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| Title | Topology-based Simplification for Feature Extraction from 3D Scalar Fields
(In Proceedings) |
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| in | Proceedings of IEEE Conference on Visualization |
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| Author(s) |
Attila Gyulassy, Vijay Natarajan, Valerio Pascucci, Peer Timo Bremer, Bernd Hamann |
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| Keyword(s) | Morse theory, Morse-Smale complexes, computational topology, multiresolution, simplification, feature detection, 3D scalar fields |
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| Year |
2005
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| Location | Minneapolis, MN |
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| Date | October 2005 |
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| URL | http://graphics.idav.ucdavis.edu/~vijayn/research/research.html#vis2005 |
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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 combinatorial algorithm that simplifies the Morse-Smale complex by repeated application of these operations. The Morse-Smale complex is a topological data structure that provides a compact representation of gradient flow between critical points of a function. Critical points paired by the Morse-Smale complex identify topological features and their importance. The simplification procedure leaves important critical points untouched, and is therefore useful for extracting desirable features. We also present a visualization of the simplified topology.
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