Topology-based Simplification for Feature Extraction from 3D Scalar Fields
Attila G. Gyulassy, Vijay Natarajan, Valerio Pascucci, Peer‐Timo Bremer, Bernd Hamann · 2006
Figure 1: Topology simplification applied on electron density data for a hydrogen atom: the input has a large number of critical points, several of which are identified as being insignificant and removed by repeated application of two atomic operations. Features are identified by the surviving critical points and enhanced in a volume rendered image by an automatically designed transfer function. This paper describes a topological approach for simplifying continuous functions defined on volumetric domains. We present a combinatorial algorithm that simplifies the Morse-Smale complex by repeated application of two atomic operations that removes pairs of critical points. The Morse-Smale complex is a topological data structure that provides a compact representation of gradient flows 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.