  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.
