Herbert Edelsbrunner
Valerio Pascucci
ABSTRACT
We continue the study of topological persistence [5] by investigating the problem of simplifying a function f in a way that removes topological noise as determined by its persistence diagram [2]. To state our results, we call a function g an ε-simplification of another function f if ¦¦f−g¦¦∞≤ε, and the persistence diagrams of g are the same as those of f except all points within L1-distance at most ε from the diagonal have been removed. We prove that for functions f on a 2-manifold such ε-simplification exists, and we give an algorithm to construct them in the piecewise linear case.
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- David Cohen-Steiner, Herbert Edelsbrunner and John Harer. Stability of persistence diagrams. In Proc. 21st Ann. Sympos. Comput. Geom., pages 263--271, New York, NY, USA, 2005. Google ScholarDigital Library
- David Cohen-Steiner, Herbert Edelsbrunner and Dmitriy Morozov. Vines and vineyards by updating persistence in linear time. To appear in Proc. 22st Ann. Sympos. Comput. Geom., Sedona, Arizona, USA, 2006. Google ScholarDigital Library
- Herbert Edelsbrunner, John Harer and Afra Zomorodian. Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds. Discrete Comput. Geom., 30:87--107, 2003.Google ScholarCross Ref
- Herbert Edelsbrunner, David Letscher and Afra Zomorodian. Topological persistence and simplification. Discrete Comput. Geom., 28:511--533, 2002.Google ScholarDigital Library
- Attila Gyulassy, Vijay Natarajan, Valerio Pascucci, Peer-Timo Bremer and Bernd Hamann. Topology-based simplification for feature extraction from 3D scalar fields. In Proc. IEEE Conf. Visualization, pages 275--280, 2005.Google Scholar
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Index Terms
- Persistence-sensitive simplification functions on 2-manifolds
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