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- (<i>I</i><sub>2</sub>) and three-pixel (<i>I</i><sub>3</sub>) luminance correlations for a large ensemble of natural images analyzed at various spatial scales and pixel depths <i>b</i>. It is shown that both <i>I</i><sub>2</sub> and <i>I</i><sub>3</sub> saturate at b ~ 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.
© 2003 Optical Society of America
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(110.2960) Imaging systems : Image analysis
(200.3050) Optics in computing : Information processing
(330.4270) Vision, color, and visual optics : Vision system neurophysiology
Yury Petrov and L. Zhaoping, "Local correlations, information redundancy, and sufficient pixel depth in natural images," J. Opt. Soc. Am. A 20, 56-66 (2003)