Patch redundancy in images: a statistical testing framework and some applications
This work addresses the challenge of analyzing local redundancy in images for applications in image processing, though it appears incremental as it builds on existing statistical methods.
The authors tackled the problem of quantifying spatial redundancy in natural images by developing a statistical testing framework based on similarity measurements between patches, using Gaussian random fields as a background model to derive non-asymptotic probability distributions, and applied it to tasks like denoising, periodicity analysis, and texture ranking.
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.