Introduction

Natural images have been shown to demonstrate enormous structural redundancy; this rinding has motivated the incorporation of statistical image models into computational theories of visual processing, producing a variety of candidate encoding strategies (Field, 1987; Sirovich and Kirby, 1987; Baddeley and Hancock, 1991). Many of these strategies effectively filter out predictable correlational structure so as to reduce directly or indirectly the dimensionality of the visual input. One advantage of such strategies is that if the image data can be encoded into a representation whose axes lie closer to the “natural” axes of the visual input, thresholding might produce a “sparse-distributed” representation, i.e. one which would show only sparse neural activity in response to an expected stimulus. Perhaps the best-documented support for such a strategy has come from work by D. J. Field (1987), who investigated the global 2-D amplitude spectra (averaged across all orientations) of an ensemble of natural images; he found that the amplitude falls off typically as the inverse of radial spatial frequency f, that is, the corresponding power spectra Ŝ(f) fall off as f-2. If visual signals with these properties were to be encoded by a bank of spatial-frequency-selective mechanisms or “channels” whose spatial-frequency bandwidths are constant in octaves, the outputs of each channel (Field, 1987) should exhibit similar energies (and therefore similar r.m.s. contrasts, since the channel outputs are assumed to have zero mean). The advantage of this so-called “scale invar-iance” is that by thresholding these channel outputs, a visual system can easily discount the “expected” struture of natural scenes.