Visual sensitivity, blur and the sources of variability in the amplitude spectra of natural scenes

A number of researchers have suggested that in order to understand the response properties of cells in the visual pathway, we must consider the statistical structure of the natural environment. In this paper, we focus on one aspect of that structure, namely, the correlational structure which is described by the amplitude or power spectra of natural scenes. We propose that the principle insight one gains from considering the image spectra is in understanding the relative sensitivity of cells tuned to different spatial frequencies. This study employs a model in which the peak sensitivity is constant as a function of frequency with linear bandwith increasing (i.e., approximately constant in octaves). In such a model, the "response magnitude" (i.e., vector length) of cells increases as a function of their optimal (or central) spatial frequency out to about 20 cyc/deg. The result is a code in which the response to natural scenes, whose amplitude spectra typically fall as 1/f, is roughly constant out to 20 cyc/deg. An important consideration in evaluating this model of sensitivity is the fact that natural scenes show considerable variability in their amplitude spectra, with individual scenes showing falloffs which are often steeper or shallower than 1/f. Using a new measure of image structure (the "rectified contrast spectrum" or "RCS") on a set of calibrated natural images, it is shown that a large part of the variability in the spectra is due to differences in the sparseness of local structure at different scales. That is, an image which is "in focus" will have structure (e.g., edges) which has roughly the same magnitude across scale. That is, the loss of high frequency energy in some images is due to the reduction of the number of regions that contain structure rather than the amplitude of that structure. An "in focus" image will have structure (e.g., edges) across scale that have roughly equal magnitude but may vary in the area covered by structure. The slope of the RCS was found to provide a reasonable prediction of physical blur across a variety of scenes in spite of the variability in their amplitude spectra. It was also found to produce a good prediction of perceived blur as judged by human subjects.