Topological landscapes: A terrain metaphor for scientific data

IEEE Transactions on Visualization and Computer Graphics

Volumn 13, Issue 6, 2007, Pages 1416-1423

  Weber, Gunther H ^a,b   Bremer, Peer Timo ^a,c   Pascucci, Valerio ^a,c  

^a IEEE   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

^c LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Contour tree; Feature detection (primary keyword); SOAR; Terrain; Topology; User interfaces; Visual analytics

Indexed keywords

CONTOUR TREE; FEATURE DETECTION (PRIMARY KEYWORD); TERRAIN; VISUAL ANALYTICS;

INFORMATION ANALYSIS; TOPOLOGY; USER INTERFACES;

DATA VISUALIZATION;

EID: 35948946511     PISSN: 10772626     EISSN: None     Source Type: Journal    
DOI: 10.1109/TVCG.2007.70601     Document Type: Article

References (49)

1. W. E. Lorensen and H. E. Cline, "Marching cubes: A high resolution 3D surface construction algorithm," Computer Graphics (Proceedings of ACM SIGGRAPH 87), vol. 21, no. 4, pp. 163-169, Jul. 1987.
2. M. Levoy, "Display of surfaces from volume data," IEEE Computer Graphics and Applications, vol. 8, no. 3, pp. 29-37, May 1988.
3. W. Hibbard, C. R. Dyer, and B. Paul, "Display of scientific data structures for algorithm visualization," in VIS '92: Proceedings of the 3rd conference on Visualization '92, 1992, pp. 139-146.
4. H. Akiba, N. Fout, and K.-L. Ma, "Simultaneous classification of time-varying volume data based on the time histogram," in Proceedings of Eurographics Visualization Symposium, May 2006, pp. 1-8.
5. K. Stockinger, E. W. Bethel, S. Campbell, E. Dart, , and K. Wu, "Detecting Distributed Scans Using High-Performance Query-Driven Visualization," in SC '06: Proceedings of the 2006 ACM/IEEE Conference on High Performance Computing, Networking, Storage and Analysis, October 2006.
6. J. Kniss, G. Kindlmann, and C. Hansen, "Multidimensional transfer functions for interactive volume rendering," IEEE Transactions on Visualization and Computer Graphics, vol. 8, no. 3, pp. 270-285, 2002.
7. C. L. Bajaj, V. Pascucci, and D. R. Schikore, "The contour spectrum," in Proc. IEEE Visualization '97, Oct. 19-24 1997, pp. 167-173.
8. F.-Y. Tzeng, E. Lum, and K.-L. Ma, "An intelligent system approach to higher-dimensional classification of volume data," IEEE Transactions on Visualization and Computer Graphics, vol. 11, no. 3, pp. 273-284, 2005.
9. F.-Y. Tzeng and K.-L. Ma, "Inelligent feature extraction and tracking for large-scale 4d flow simulations," in Proceedings of Supercomputing 2005, 2005.
10. M. van Kreveld, R. van Oostrum, C. Bajaj, V. Pascucci, and D. R. Schikore, "Contour trees and small seed sets for isosurface traversal," in Proceedings of the 13th Annual ACM Symposium on Computational Geometry (SoCG), 1997, pp. 212-220.
11. V. Pascucci and K. Cole-McLaughlin, "Parallel computation of the topology of level sets," Algorithmica, vol. 38, no. 2, pp. 249-268, Oct. 2003.
12. H. Carr, J. Snoeyink, and U. Axen, "Computing contour trees in all dimensions," Computational Geometry - Theory and Applications, vol. 24, no. 2, pp. 75-94, Feb. 2003.
13. G. H. Weber, G. Scheuermann, and B. Hamann, "Detecting critical regions in scalar fields," in Data Visualization 2003 (Proceedings of VisSym 2003), 2003, pp. 85-94.
14. H. Carr, J. Snoeyink, and M. van de Panne, "Simplifying flexible isosurfaces using local geometric measures," in Proc. IEEE Visualization 2004, Oct. 2004, pp. 497-504.
15. V. Pascucci, "On the topology of the level sets of a scalar field," in "Proceedings of the 13th Canadian Conference on Computational Geometry", August 2001, pp. 141-144.
16. G. H. Weber, G. Scheuermann, H. Hagen, and B. Hamann, "Exploring scalar fields using critical isovalues," in Proc. IEEE Visualization 2002, 2002, pp. 171-178.
17. V. Pascucci, K. Cole-McLaughlin, and G. Scorzelli, "Multi-resolution computation and presentation of contour trees," Lawrence Livermore National Laboratory, Tech. Rep. UCRL-PROC-208680, 2005, preliminary version appeared in the proceedings of the IASTED conference on Visualization, Imaging, and Image Processing (VIIP 2004), 2004, pp.452-290.
18. J. Cat, "On understanding: Maxwell on the methods of illustration and scientific metaphor," Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics September 2001, vol.32, no. 3, pp. 395-441, 2001.
19. Y. Shinagawa, T. L. Kunii, and Y. L. Kergosien, "Surface coding based on Morse theory," IEEE Computer Graphics and Applications, vol. 11, no. 5, pp. 66-78, 1991.
20. A. V. Gelder and J. Wilhelms, "Topological considerations in isosurface generation," ACM Transactions on Graphics, vol. 13, no. 4, pp. 337-375, Oct. 1994.
21. M. Morse, "Relations between the critical points of a real functions of n independent variables," Transactions of the American Mathematical Society, vol. 27, pp. 345-396, July 1925.
22. G. Reeb, "Sur les points singuliers d'une forme de pfaff complètement intégrable ou d'une fonction numérique," Comptes Rendus de l'Acadèmie des Sciences de Paris, vol. 222, pp. 847-849, 1946.
23. J. W. Milnor, Morse Theory. Princeton University Press, May 1963.
24. H. Edelsbrunner, J. Harer, and A. Zomorodian, "Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds," Discrete Comput. Geom., vol. 30, pp. 87-107, 2003.
25. A. Gyulassy, V. Natarajan, V. Pascucci, P.-T. Bremer, and B. Hamann, "Topology-based simplification for feature extraction from 3D scalar fields," IEEE Transactions on Computer Graphics and Visualization (TVCG), vol. 12, no. 4, pp. 474-484, 2006.
26. J. L. Helman and L. Hesselink, "Visualizing vector field topology in fluid flows," IEEE Computer Graphics and Applications, vol. 11, no. 3, pp. 36-46, May/Jun. 1991.
27. H. Theisel, T. Weinkauf, H.-C. Hege, and H.-P.Seidel, "Saddle connectors - An approach to visualizing the topological skeleton of complex 3d vector fields," in Proc. IEEE Visualization '03, 2003, pp. 225-232.
28. S. Mizuta, Y. Suwa, T. Ono, and T. Matsuda, "Description of the topological structure of digital images by contour tree and its application," Institute of Electronics, Information and Communication Engineers, Tech. Rep., 2004.
29. I. Fujishiro, Y. Takeshima, T. Azuma, and S. Takahashi, "Volume data mining using 3D field topology analysis," IEEE Computer Graphics and Applications, vol. 20, no. 5, pp. 46-51, Sep./Oct. 2000.
30. I. Fujishiro, T. Azuma, and Y. Takeshima, "Automating transfer function design for comprehensible volume rendering based on 3D field topology analysis," in Proc. IEEE Visualization '99, Oct. 25-29, 1999, pp. 467-470.
31. S. Takahashi, I. Fujishiro, and Y. Takeshima, "Interval volume decomposer: A topological approach to volume traversal," in Visualization and Data Analysis 2005 (Proceedings of the SPIE), 2005.
32. L. Kettner, J. Rossignac, and J. Snoeyink, "The safari interface for visualizing time-dependent volume data using iso-surfaces and contour spectra," Computational Geometry: Theory and Applications, vol. 25, no. 1-2, pp. 97-116, 2003.
33. H. Carr, "Topological manipulation of isosurfaces," Ph.D. dissertation, University of British Columbia, Apr. 2004.
34. J. L. Pfaltz, "Surface networks," Geographical Analysis, vol. 8, pp. 77-93, 1976.
35. L. R. Nackman, "Two-dimensional critical point configuration graphs," IEEE Transcactions on Pattern Analysis and Machine Intelligence, vol. 6, no. 4, pp. 442-450, 1984.
36. S. Takahashi, T. Ikeda, Y. Shinagawa, T. L. Kunii, and M. Ueda, "Algorithms for extracting correct critical points and constructing topological graphs from discrete geographical elevation data," Computer Graphics Forum, vol. 14, no. 3, pp. 181-192, 1995.
37. D. H. House and C. J. Kocmoud, "Continuous cartogram construction," in IEEE Visualization, 1998, pp. 197-204.
38. D. A. Keim, S. C. North, and C. Panse, "Cartodraw: A fast algorithm for generating contiguous cartograms," IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 1, pp. 95-110, 2004.
39. R. Heilmann, D. A. Keim, C. Panse, and M. Sips, "Recmap: Rectangular map approximations," in IEEE Symp. on Information Visualization, 2004, pp. 33-40.
40. R. Hadany and D. Hardel, "A multi-scale method for drawing graphs nicely," Discrete Applied Mathematics, vol. 113, no. 3-21, 2001.
41. D. Harel and Y. Koren, "A fast multi-scale method for drawing large graphs," in Graph Drawing: 8th International Symposium (GD'00), 2000, pp. 183-196.
42. Y. Koren, L. Carmel, and D. Harel, "Ace: A fast multiscale eigenvectors computation for drawing huge graphs," in IEEE Symposium on Information Visualization, 2002, pp. 137-144.
43. M. A. Duchaineau, M. Wolinsky, D. E. Sigeti, M. C. Miller, C. Aldrich, and M. B. Mineev-Weinstein, "Roaming terrain: Real-time optimally adapting meshes," in Proc. IEEE Visualization '97. IEEE, Nov. 1997, pp. 81-88.
44. L. Velho and D. Zorin, "4-8 subdivision," Computer-Aided Geometric Design, vol. 18, no. 5, pp. 397-427, 2001, special Issue on Subdivision Techniques.
45. P. Lindstrom and V. Pascucci, "Terrain simplification simplified: A general framework for view-dependent out-of-core visualization," IEEE Transactions on Visualization and Computer Graphics, vol. 8, no. 3, pp. 239-254, 2002.
46. H. Edelsbrunner, D. Letscher, and A. Zomorodian, "Topological persistence and simplification," Discrete Comput. Geom., vol. 28, pp. 511-533, 2002.
47. G. H. Weber, S. Dillard, H. Carr, V. Pascucci, and B. Hamann, "Topologycontrolled volume rendering," IEEE Transactions on Visualization and Computer Graphics, vol. 13, no. 2, pp. 330-341, 2007.
48. S. Takahashi, Y. Takeshima, and I. Fujishiro, "Topological volume skeletonization and its application to transfer function design," Graphical Models, vol. 66, no. 1, pp. 24-49, Jan. 2004.
49. S. Takahashi, G. M. Nielson, Y. Takeshima, and I. Fujishiro, "Topological volume skeletonization using adaptive tetrahedrization," in Proceedings of Geometric Modeling and Processing 2004, 2004, pp. 227-236.