Joint contour nets

IEEE Transactions on Visualization and Computer Graphics

Volumn 20, Issue 8, 2014, Pages 1100-1113

  Carr, Hamish ^a   Duke, David ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Computational topology; contour analysis; contour tree; joint contour net; multivariate; reeb graph; reeb space

Indexed keywords

FORESTRY; TOPOLOGY; TREES (MATHEMATICS);

COMPUTATIONAL TOPOLOGY; CONTOUR ANALYSIS; CONTOUR TREES; MULTIVARIATE; REEB GRAPH; REEB SPACE;

MULTIVARIANT ANALYSIS;

FORESTRY; MATHEMATICS; TREES;

EID: 84904312270     PISSN: 10772626     EISSN: None     Source Type: Journal    
DOI: 10.1109/TVCG.2013.269     Document Type: Article

References (46)

1. M. Allili, M. Ethier, and T. Kaczynski, "Critical Region Analysis of Scalar Fields in Arbitrary Dimensions," Proc. Visualization and Data Analysis, pp. 753008-753012, 2010.
2. S. Bachthaler and D. Weiskopf, "Continuous Scatterplots," IEEE Trans. Visualization and Computer Graphics, vol. 14, no. 6, pp. 1428-1435, Nov. 2008.
3. R.L. Boyell and H. Ruston, "Hybrid Techniques for Real-Time Radar Simulation," Proc. Fall Joint Computer Conf., pp. 445-458, 1963.
4. D. Canino, L. de Floriani, and K. Weiss, "IA: An Adjacency-Based Representation for Non-Manifold Simplices in Arbitrary Dimensions," Computers and Graphics, vol. 35, no. 3, pp. 747-753, 2011.
5. G. Carlsson, G. Singh, and A. Zomorodian, "Computing Multidimensional Persistence," J. Computational Geometry, vol. 1, no. 1, pp. 72-100, 2010.
6. H. Carr, B. Duffy, and B. Denby, "On Histograms and Isosurface Statistics," IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 5, pp. 1259-1266, Sept./Oct. 2006.
7. H. Carr and J. Snoeyink, "Representing Interpolant Topology for Contour Tree Computation," Topology-Based Methods in Visualization II (Mathematics and Visualization), H.-C. Hege, K. Polthier, and G. Scheuermann, eds., pp. 59-74, Springer, 2009.
8. 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, 2003. (Pubitemid 35217991)
9. H. Carr, J. Snoeyink, and M. van de Panne, "Flexible Isosurfaces: Simplifying and Displaying Scalar Topology Using the Contour Tree," Computational Geometry: Theory and Applications, vol. 43, no. 1, pp. 42-58, 2010.
10. Y.-J. Chiang, T. Lenz, X. Lu, and G. Rote, "Simple and Optimal Output-Sensitive Construction of Contour Trees Using Monotone Paths," Computational Geometry: Theory and Applications, vol. 30, pp. 165-195, 2005.
11. C.D. Correa and P. Lindstrom, "Towards Robust Topology of Sparsely Sampled Data," IEEE Trans. Visualization and Computer Graphics, vol. 17, no. 12, pp. 1852-1861, Dec. 2011.
12. H. Doraiswamy and V. Natarajan, "Computing Reeb Graphs as a Union of Contour Trees," IEEE Trans. Visualization and Computer Graphics, vol. 19, no. 2, pp. 249-262, Feb. 2013, DOI: 10.1109/ TVCG.2012.115.
13. B. Duffy and H. Carr, "Interval Based Data Structure Optimisation," Proc. Theory and Practice of Computer Graphics, pp. 151-158, 2010.
14. B. Duffy, H. Carr, and T. Möller, "Integrating Histograms and Isosurface Statistics," IEEE Trans. Visualization and Computer Graphics, vol. 19, no. 2, pp. 263-77, Feb. 2013, DOI: 10.1109/ TVCG.2012.118.
15. D. Duke, H. Carr, A. Knoll, N. Schunck, H.A. Nam, and A. Staszczak, "Visualizing Nuclear Scission through a Multifield Extension of Topological Analysis," IEEE Trans. Visualization and Computer Graphics, vol. 18, no. 12, pp. 2033-40, Dec. 2012.
16. H. Edelsbrunner, Algorithms in Combinatorial Geometry. Springer- Verlag, 1987.
17. H. Edelsbrunner and J. Harer, "Jacobi Sets of Multiple Morse Functions," Foundations in Computational Mathematics, pp. 37-57, Cambridge Univ. Press, 2002.
18. H. Edelsbrunner, J. Harer, A. Mascarenhas, V. Pascucci, and J. Snoeyink, "Time-Varying Reeb Graphs for Continuous Space- Time Data," Computational Geometry, vol. 41, no. 3, pp. 149-166, 2008.
19. H. Edelsbrunner, J. Harer, and A.K. Patel, "Reeb Spaces of Piecewise Linear Mappings," Proc. ACM Symp. Computational Geometry, pp. 242-250, 2008.
20. H. Edelsbrunner, J. Harer, and A. Zomorodian, "Hierarchical Morse Complexes for Piecewise Linear 2-Manifolds," Proc. 17th ACM Symp. Computational Geometry, pp. 70-79, 2001. (Pubitemid 32865848)
21. H. Edelsbrunner and E.P. Mücke, "Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms," ACM Trans. Graphics, vol. 9, no. 1, pp. 66-104, 1990. (Pubitemid 20686102)
22. R. Forman, "Discrete Morse Theory for Cell Complexes," Advances in Math., vol. 134, pp. 90-145, 1998. (Pubitemid 128347573)
23. W. Harvey and Y. Wang, "Generating and Exploring a Collection of Topological Landscapes for Visualization of Scalar-Valued Functions," Computer Graphics Forum, vol. 29, no. 3, pp. 993-1002, 2010.
24. W. Harvey, Y. Wang, and R. Wenger, "A Randomized O(m log m) Algorithm for Computing Reeb Graphs of Arbitrary Simplicial Complexes," Proc. ACM Symp. Computational Geometry, pp. 267-276, 2010.
25. C. Heine, D. Schneider, H. Carr, and G. Scheuermann, "Drawing Contour Trees in the Plane," IEEE Trans. Visualization and Computer Graphics, vol. 17, no. 11, pp. 1599-1611, Nov. 2011.
26. W. Hibbard and D. Santek, "Visualizing Large Data Sets in the Earth Sciences," Computer, vol. 22, no. 8, pp. 53-57, 1989. (Pubitemid 20617581)
27. M. Hilaga, Y. Shinagawa, T. Kohmura, and T.L. Kunii, "Topology Matching for Fully Automatic Similarity Estimation of 3D Shapes," Proc. 28th ACM SIGGRAPH 2001, pp. 203-212, 2001. (Pubitemid 33047305)
28. S. Maadasamy, H. Doraiswamy, and V. Natarajan, "A Hybrid Parallel Algorithm for Computing and Tracking Level Set Topology," Proc. 19th Int'l Conf. High Performance Computing (HiPC), pp. 1-10, 2012.
29. D. Morozov and G. Weber, "Distributed Merge Trees," Proc. 18th ACM SIGPLAN Symp. Principles and Practice of Parallel Programming (PPoPP '13), pp. 93-102, 2013.
30. S. Nagaraj and V. Natarajan, "Simplification of Jacobi Sets," Topological Data Analysis and Visualization: Theory, Algorithms and Applications (Mathematics and Visualization), V. Pascucci, X. Tricoche, H. Hagen, and J. Tierny, eds., pp. 91-102, Springer, 2011.
31. S. Parsa, "A Deterministic O(m log m) Time Algorithm for the Reeb Graph," Proc. ACM Symp. Computational Geometry, pp. 269-276, 2012.
32. V. Pascucci and K. Cole-McLaughlin, "Parallel Computation of the Topology of Level Sets," Algorithmica, vol. 38, no. 2, pp. 249-268, 2003. (Pubitemid 40877170)
33. V. Pascucci, G. Scorzelli, P.-T. Bremer, and A. Mascarenhas, "Robust On-line Computation of Reeb Graphs: Simplicity and Speed," ACM Trans. Graphics, vol. 26, no. 3, pp. 58.1-58.9, 2007.
34. G. Reeb, "Surles Points Singuliers d'une Forme de Pfaff Complétement Intégrable ou d'une Fonction Numérique.," Comptes Rendus de l'Académie des Sciences de Paris, vol. 222, pp. 847-849, 1946.
35. O. Saeki, Topology of Singular Fibers of Differentiable Maps(Number 1854 in Lecture Notes in Mathematics). Springer, 2004.
36. C.E. Scheidegger, J.M. Schreiner, B. Duffy, H. Carr, and C.T. Silva, "Revisiting Histograms and Isosurface Statistics," IEEE Trans. Visualization and Computer Graphics, vol. 14, no. 6, pp. 1659-1666, Nov. 2008.
37. D. Schneider, A. Wiebel, H. Carr, M. Hlawitschka, and G. Scheuermann, "Interactive Comparison of Scalar Fields Based on Largest Contours with Applications to Flow Visualization," IEEE Trans. Visualization and Computer Graphics, vol. 14, no. 6, pp. 1475-1482, Nov./Dec. 2008.
38. W. Schroeder, K. Martin, and B. Lorensen, The Visualization Toolkit: An Object-Oriented Approach to 3D Graphics. fourth edition ed., Kitware, Inc., 2006.
39. R.E. Tarjan, "Efficiency of a Good but not Linear Set Union Algorithm," J. ACM, vol. 22, pp. 215-225, 1975.
40. J. Tierny, A. Gyulassy, E. Simon, and V. Pascucci, "Loop Surgery for Volumetric Meshes: Reeb Graphs Reduced to Contour Trees," IEEE Trans. Visualization and Computer Graphics, vol. 15, no. 6, pp. 1177-1184, Nov./Dec. 2009.
41. M. van Kreveld, R. van Oostrum, C.L. Bajaj, V. Pascucci, and D.R. Schikore, "Contour Trees and Small Seed Sets for Isosurface Traversal," Proc. 13th ACM Symp. Computational Geometry, pp. 212-220, 1997.
42. M. J. van Kreveld, R. van Oostrum, C. L. Bajaj, V. Pascucci, and D. R. Schikore, "Efficient Contour Tree and Minimum Seed Set Construction," Topological Data Structures for Surfaces: An Introduction for Geographical Information Science, chapter 5, pp. 71-86, John Wiley & Sons, May. 2004.
43. G. Weber, P.-T. Bremer, and V. Pascucci, "Topological Landscapes: A Terrain Metaphor for Scientific Data," IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 6, pp. 1416-1423, Nov./Dec. 2007. (Pubitemid 350076616)
44. G. Weber, S. Dillard, H. Carr, V. Pascucci, and B. Hamann, "Topology-Controlled Volume Rendering," IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 2, pp. 330-341, Mar./Apr. 2007. (Pubitemid 46183078)
45. G. Weber, G. Scheuermann, and H. Hagen, "Detecting Critical Regions in Scalar Fields," Proc. Eurographics-IEEE Symp. Visualization, pp. 85-94,288, 2003.
46. X. Zhang, C.L. Bajaj, and N. Baker, "Fast Matching of Volumetric Functions Using Multi-resolution Dual Contour Trees," technical report, 2004.