Scalar field analysis over point cloud data

DOI10.1007/s00454-011-9360-xzbMath1230.94002OpenAlexW2134803627MaRDI QIDQ650107

Leonidas J. Guibas, Primoz Skraba, Steve Y. Oudot, Fréderic Chazal

Publication date: 25 November 2011

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

Full work available at URL: https://doi.org/10.1007/s00454-011-9360-x

zbMATH Keywords

Morse theoryclusteringsampling theorypersistent homologysensor networksVietoris-Rips complexespersistence modules

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Simplicial sets and complexes in algebraic topology (55U10) Other homology theories in algebraic topology (55N35) Sampling theory in information and communication theory (94A20)

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Structure and stability of the one-dimensional Mapper ⋮ Zigzag zoology: Rips zigzags for homology inference ⋮ Barcodes as summary of loss function topology ⋮ Computing the multicover bifiltration ⋮ Probabilistic convergence and stability of random mapper graphs ⋮ Analysis of Kolmogorov flow and Rayleigh-Bénard convection using persistent homology ⋮ An approximate nerve theorem ⋮ Elder-Rule-Staircodes for Augmented Metric Spaces ⋮ Implementing Persistence-Based Clustering of Point Clouds in the Topology ToolKit ⋮ Graph induced complex on point data ⋮ The theory of the interleaving distance on multidimensional persistence modules

Cites Work

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• Finding the homology of submanifolds with high confidence from random samples
• Towards persistence-based reconstruction in euclidean spaces
• Morse Theory. (AM-51)
• Hierarchical morse complexes for piecewise linear 2-manifolds
• Molecular shape analysis based upon the morse-smale complex and the connolly function
• Stability of persistence diagrams
• Proximity of persistence modules and their diagrams
• Persistence-based clustering in riemannian manifolds
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