A Mayer-Vietoris formula for persistent homology with an application to shape recognition in the presence of occlusions

DOI10.1007/s10208-011-9100-xzbMath1231.55004OpenAlexW2168349010MaRDI QIDQ660672

Barbara Di Fabio, Landi, Claudia

Publication date: 4 February 2012

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10208-011-9100-x

zbMATH Keywords

Čech homologyMayer-Vietoris sequencepartial matchingpersistence diagramshape occlusion

Mathematics Subject Classification ID

Pattern recognition, speech recognition (68T10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Other homology theories in algebraic topology (55N35)

Related Items (10)

Rank-based persistence ⋮ Object-oriented persistent homology ⋮ A topological approach for protein classification ⋮ Filtrations induced by continuous functions ⋮ Multiscale persistent functions for biomolecular structure characterization ⋮ Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis ⋮ Necessary conditions for discontinuities of multidimensional persistent Betti numbers ⋮ Singular persistent homology with geometrically parallelizable computation ⋮ Evolutionary de Rham-Hodge method ⋮ Topological data analysis for the energy and stability of endohedral metallofullerenes

Cites Work

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• Stability of persistence diagrams
• Localized homology
• Natural pseudo-distance and optimal matching between reduced size functions
• Betti numbers in multidimensional persistent homology are stable functions
• Topology and data
• Size functions and formal series

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