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 spacetime-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, driftbalanced) 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 spacedomain problem of detecting orientation in a texture pattern.

For a patch of random visual texture embedded in a surrounding background of similar texture, we demonstrate that the perceived contrast of the texture patch depends substantially on the contrast of the background. When the texture patch is surrounded by high-contrast texture, the bright points of the texture patch appear dimmer, and simultaneously, its dark points appear less dark than when it is surrounded by a uniform background. The induced reduction of apparent contrast is greatly diminished when (i) the texture patch and background are filtered into nonoverlapping spatial frequency bands or (i) the texture patch and background are presented to different eyes. Our results are unanticipated by all current theories of lightness perception and point to a perceptual mechanism for contrast gain control occurring at an early cortical or precortical neural locus.Simultaneous Brightness Contrast. The perceived lightness of a uniformly ruminant disc viewed on a large uniform surrounding background depends not directly on the luminance of the disc, but rather on the ratio of disc luminance to background luminance (1-3). Even a spatially restricted background affects perceived lightness as illustrated by the illusion shown in Fig. 1 a and b. The discs in Fig. 1 a and b are equiluminant; nonetheless, the disc in a appears lighter than the disc in b. This phenomenon ofsimultaneous contrast is interpreted in terms of a ratio rule by noting that in a the ratio of the disc's luminance to background luminance is greater than 1; in b, the ratio is less than 1.Lateral Inhibition. A natural way to explain simultaneous contrast is in terms of lateral inhibition. Many models based on lateral inhibition have proposed that, at some level of visual processing, neurons strongly stimulated by the highintensity background of the disc in Fig. lb suppress the less strongly stimulated neurons responding to the interior of the disc. In Fig. la, the corresponding neurons within the disc receive no such inhibition from the weakly stimulated neurons surrounding them. Consequently, the neurons located within thet disc of Under the crudest lateral inhibition model, the lightness of a given point in the visual field would be suppressed in proportion to the intensity of each nearby point (1). But such a scheme would result, for example, in lower lightness values for points near the edge of the disc in Fig. lb than for points in its interior. The fact that both discs in Fig. 1 a and b appear to be of uniform lightness across their full expanse suggests a more complex form of lateral inhibition (4). Regardless of their details, all models that invoke the principle of lateral inhibition rest on the assumption that the primary factor determining the perceived lightness of either disc in Fig. 1 a or b is the ratio, at the disc edge, of disc luminance to background luminance. Induced Reduction of Apparent Contrast. We report here an apparent lightness phenomenon that is beyond the scope of all such models. The basic effect can be observed in a...

Individual cuttlefish, octopus and squid have the versatile capability to use body patterns for background matching and disruptive coloration. We define-qualitatively and quantitatively-the chief characteristics of the three major body pattern types used for camouflage by cephalopods: uniform and mottle patterns for background matching, and disruptive patterns that primarily enhance disruptiveness but aid background matching as well. There is great variation within each of the three body pattern types, but by defining their chief characteristics we lay the groundwork to test camouflage concepts by correlating background statistics with those of the body pattern. We describe at least three ways in which background matching can be achieved in cephalopods. Disruptive patterns in cuttlefish possess all four of the basic components of 'disruptiveness', supporting Cott's hypotheses, and we provide field examples of disruptive coloration in which the body pattern contrast exceeds that of the immediate surrounds. Based upon laboratory testing as well as thousands of images of camouflaged cephalopods in the field (a sample is provided on a web archive), we note that size, contrast and edges of background objects are key visual cues that guide cephalopod camouflage patterning. Mottle and disruptive patterns are frequently mixed, suggesting that background matching and disruptive mechanisms are often used in the same pattern.

We measured the just-noticeable difference (JND) in orientation variance between two textures (Figure 1) as we varied the baseline (pedestal) variance present in both textures. JND's first fell as pedestal variance increased and then rose, producing a 'dipper' function similar to those previously reported for contrast, blur, and orientation-contrast discriminations. A dipper function (both facilitation and masking) is predicted on purely statistical grounds by a noisy variance-discrimination mechanism. However, for two out of three observers, the dipper function was significantly better fit when the mechanism was made incapable of discriminating between small sample variances. We speculate that a threshold nonlinearity like this prevents the visual system from including its intrinsic noise in texture representations and suggest that similar thresholds prevent the visibility of other artifacts that sensory coding would otherwise introduce, such as blur.

Cuttlefish are cephalopod molluscs that achieve dynamic camouflage by rapidly extracting visual information from the background and neurally implementing an appropriate skin (or body) pattern. We investigated how cuttlefish body patterning responses are influenced by contrast and spatial scale by varying the contrast and the size of checkerboard backgrounds. We found that: (1) at high contrast levels, cuttlefish body patterning depended on check size; (2) for low contrast levels, body patterning was independent of "check" size; and (3) on the same check size, cuttlefish fine-tuned the contrast and fine structure of their body patterns, in response to small contrast changes in the background. Furthermore, we developed an objective, automated method of assessing cuttlefish camouflage patterns that quantitatively differentiated the three body patterns of uniform/stipple, mottle and disruptive. This study draws attention to the key roles played by background contrast and particle size in determining an effective camouflage pattern.