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Barcodes: the persistent topology of data. (English) Zbl 1391.55005
Summary: This article surveys recent work of G. Carlsson and collaborators on applications of computational algebraic topology to problems of feature detection and shape recognition in high-dimensional data. The primary mathematical tool considered is a homology theory for point-cloud data sets – persistent homology – and a novel representation of this algebraic characterization – barcodes. We sketch an application of these techniques to the classification of natural images.

MSC:
55N35 Other homology theories in algebraic topology
62H35 Image analysis in multivariate analysis
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
Software:
PLEX
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References:
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