Statistical structure of natural 4×4 image patches

Abstract

The direct computation of natural image block statistics is unfeasible due to the huge domain space. In this paper we shall propose a procedure to collect block statistics on compressed versions of natural 4×4 patches. If the reconstructed blocks are close enough to the original ones, these statistics can clearly be quite representative of the true natural patch statistics. We shall work with a fractal image compression-inspired codebook scheme, in which we will compute for each block B its contrast σ, brightness μ and a normalized codebook approximation DB of (B-μ,)/σ. Entropy and mutual information estimates suggest a first order approximation p(B) ≃ p(D B)p(μ)p(σ) of the probabibility p(B) of a given natural block, while a more precise approximation can be written as p(B) ≃ p(D B)p(μ)p(σ)φ(||∇B||). We shall also study the structure of p(σ) and p(D), the more relevant probability components. The first one presents an exponential behavior for non flat patches, while p(D) behaves uniformly with respecto to volume in patch space. © Springer-Verlag 2004.