Hierarchical Morse—Smale Complexes for Piecewise Linear 2-Manifolds

By Herbert Edelsbrunner, John Harer, Afra Zomorodian. Discrete & Computational Geometry, 2003

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Reeb graphs for shape analysis and applications (2008, methodology): “Critical points are identified analyzing the star of each vertex and classified according to the approach in [14].”
Homological illusions of persistence and stability (2008, methodology): “The work related most directly to ours is on the simplification of Morse-Smale complexes initiated in [38].”
Feature-based surface parameterization and texture mapping (2005, methodology): “This increases the subsequent processing time since the number of features is much more than what we consider large (or “persistent” as described in [Edelsbrunner et al. 2003]).”
Spectral surface quadrangulation (2006, methodology): “Discrete Morse theory [Banchoff 1967; Edelsbrunner et al. 2003] and its related data structures provide the underpinnings for a variety of topological graphics applications for implicit surfaces [Stander and Hart 1997], volumetric isosurfaces [van Kreveld et al. 1997; Pascucci and Cole-McLaughlin…”
The persistent cosmic web and its filamentary structure I: Theory and implementation (2010, methodology): “The approach has been successfully developed by Edelsbrunner, Harer & Zomorodian (2003) and Edelsbrunner et al. (2003) for the 2D and 3D cases, respectively, but at the cost of a very high algorithmic complexity.”