Date of this Version
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 characterization — barcodes. We sketch an application of these techniques to the classification of natural images.
Date Posted: 17 September 2009
This document has been peer reviewed.