Visual coding and the phase structure of natural scenes.

Although it is now well known that natural images display consistent statistical properties which distinguish them from random luminance distributions, this ecological approach to vision has so far concentrated on those second-order image statistics which are quantified by image power spectra, and it appears to be the image phase spectra which carry the majority of the image-intrinsic information. The present work describes how conventional nth-order statistics can be modified so that they are sensitive to image phase structure only. The modified measures are applied to an ensemble of natural images, and the results show that natural images do have consistent higher-order statistical properties which distinguish them from random-phase images with the same power spectra. An interpretation of this finding in terms of higher-order spectra suggests that these consistent properties arise from the ubiquity of edge structures in natural images, and raises the possibility that the properties of ideal relative-phase-sensitive mechanisms could be determined directly from analyses of the higher-order structure of natural scenes.