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This article surveys recent work of 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 characterizationbarcodes. We sketch an application of these techniques to the classification of natural images.doi:10.1142/s021819590600204x fatcat:l32fdktzqjcxxa7alwc55exnhe