It has been suggested by Geisler (
1999) and Burr (
2000) that the “motion streaks” that result from movement and the “speed-lines” that artists use to depict motion are related to the curious streakiness or “flow” seen in the moiré patterns of overlaid random dots described by Glass (
1969). This work follows up these suggestions by analyzing the distortions of the power spectrum that occur when the image of a natural scene is moved. Because the visual system responds poorly to high temporal frequencies, movement introduces characteristic anisotropies; therefore, it is proposed that the streaky flow seen in Glass patterns results from activation of mechanisms that normally detect the distortions of the local power spectrum caused by motion. It is shown that the streaks can be abolished by adding noise that evens out the power spectrum of a Glass pattern, or opposite-polarity dot pairs that cancel out the autocorrelogram of same-polarity pairs. It is also shown that the orientation or direction of flow of the streaks is determined by the local power spectrum, rather than the phase component of their local Fourier transform. Finally, it is pointed out that the known properties of neurons in V1 would produce approximate representations of the local power spectrum (Hubel & Wiesel,
1962; Campbell & Robson,
1968; Maffei & Fiorentini,
1973; Movshon, Thompson, & Tolhurst,
1978), and that neurons in V4 have been described that would detect the types of pattern that result from optic flow (Gallant, Braun, & Van Essen,
1993; Gallant, Connor, Rackshit, Lewis, & Van Essen,
1996). Wilson and Wilkinson (
1998) proposed models of the mechanism underlying the detection of Glass patterns that would also respond to the patterns resulting from motion blur, and according to our hypothesis, this is their main functional role.
To examine this argument, we must first consider how the effective power spectrum of a natural image changes when it moves over the retina. We then discuss the auto-correlation functions and power spectra of Glass patterns, showing how these share characteristics with the power spectra of natural images blurred by movement. We also show that modifying these characteristics modifies the visibility of the patterns. Finally, we discuss the neural mechanisms that may bring about this analysis.