|Title||Topology-based Simplification for Feature Extraction from 3D Scalar Fields
(In Proceedings) |
|in||Proceedings of IEEE Conference on Visualization|
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|
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.