Local correlations, information redundancy, and sufficient pixel depth in natural images

A mathematical framework that permits the factorization of a joint probability distribution into its localized components for a two-dimensional array of pixels is presented. The factorization was used to estimate the contribution to mutual information of two- (I2) and three-pixel (I3) luminance correlations for a large ensemble of natural images analyzed at various spatial scales and pixel depths b. It is shown that both I2 and I3 saturate at b approximately 6 bits per pixel. Three-pixel correlations are shown to produce only a marginal increase of information redundancy (4%) over two-pixel correlations (50%). Implications for neural representation in visual cortex are discussed.