Power spectra of the natural input to the visual system

The efficient coding hypothesis posits that sensory systems are adapted to the regularities of their signal input so as to reduce redundancy in the resulting representations. It is therefore important to characterize the regularities of natural signals to gain insight into the processing of natural stimuli. While measurements of statistical regularity in vision have focused on photographic images of natural environments it has been much less investigated, how the specific imaging process embodied by the organism's eye induces statistical dependencies on the natural input to the visual system. This has allowed using the convenient assumption that natural image data are homogeneous across the visual field. Here we give up on this assumption and show how the imaging process in a human model eye influences the local statistics of the natural input to the visual system across the entire visual field. Artificial scenes with three-dimensional edge elements were generated and the influence of the imaging projection onto the back of a spherical model eye were quantified. These distributions show a strong radial influence of the imaging process on the resulting edge statistics with increasing eccentricity from the model fovea. This influence is further quantified through computation of the second order intensity statistics as a function of eccentricity from the center of projection using samples from the dead leaves image model. Using data from a naturalistic virtual environment, which allows generation of correctly projected images onto the model eye across the entire field of view, we quantified the second order dependencies as function of the position in the visual field using a new generalized parameterization of the power spectra. Finally, we compared this analysis with a commonly used natural image database, the van Hateren database, and show good agreement within the small field of view available in these photographic images. We conclude by providing a detailed quantitative analysis of the second order statistical dependencies of the natural input to the visual system across the visual field and demonstrating the importance of considering the influence of the sensory system on the statistical regularities of the input to the visual system.