What The Statistics Of Natural Images Tell Us About Visual Coding

Why does the mammalian visual system represent information as it does? If we assume that visual systems have evolved to cope with the natural environment then we might expect the coding properties of the visual system to be related to the statistical structure of our environment. Indeed, images of the natural environment do not have random statistics. The first-order statistics (e.g., distribution of pixel values) and second-order statistics (e.g., power spectra) of natural images have been discussed previously and they bear important relations to visual coding. Statistics higher than second-order are difficult to measure but provide crucial information about the image. For example, it can be shown that the lines and edges found in natural images are a function of these higher-order statistics. In this paper, these higher-order statistics will be discussed in relation to the coding properties of the mammalian visual system. It is suggested that the spatial parameters of the cortical 'filters' (e.g., bandwidths of simple and complex cells) are closely related to these higher-order statistics. In particular, it will be shown that the spatial non-linearities shown by cortical complex cells provide the early visual system with the information required to learn about these statistics.