title: On the second order spatiochromatic structure of natural images.
abstract: We provide a theoretical analysis of some empirical facts about the second order spatiochromatic structure of natural images in color. In particular, we show that two simple assumptions on the covariance matrices of color images yield eigenvectors made by the Kronecker product of Fourier features times the triad given by luminance plus color opponent channels. The first of these assumptions is second order stationarity while the second one is commutativity between color correlation matrices. The validity of these assumptions and the predicted shape of the PCA components of color images are experimentally observed on two large image databases. As a by-product of this experimental study, we also provide novel data to support an exponential decay law of the spatiochromatic covariance between pairs of pixels as a function of their spatial distance.
authors.affiliation: Laboratoire MAP5 (UMR CNRS 8145), Université Paris Descartes, Sorbonne Paris Cité, 45 rue des Saints Pères, 75006 Paris, France. Electronic address: edoardo.provenzi@parisdescartes.fr.
authors.forename: Edoardo
authors.initials: E
authors.lastname: Provenzi
authors.affiliation: Laboratoire MAP5 (UMR CNRS 8145), Université Paris Descartes, Sorbonne Paris Cité, 45 rue des Saints Pères, 75006 Paris, France. Electronic address: julie.delon@parisdescartes.fr.
authors.forename: Julie
authors.initials: J
authors.lastname: Delon
authors.affiliation: Télécom ParisTech, LTCI, CNRS, 46 rue Barrault, 75013 Paris, France. Electronic address: yann.gousseau@telecom-paristech.fr.
authors.forename: Yann
authors.initials: Y
authors.lastname: Gousseau
authors.affiliation: Télécom ParisTech, LTCI, CNRS, 46 rue Barrault, 75013 Paris, France. Electronic address: baptiste.mazin@telecom-paristech.fr.
authors.forename: Baptiste
authors.initials: B
authors.lastname: Mazin
mesh_terms: D055253:Color Vision / Q000502:physiology*; D006801:Humans; D015233:Models, Statistical; D010364:Pattern Recognition, Visual / Q000502:physiology*; D065855:Spatial Processing / Q000502:physiology*
keywords: Color images; Fourier basis; Natural image statistics; Opponent channels; Second order stationarity; Spatio-chromatic correlation