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

arXiv: https://arxiv.org/abs/1904.06428 · HTML: https://mlsanity.com/paper/1904.06428/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2019.

## Built on by (most cited first, 1 of 1)

- [DocEnTr: An End-to-End Document Image Enhancement Transformer](https://mlsanity.com/paper/2201.10252/) (2022)

## Abstract (arXiv)

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.