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Article Dans Une Revue SIAM Journal on Imaging Sciences Année : 2019

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

Bruno Galerne
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Arthur Leclaire

Résumé

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.
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Dates et versions

hal-01931733 , version 1 (22-11-2018)
hal-01931733 , version 2 (30-04-2019)

Identifiants

Citer

Valentin de Bortoli, Agnès Desolneux, Bruno Galerne, Arthur Leclaire. PATCH REDUNDANCY IN IMAGES: A STATISTICAL TESTING FRAMEWORK AND SOME APPLICATIONS. SIAM Journal on Imaging Sciences, 2019, 12 (2), pp.893-926. ⟨10.1137/18M1228219⟩. ⟨hal-01931733v2⟩
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