Patch Redundancy in Images: A Statistical Testing Framework and Some Applications
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. To do so, we define an auto-similarity function which, given one image, computes a dissimilarity measurement between patches. 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 dissimilarity measurement is unlikely to happen in a background model. Choosing Gaussian random fields as background models, we derive nonasymptotic expressions for the probability distribution function of similarity measurements. We present an algorithm in order to assess redundancy in natural images and discuss applications in denoising, periodicity analysis, and texture ranking.
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© 2019, Society for Industrial and Applied Mathematics.
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Submitted: 21 November 2018
Accepted: 15 April 2019
Published online: 23 May 2019
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