To some degree, all current models of visual motion-perception mechanisms depend on the power of the visual signal in various spatiotemporal-frequency bands. Here we show how to construct counterexamples: visual stimuli that are consistently perceived as obviously moving in a fixed direction yet for which Fourier-domain power analysis yields no systematic motion components in any given direction. We provide a general theoretical framework for investigating non-Fourier motion-perception mechanisms; central are the concepts of drift-balanced and microbalanced random stimuli. A random stimulus S is drift balanced if its expected power in the frequency domain is symmetric with respect to temporal frequency, that is, if the expected power in S of every drifting sinusoidal component is equal to the expected power of the sinusoid of the same spatial frequency, drifting at the same rate in the opposite direction. Additionally, S is microbalanced if the result WS of windowing S by any space-time-separable function W is drift balanced. We prove that (i) any space-time-separable random (or nonrandom) stimulus is microbalanced; (ii) any linear combination of pairwise independent microbalanced (respectively, drift-balanced) random stimuli is microbalanced and drift balanced if the expectation of each component is uniformly zero; (iii) the convolution of independent microbalanced and drift-balanced random stimuli is microbalanced and drift balanced; (iv) the product of independent microbalanced random stimuli is microbalanced; and (v) the expected response of any Reichardt detector to any microbalanced random stimulus is zero at every instant in time. Examples are provided of classes of microbalanced random stimuli that display consistent and compelling motion in one direction. All the results and examples from the domain of motion perception are transposable to the space-domain problem of detecting orientation in a texture pattern.

The finding that an item of type A pops out from an array of distractors of type B typically is taken to support the inference that human vision contains a neural mechanism that is activated by items of type A but not by items of type B. Such a mechanism might be expected to yield a neural image in which items of type A produce high activation and items of type B low (or zero) activation. Access to such a neural image might further be expected to enable accurate estimation of the centroid of an ensemble of items of type A intermixed with to-be-ignored items of type B. Here, it is shown that as the number of items in stimulus displays is increased, performance in estimating the centroids of horizontal (vertical) items amid vertical (horizontal) distractors degrades much more quickly and dramatically than does performance in estimating the centroids of white (black) items among black (white) distractors. Together with previous findings, these results suggest that, although human vision does possess bottom-up neural mechanisms sensitive to abrupt local changes in bar-orientation, and although human vision does possess and utilize top-down global attention filters capable of selecting multiple items of one brightness or of one color from among others, it cannot use a top-down global attention filter capable of selecting multiple bars of a given absolute orientation and filtering bars of the opposite orientation in a centroid task.