Photoreceptors strongly attenuate high temporal frequencies. Hence when an image moves, high spatial frequency components are lost if their direction of modulation coincides with the direction of movement, but not if it is orthogonal. The power spectra of natural images are remarkably consistent in having a 1/f 2 falloff in power in all directions. For moving images, the spatial power spectra will be distorted by becoming steeper in the direction corresponding to modulation in the direction of motion, and the contours of equal power will tend to become elliptical. This study demonstrates that the mammalian visual system is specifically sensitive to such anisotropic changes of the local power spectrum, and it is suggested that these distortions are used to determine patterns of optic flow. Convergent evidence from work on Glass figures, motion streaks, and sensitivity to non-Cartesian gratings is called on in support of this interpretation, which has been foreshadowed in several recent publications.

*x*and

*y*directions. The full transform has two parts, the power spectrum formed by squaring and summing the sine and cosine coefficients at each locus in the

*X*,

*Y*frequency plane, and the phase spectrum, which is tan

^{−1}of the ratio of each pair of coefficients. Neither of these alone contains all the information in the Fourier transform and both are required to reconstruct the original picture accurately, but the phase spectrum is more critical for the overall visual appearance of a reconstituted image (Oppenheim & Lim, 1981; Piotrowski & Campbell, 1982), though there are exceptions (Tadmor & Tolhurst, 1993). By contrast, we shall show that the local power spectrum is important, and the phase spectrum unimportant, for the image characteristics we are concerned with here.

*ϑ*, and so the attenuations are obtained along lines corresponding to slower speeds (e.g., dashed line in Figure 2, left). The attenuations thus obtained for each spatial-frequency in the 2D-Fourier plane are then divided by the attenuations due to the spatial CSF at 0.1 HZ. This approximates the additional attenuation just due to motion (without the static portion of the CSF) and is shown in Figure 2 (right).

*mean*excitation of those orientation selective neurons that are aligned with the orientation of the Glass pairs, but it may result from increased

*variation*in the excitation of these neurons. To develop this insight further, consider the auto-correlation function of a Glass pattern, which can be deduced rather directly from the way they are made. Power spectra contain exactly the same information as auto-correlation functions and can be derived from them.

*L-L*

_{mean})/

*L*

_{mean}) of corresponding pixels in shifted and unshifted images, and summing the products over the whole image. This gives a figure proportional to the total number of coincidences between dot positions in shifted and unshifted figures. The center corresponds to zero shift, and the peak here is caused by every dot coinciding with itself, seed with seed and daughter with daughter, so each of the

*2N*dots coincides with itself and there are

*2N*coincidences. The peak down and to the right is caused by shifted seed coinciding with unshifted daughter, and the peak above and to the left by coincidence of unshifted seed with shifted daughter; each of these contributes N coincidences. Everywhere else there is a low and variable number of coincidences resulting from the shifts happening to correspond to the separations of dot pairs in the combined pattern. The number of these coincidences depends on the fraction of the available positions that is occupied by a dot, and half the expected number of accidental coincidences per position will be added to the N coincidences at each of the lesser peaks.