Higher-order structure in natural scenes

Real-world visual scenes display consistent first- and second-order statist ical regularities to which visual neural representations may be perceptuall y matched, but these lower-order regularities stem from constraints on imag e power spectra, which appear to carry much less perceptual information tha n image phase spectra. Natural scenes are shown also to display consistent higher-order statistical regularities, and an analysis of these regularitie s in terms of fourth-order spectra shows that they are strongly dependent o n spatial frequency. These findings have important consequences for the des ign of a visual system that aims to maximize sparseness in neural represent ations. (C) 1999 Optical Society of America [S0740-3232(99)01207-7].