Ghrist, Robert2023-05-222023-05-222008-01-012009-09-17https://repository.upenn.edu/handle/20.500.14332/34758This 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 characterization — barcodes. We sketch an application of these techniques to the classification of natural images.Article