Stable comparison of multidimensional persistent homology groups with torsion

DOI10.1007/s10440-012-9769-0zbMath1264.55005arXiv1012.4169OpenAlexW2125103385WikidataQ59442790 ScholiaQ59442790MaRDI QIDQ1947023

Patrizio Frosini

Publication date: 11 April 2013

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.4169

zbMATH Keywords

torsionpseudo-distancepersistent homologyshape comparisonmatching distance

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Other homology theories in algebraic topology (55N35)

Related Items

Metrics for generalized persistence modules

Cites Work

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• Finiteness of rank invariants of multidimensional persistent homology groups
• Stability of persistence diagrams
• Invitation to topological robotics
• Natural pseudo-distance and optimal matching between reduced size functions
• Lipschitz functions have \(L_{p}\)-stable persistence
• Natural pseudodistances between closed surfaces
• The theory of multidimensional persistence
• Size homotopy groups for computation of natural size distances
• On the use of size functions for shape analysis
• Topological persistence and simplification
• Coverage in sensor networks via persistent homology
• Betti numbers in multidimensional persistent homology are stable functions
• Natural pseudo-distances between closed curves
• One-dimensional reduction of multidimensional persistent homology
• Computing Multidimensional Persistence
• Topology for Computing
• Natural pseudodistances between closed manifolds
• Proximity of persistence modules and their diagrams
• PERSISTENCE BARCODES FOR SHAPES
• Barcodes: The persistent topology of data