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A Topological Approach to Simplification of Three-Dimensional Scalar Functions
July/August 2006 (vol. 12 no. 4)
pp. 474-484

Abstract—This paper describes an efficient combinatorial method for simplification of topological features in a 3D scalar function. The Morse-Smale complex, which provides a succinct representation of a function's associated gradient flow field, is used to identify topological features and their significance. The simplification process, guided by the Morse-Smale complex, proceeds by repeatedly applying two atomic operations that each remove a pair of critical points from the complex. Efficient storage of the complex results in execution of these atomic operations at interactive rates. Visualization of the simplified complex shows that the simplification preserves significant topological features while removing small features and noise.

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Index Terms:
Morse theory, Morse-Smale complexes, computational topology, computational geometry, simplification, multiresolution, feature detection, volumetric data.
Citation:
Attila Gyulassy, Vijay Natarajan, Valerio Pascucci, Peer-Timo Bremer, Bernd Hamann, "A Topological Approach to Simplification of Three-Dimensional Scalar Functions," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 4, pp. 474-484, July-Aug. 2006, doi:10.1109/TVCG.2006.57
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