Estimating Multidimensional Persistent Homology Through a Finite Sampling

DOI10.1142/S0218195915500119zbMath1344.68255arXiv1507.05277OpenAlexW1529935654MaRDI QIDQ3459047

Massimo Ferri, N. Cavazza, Landi, Claudia

Publication date: 30 December 2015

Published in: International Journal of Computational Geometry & Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.05277

zbMATH Keywords

Voronoi diagrampersistent Betti numbersball coveringblind strip

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Other homology theories in algebraic topology (55N35) Algebraic topology on manifolds and differential topology (57R19)

Cites Work

• Stability of persistence diagrams
• The theory of multidimensional persistence
• The union of balls and its dual shape
• Finding the homology of submanifolds with high confidence from random samples
• Betti numbers in multidimensional persistent homology are stable functions
• Natural pseudo-distances between closed curves
• One-dimensional reduction of multidimensional persistent homology
• Topology and data
• Size functions and formal series

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