A topological hierarchy for functions on triangulated surfaces.
We combine topological and geometric methods to construct a multiresolution representation for a function over a two-dimensional domain. In a preprocessing stage, we create the Morse-Smale complex of the function and progressively simplify its topology by cancelling pairs of critical points. Based on a simple notion of dependency among these cancellations, we construct a hierarchical data structure supporting traversal and reconstruction operations similarly to traditional geometry-based representations. We use this data structure to extract topologically valid approximations that satisfy error bounds provided at runtime.
Bremer
Peer-Timo
PT
Center for Image Processing and Integrated Computing, Department of Science, University of California, Davis, CA 95616, USA. tbremer@ucdavis.edu
Edelsbrunner
Herbert
H
Hamann
Bernd
B
Pascucci
Valerio
V
D000465:Algorithms; D003196:Computer Graphics; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*