Topological spines: A structure-preserving visual representation of scalar fields

IEEE Transactions on Visualization and Computer Graphics

Volumn 17, Issue 12, 2011, Pages 1842-1851

  Correa, Carlos ^a   Lindstrom, Peter ^a   Bremer, Peer Timo ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

extremum graph; Morse Smale complex.; Scalar field topology; topological spine

Indexed keywords

3-D SCALAR; CONTOUR TREES; EXPLORATORY ANALYSIS; EXTREMUM GRAPH; GEOMETRIC STRUCTURE; HIGH-DIMENSIONAL; MORSE-SMALE COMPLEX; MULTIRESOLUTION STRUCTURES; OCCLUSION PROBLEMS; SCALAR FIELD TOPOLOGY; SCALAR FIELDS; SPATIAL RELATIONSHIPS; STRUCTURAL INFORMATION; STRUCTURE-PRESERVING; TOPOLOGICAL FEATURES; TOPOLOGICAL REPRESENTATION; TOPOLOGICAL SPINE; VISUAL REPRESENTATIONS;

HIGH ENERGY PHYSICS; IMAGE QUALITY; THREE DIMENSIONAL COMPUTER GRAPHICS; TREES (MATHEMATICS); VISUALIZATION;

TOPOLOGY;

EID: 80855130074     PISSN: 10772626     EISSN: None     Source Type: Journal    
DOI: 10.1109/TVCG.2011.244     Document Type: Article

References (36)

1. D. H. Ackley. A connectionist machine for genetic hillclimbing. Kluwer, Boston, 1987.
2. R. F. W. Bader. Atoms in Molecules: A Quantum Theory. Oxford University Press, 1994.
3. K. Beketayev, G. Weber, M. Haranczyk, M. Hlawitschka, P.-T. Bremer, and B. Hamann. Topology-based visualization of transformation pathways in complex chemical systems. In Eurographics Symposium on Visualization, 2011. To appear.
4. P.-T. Bremer, V. Pascucci, and B. Hamann. Maximizing adaptivity in hierarchical topological models. In Shape Modeling and Applications, pages 298-307, 2005.
5. P.-T. Bremer, G. Weber, J. Tierny, V. Pascucci, M. Day, and J. B. Bell. Interactive exploration and analysis of large scale simulations using topology-based data segmentation. IEEE Transactions on Visualization and Computer Graphics, 2010. To appear.
6. H. Carr, J. Snoeyink, and U. Axen. Computing contour trees in all dimensions. Computational Geometry, 24(2):75-94, 2003. (Pubitemid 35217991)
7. H. Carr, J. Snoeyink, and M. van de Panne. Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree. Computational Geometry, 43(1):42-58, 2010.
8. F. Chazal, L. Guibas, S. Oudot, and P. Skraba. Analysis of scalar fields over point cloud data. In ACM-SIAM Symposium on Discrete Algorithms, pages 1021-1030, 2009.
9. H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci. Morse-Smale complexes for piecewise linear 3-manifolds. In ACM Symposium on Computational geometry, pages 361-370, 2003.
10. H. Edelsbrunner, D. Morozov, and V. Pascucci. Persistence-sensitive simplification functions on 2-manifolds. In Proceedings of the twenty-second annual symposium on Computational geometry, SCG '06, pages 127-134, New York, NY, USA, 2006. ACM.
11. E. Espinosa, M. Souhassou, H. Lachekar, and C. Lecomte. Topological analysis of the electron density in hydrogen bonds. Acta Crystallographica Section B-structural Science, 55:563-572, 1999. (Pubitemid 129533762)
12. I. Fujishiro, Y. Takeshima, T. Azuma, and S. Takahashi. Volume data mining using 3D field topology analysis. IEEE Computer Graphics & Applications, 20(5):46-51, 2000.
13. S. Gerber, P.-T. Bremer, V. Pascucci, and R. T. Whitaker. Visual exploration of high dimensional scalar functions. IEEE Transactions on Visualization and Computer Graphics, 16(6):1271-1280, 2010.
14. A. Gyulassy, P.-T. Bremer, V. Pascucci, and B. Hamann. A practical approach to Morse-Smale complex computation: Scalability and generality. IEEE Transactions on Visualization and Computer Graphics, 14(6):1619-1626, 2008.
15. 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, 12(4):474-484, 2006.
16. A. Gyulassy, V. Natarajan, V. Pascucci, and B. Hamann. Efficient computation of Morse-Smale complexes for three-dimensional scalar functions. IEEE Transactions on Visualization and Computer Graphics, 13(6):1440-1447, 2007. (Pubitemid 350076619)
17. W. Harvey and Y. Wang. Topological landscape ensembles for visualization of scalar-valued functions. Computer Graphics Forum, 29(3):993-1002, 2010.
18. J. L. Helman and L. Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics & Applications, 11(3):36-46, 1991. (Pubitemid 21662688)
19. C. K. Johnson, M. N. Burnett, andW. D. Dunbar. Crystallographic Topology and its Applications, pages 1-25. 1996.
20. D. Laney, P.-T. Bremer, A. Mascarenhas, P. Miller, and V. Pascucci. Understanding the structure of the turbulent mixing layer in hydrodynamic instabilities. IEEE Transactions on Visualization and Computer Graphics, 12(5):1052-1060, 2006.
21. L. Leherte, J. Glasgow, K. Baxter, E. Steeg, and S. Fortier. Analysis of Three-Dimensional Protein Images. Journal of Artificial Intelligence Research, 7:125-159, 1997.
22. P. Oesterling, C. Heine, H. Janicke, G. Scheuermann, and G. Heyer. Visualization of high dimensional point clouds using their density distribution's topology. IEEE Transactions on Visualization and Computer Graphics, 2011. To appear.
23. V. Pascucci, K. Cole-MacLaughlin, and G.Scorzelli. Multi-resolution computation and presentation of contour trees. Technical Report UCRLPROC-208680, Lawrence Livermore National Laboratory, 2005.
24. V. Pascucci and K. Cole-McLaughlin. Parallel computation of the topology of level sets. Algorithmica, 38:249-268, 2003. (Pubitemid 40877170)
25. V. Pascucci, G. Scorzelli, P.-T. Bremer, and A. Mascarenhas. Robust on-line computation of Reeb graphs: Simplicity and speed. ACM Transactions on Graphics, 26(3):58.1-58.9, 2007.
26. J. Sahner, B. Weber, S. Prohaska, and H. Lamecker. Extraction of feature lines on surface meshes based on discrete Morse theory. Computer Graphics Forum, 27(3):735-742, 2008.
27. H. Schwefel. Numerical optimization of computer models. Wiley, 1981.
28. Y. Shinagawa and T. Kunii. Constructing a Reeb graph automatically from cross sections. IEEE Computer Graphics & Applications, 11(5):44-51, 1991.
29. S. Takahashi, Y. Takeshima, and I. Fujishiro. Topological volume skeletonization and its application to transfer function design. Graphical Models, 66(1):24-49, 2004. (Pubitemid 38245838)
30. 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 IEEE Visualization, pages 225-232, 2003.
31. J. Tierny, A. Gyulassy, E. Simon, and V. Pascucci. Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees. IEEE Transactions on Visualization and Computer Graphics, 15(6):1177-1184, 2009.
32. I. G. Tollis, G. Di Battista, P. Eades, and R. Tamassia. Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, July 1998.
33. M. J. van Kreveld, R. van Oostrum, C. L. Bajaj, V. Pascucci, and D. Schikore. Contour trees and small seed sets for isosurface traversal. In ACM Symposium on Computational Geometry, pages 212-220, 1997.
34. G. Weber, P.-T. Bremer, and V. Pascucci. Topological landscapes: A terrain metaphor for scientific data. IEEE Transactions on Visualization and Computer Graphics, 13(6):1077-2626, 2007.
35. G. Weber, G. Scheuermann, H. Hagen, and B. Hamann. Exploring scalar fields using critical isovalues. In IEEE Visualization, pages 171-178, 2002. (Pubitemid 35444848)
36. T.Weinkauf and D. G̈unther. Separatrix persistence: Extraction of salient edges on surfaces using topological methods. Computer Graphics Forum, 28(5):1519-1528, 2009.