title: A topological approach to simplification of three-dimensional scalar functions.
abstract: This paper describes an efficient combinatorial method for simplification of topological features in a 3D scalar function. The Morse-Smale complex, which provides a succinct representation of a function's associated gradient flow field, is used to identify topological features and their significance. The simplification process, guided by the Morse-Smale complex, proceeds by repeatedly applying two atomic operations that each remove a pair of critical points from the complex. Efficient storage of the complex results in execution of these atomic operations at interactive rates. Visualization of the simplified complex shows that the simplification preserves significant topological features while removing small features and noise.
authors.affiliation: Institute for Data Analysis and Visualization and the Department of Computer Science, University of California, Davis 95616, USA. aggyulassy@ucdavis.edu
authors.forename: Attila
authors.initials: A
authors.lastname: Gyulassy
authors.forename: Vijay
authors.initials: V
authors.lastname: Natarajan
authors.forename: Valerio
authors.initials: V
authors.lastname: Pascucci
authors.forename: Peer-Timo
authors.initials: PT
authors.lastname: Bremer
authors.forename: Computer
authors.initials: C
authors.lastname: Society
authors.forename: Bernd
authors.initials: B
authors.lastname: Hamann
mesh_terms: D000465:Algorithms; D003196:Computer Graphics; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014584:User-Computer Interface