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TitleTopology-based simplification for feature extraction from 3D scalar fields (In Proceedings)
inProc. IEEE Conference on Visualization
Author(s) Attila Gyulassy, Vijay Natarajan, Valerio Pascucci, Peer Timo Bremer, Bernd Hamann
Keyword(s)Morse theory, Morse-Smale complexes, computational topology, multi resolution, simplification, feature detection, 3D scalar fields
Year 2005
Pages535--542
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Abstract In this paper, we present a topological approach for simplifying continuous functions defined on volumetric domains. We introduce two atomic operations that remove pairs of critical points of the function and design a combinator ial algorithm that simplifies the Morse-Smale complex by repeated applicatio n of these operations. The Morse-Smale complex is a topological data structu re that provides a compact representation of gradient flow between critical points of a function. Critical points paired by the Morse-Smale complex iden tify topological features and their importance. The simplification procedure leaves important critical points untouched, and is therefore useful for ext racting desirable features. We also present a visualization of the simplifie d topology.