and Computer Graphics 6, 2, 139-149.
11. EDELSBRUNNER, H., AND MÜCKE, E. 1990. Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms. ACM Trans. Graph. 9, 1, 66-104.
12. EDELSBRUNNER, H., LETSCHER, D., AND ZOMORODIAN, A. 2000. Topological persistence and simplification. In Proc. 41st Ann. IEEE Sympos. Found Comput. Sci., 454-463.
13. EDELSBRUNNER, H., RARER, J., AND ZOMORODIAN, A. 2001. Hierarchical Morse complexes for piecewise linear 2-manifolds. In Proc. 17th Ann. ACM Sympos. Comput. Geom., 70-79.
14. EDELSBRUNNER, H., HARER, J., NATARAJAN, V., AND PASCUCCI, V. 2003. Morse-Smale complexes for piecewise linear 3-manifolds. In Proc. 19th Ann. Sympos. Comput. Geom., 361-370.
15. EL-SANA, J., AND VARSHNEY, A. 1997. Controlled simplification of genus for polygonal models. In IEEE Visualization '97, 403-412.
16. FLORACK, L., AND KUIJPER, A. 2000. The topological structure of scale-space images. J. Math. Imaging Vis. 12, 1, 65-79.
17. FREEMAN, H., AND MORSE, S. P. 1967. On searching a contour map for a given terrain profile. Journal of the Franklin Institute 248, 1-25.
18. GUSKOV, I., AND WOOD, Z. 2001. Topological noise removal. In Graphics Interface 2001, 19-26.
19. HAN, X., XU, C., AND PRINCE, J. 2001. A topology preserving deformable model using level sets. In Computer Vision and Pattern Recognition, vol. 2, 765-770.
20. HART, J. C. 1998. Morse theory for implicit surface modeling. In Mathematical Visualization, H.-C. Hege and K. Polthier, Eds. Springer-Verlag, Oct., 257-268.
21. HE, T., HONG, L., VARSHNEY, A., AND WANG, S. W. 1996. Controlled topology simplification. IEEE Transactions on Visualization and Computer Graphics 2, 2, 171-184.
22. HELMAN, J. L., AND HESSELINK, L. 1991. Visualizing vector field topology in fluid flows. IEEE Comput. Graph. Appl. 11, 3, 36-46.
23. MAHROUS, K., BENNETT, J., SCHEUERMANN, G., HAMANN, B., AND JOY, K. I. 2004. Topological segmentation in three-dimensional vector fields. IEEE Transactions on Visualization and Computer Graphics 10, 2, 198-205.
24. MILNOR, J. 1963. Morse Theory. Princeton Univ. Press, New Jersey.
25. NI, X., GARLAND, M., AND HART, J. C. 2004. Fair Morse functions for extracting the topological structure of a surface mesh. ACM Transactions on Graphics 23, 3 (Aug.), 613-622.
26. P.-T.BREMER, PASCUCCI, V., AND HAMANN, B. 2005. Maximizing adaptivity in hierarchical topological models. In Proceedings of International Conference on Shape Modeling and Applications, 298-307.
27. PERONA, P., AND MALIK, J. 1990. Scale-space and edge detection using anisotropic diffusion. IEEE Trans. PAMI 12, 7 (July), 629-639.
28. RANA, S., Ed. 2004. Topological Data Structures for Surfaces: An Introduction to Geographical Information Science. Wiley and Sons.
29. SIRCAR, J. K., AND CERBRIAN, J. A. 1986. Application of image processing techniques to the automated labelling of raster figitized contours. In Int. Symp. on Spatial Data Handling, 171-184.
30. SOHN, B., AND BAJAJ, C. 2005. Time-varying contour topology. IEEE Transactions on Visualization and Computer Graphics 12, 1, 14-25.
31. TONG, Y., LOMBEYDA, S., HIRANI, A. N., AND DESBRUN, M. 2003. Discrete multiscale vector field decomposition. ACM Transactions on Graphics 22, 3 (July), 445-452.
32. TRICOCHE, X., SCHEUERMANN, G., AND HAGEN, H. 2000. A topology simplification method for 2d vector fields. In IEEE Visualization 2000, 359-366.
33. TRICOCHE, X., SCHEUERMANN, G., AND HAGEN, H. 2001. Continuous topology simplification of planar vector fields. In IEEE Visualization 2001, 159-166.
34. TRICOCHE, X., WISCHGOLL, T., SCHEUERMANN, G., AND HAGEN, H. 2002. Topology tracking for the visualization of time-dependent two-dimensional flows. Computers & Graphics 26, 2 (Apr.), 249-257.
35. TRICOCHE, X. 2002. Vector and Tensor Field Topology Simplification, Tracking, and Visualization. PhD thesis, Universitat Kaiserslautern.
36. VAN KREVELD, M. J., VAN OOSTRUM, R., BAJAJ, C. L., PASCUCCI, V., AND SCHIKORE, D. 1997. Contour trees and small seed sets for isosurface traversal. In Symposium on Computational Geometry, 212-220.
37. WITKIN, A. P. 1983. Scale-space filtering. In International Joint Conference on Artificial Intelligence, 1019-1022.
38. WOOD, Z., HOPPE, H., DESBRUN, M., AND SCHRÖDER, P. 2004. Removing excess topology from isosurfaces. ACM Transactions on Graphics 23, 2 (Apr.), 190-208.
39. ZOMORODIAN, A. 2001. Computing and Comprehending Topology: Persistence and Hierarchical Morse Complexes. PhD thesis, University of Illinois at Urbana-Champaign.
40. ZOMORODIAN, A. 2005. Topology for Computing. Cambridge University Press, New York, NY.