title: A topological hierarchy for functions on triangulated surfaces.
abstract: 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.
authors.affiliation: Center for Image Processing and Integrated Computing, Department of Science, University of California, Davis, CA 95616, USA. tbremer@ucdavis.edu
authors.forename: Peer-Timo
authors.initials: PT
authors.lastname: Bremer
authors.forename: Herbert
authors.initials: H
authors.lastname: Edelsbrunner
authors.forename: Bernd
authors.initials: B
authors.lastname: Hamann
authors.forename: Valerio
authors.initials: V
authors.lastname: Pascucci
mesh_terms: D000465:Algorithms; D003196:Computer Graphics; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*