TitleTopology-based Simplification for Feature Extraction from 3D Scalar Fields (In Proceedings)
inProceedings of 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, multiresolution, simplification, feature detection, 3D scalar fields
Year 2005
LocationMinneapolis, MN
DateOctober 2005
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.