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

doi:10.1137/18M1228219

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DE BORTOLI, Valentin
Centre de Mathématiques et de Leurs Applications [CMLA]

DESOLNEUX, Agnès
Centre de Mathématiques et de Leurs Applications [CMLA]

GALERNE, Bruno
Institut Denis Poisson [IDP]

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SIAM Journal on Imaging Sciences. 2019, vol. 12, n° 2, p. 893-926

Society for Industrial and Applied Mathematics

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In this work we introduce a statistical framework in order to analyze the spatial redundancy in natural images. This notion of spatial redundancy must be defined locally and thus we give some examples of functions (auto-similarity and template similarity) which, given one or two images, computes a similarity measurement between patches. Two patches are said to be similar if the similarity measurement is small enough. To derive a criterion for taking a decision on the similarity between two patches we present an a contrario model. Namely, two patches are said to be similar if the associated similarity measurement is unlikely to happen in a background model. Choosing Gaussian random fields as background models we derive non-asymptotic expressions for the probability distribution function of similarity measurements. We introduce a fast algorithm in order to assess redundancy in natural images and present applications in denoising, periodicity analysis and texture ranking.< Réduire

Mots clés en anglais

patch

redundancy

statistical framework

a contrario method

image denoising

texture

periodicity analysis

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PATCH REDUNDANCY IN IMAGES: A STATISTICAL TESTING FRAMEWORK AND SOME APPLICATIONS

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