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

Valentin de Bortoli (1) , Agnès Desolneux (1) , Bruno Galerne (2) , Arthur Leclaire (3)

1 CMLA - Centre de Mathématiques et de Leurs Applications
2 IDP - Institut Denis Poisson
3 IMB - Institut de Mathématiques de Bordeaux

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.

Keywords: patch; redundancy; statistical framework; a contrario method; image denoising; texture; periodicity analysis

Domains: Statistics [stat]; Computer Vision and Pattern Recognition [cs.CV]; Image Processing [eess.IV]

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⟩