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Topology-based simplification for feature extraction from 3D scalar fields

  • Author(s): Gyulassy, Attila
  • Natarajan, Vijay
  • Pascucci, Valerio
  • Bremer, Peer Timo
  • Hamann, Bernd
  • et al.
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.

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