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arXiv · 1904.06428

Patch redundancy in images: a statistical testing framework and some applications

De Bortoli Valentin·Desolneux Agnès·Galerne Bruno·Leclaire Arthur
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Abstract

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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De Bortoli Valentin, Desolneux Agnès, Galerne Bruno, Leclaire Arthur. 2019-04-12. Patch redundancy in images: a statistical testing framework and some applications. https://arxiv.org/abs/1904.06428

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