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

## TL;DR

This paper introduces a statistical testing framework to analyze local spatial redundancy in natural images, enabling applications like denoising, periodicity detection, and texture ranking through a fast algorithm.

## Contribution

The work develops a novel a contrario statistical model for patch similarity, providing a rigorous criterion for redundancy detection in images.

## Key findings

- Effective redundancy detection algorithm
- Applications in denoising and texture analysis
- Non-asymptotic probability expressions for similarity measures

## 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.