DE BORTOLI, Valentin; DESOLNEUX, Agnès; GALERNE, Bruno; LECLAIRE, Arthur

doi:10.1051/ps/2020010

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DE BORTOLI, Valentin
CB - Centre Borelli - UMR 9010 [CB]

DESOLNEUX, Agnès
CB - Centre Borelli - UMR 9010 [CB]

GALERNE, Bruno
Institut Denis Poisson [IDP]

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ESAIM: Probability and Statistics. 2020, vol. Vol. 24, p. pp. 627-660

EDP Sciences

Résumé en anglais

We introduce and study a notion of spatial redundancy in Gaussian random fields. we define similarity functions with some properties and give insight about their statistical properties in the context of image processing. We compute these similarity functions on local windows in random fields defined over discrete or continuous domains. We give explicit asymptotic Gaussian expressions for the distribution of similarity function random variables when computed over Gaussian random fields and illustrate the weaknesses of such Gaussian approximations by showing that the approximated probability of rare events is not precise enough, even for large windows. In the special case of the squared L 2 norm, non-asymptotic expressions are derived in both discrete and continuous periodic settings. A fast and accurate approximation is introduced using eigenvalues projection and moment methods.< Réduire

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Random fields

spatial redundancy

central limit theorem

law of large numbers

eigenvalues approximation

moment methods

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REDUNDANCY IN GAUSSIAN RANDOM FIELDS

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