This Article 
 Bibliographic References 
 Add to: 
Visualization Corner: Robust Topology-Based Multiscale Analysis of Scientific Data
September/October 2009 (vol. 11 no. 5)
pp. 88-95
During multiscale analysis, hierarchical function decompositions and error-driven simplifications can't guarantee precise control of topological features. Topology-based multiscale analysis has emerged as an alternative to help researchers understand complex scientific data.

1. J.C. Maxwell, "On Hills and Dales," The London, Edinburgh and Dublin Philosophical Magazine and J. Science, Dec. 1870, pp. 421–427.
2. J.M. Munkres, Elements of Algebraic Topology, Benjamin/Cummings, 1984.
3. J. Milnor, Morse Theory, Princeton Univ. Press, 1963.
4. H. Edelsbrunner and J. Harer, "Persistent Homology—A Survey," J.E. Goodman, J. Pach, and R. Pollack eds., , Surveys on Discrete and Computational Geometry, Twenty Years Later, vol. 453, Amer. Mathematical Soc., 2008, pp. 257–282.
5. S. Biasotti et al., "Describing Shapes by Geometrical-Topological Properties of Real Functions," ACM Computing Surveys, vol. 40, no. 4, 2008, pp. 1–87.
6. H. Edelsbrunner et al., "Morse Complexes for Piecewise Linear 3-Manifolds," Proc. 19th ACM Symp. Computational Geometry (SoCG), 2003, ACM Press, pp. 361–370.
7. H. Edelsbrunner and J. Harer, "Jacobi Sets of Multiple Morse Functions," F. Cucker et al., eds., Foundations of Computational Mathematics, Cambridge Univ. Press, 2002, pp. 37–57.
8. D. Cohen-Steiner, H. Edelsbrunner, and J. Harer, "Stability of Persistence Diagrams," Discrete Computational Geometry, vol. 37, no. 1, 2007, pp. 103–120.
9. V. Pascucci et al., "Robust Online Computation of Reeb Graphs: Simplicity and Speed," ACM Trans. Graph., vol. 26, no. 3, 2007, p. 58.
10. A. Gyulassy et al., "Topologically Clean Distance Fields," IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 6, 2007, pp. 1432–1439.

Index Terms:
Data visualization,Robustness,Data analysis,Error correction,Approximation error,Monitoring,Smoothing methods,Information analysis,scientific data,multiscale analysis,topology-based multiscale analysis
A. Gyulassy, L.G. Nonato, P.-T. Bremer, C. Silva, V. Pascucci, "Visualization Corner: Robust Topology-Based Multiscale Analysis of Scientific Data," Computing in Science and Engineering, vol. 11, no. 5, pp. 88-95, Sept.-Oct. 2009, doi:10.1109/MCSE.2009.152
Usage of this product signifies your acceptance of the Terms of Use.