Reeb graphs: approximation and persistence

DOI10.1007/s00454-012-9463-zzbMath1261.68095OpenAlexW2151335375MaRDI QIDQ1942305

Yusu Wang, Tamal Krishna Dey

Publication date: 18 March 2013

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-012-9463-z

zbMATH Keywords

persistent Reeb graph homology

Mathematics Subject Classification ID

Graph theory (including graph drawing) in computer science (68R10) Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (7)

Structure and stability of the one-dimensional Mapper ⋮ Object-oriented persistent homology ⋮ Reeb Graphs of Piecewise Linear Functions ⋮ Multiscale persistent functions for biomolecular structure characterization ⋮ Statistical Analysis and Parameter Selection for Mapper ⋮ Generalized persistence diagrams for persistence modules over posets ⋮ Graph induced complex on point data

Uses Software

• ShortLoop

Cites Work

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• Topological persistence and simplification
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• Finding the homology of submanifolds with high confidence from random samples
• Approximating cycles in a shortest basis of the first homology group from point data
• Curve and Surface Reconstruction
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• Towards persistence-based reconstruction in euclidean spaces
• Cut locus and topology from surface point data
• Zigzag persistent homology and real-valued functions
• Persistence-based clustering in riemannian manifolds
• Vietoris-rips complexes also provide topologically correct reconstructions of sampled shapes
• A randomized O ( m log m ) time algorithm for computing Reeb graphs of arbitrary simplicial complexes

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