Optical specification of time-to-passage: observers' sensitivity to global tau.

Despite its general mathematical formulation, most empirical work on the visual perception of tau (defined as a quantity divided by its temporal derivative) has focused on the case of direct approach, with tau defined as image angle/rate of expansion. Empirical investigators tend to generalize image size analyses to off-axis approaches. However, this generalization is inappropriate for all but a few classes of objects. After mathematically reestablishing the appropriate optical cues specifying time to passage for noncollision cases, we report a series of studies in which we examined observers' sensitivities to this information in both relative- and absolute-judgment paradigms. In general, we found observers' judgments to be accurate and robust.

Temporal factors in the discrimination of coherent motion.

When observers view the relative movements of a pair of bars defined by the difference of spatial Gaussian functions (DOGs), they can accurately discriminate coherent movements over a range of temporal frequencies and temporal asynchronies. Of particular interest is the fact that performance accuracy is maintained even when the two bars differ in spatial-frequency content and contrast. On each trial, observers viewed two brief presentation intervals in which a pair of vertically oriented DOGs moved randomly back and forth within a restricted range. During one observation interval, both elements moved in the same direction and by the same magnitude (correlated), and in the other interval, the movements were independent (uncorrelated). Temporal asynchronies were introduced by delaying the displacement of the right bar relative to that of the left bar in each interval. Observers were able to discriminate correlated versus uncorrelated movements up to a 45-60-msec temporal delay between the two elements' relative displacements. If motion processing is accomplished by mechanisms operating over multiple spatial and temporal scales, the visual system's tolerance of temporal delays among correlated signals may facilitate their space-time integration, thereby capitalizing on the perceptual utility of coherent-motion information for image segmentation and interpolating surface structure from the movements of spatially separated features.

The detectability of geometric structure in rapidly changing optical patterns.

Human vision is sensitive to the coherent structure and motion of simple dot patterns undergoing rapid random transformations, even when the component dots are widely separated spatially. A study is reported in which visual sensitivity to translations, rotations, expansions, pure shear, and additive combinations of these transformations was investigated. Observers discriminated between coherent (correlated) movements, in which all the component dots moved simultaneously in corresponding directions and distances, and incoherent (uncorrelated) movements, in which the movements of individual dots were statistically independent. In experiment 1 the accuracy of coherence discrimination was found to be similar for all four of the basic transformations and to increase linearly with the distance of the movements. The discriminability of coherent versus incoherent motion was also found to be similar to the detectability of any motion, suggesting that concurrent movements of individual dots are visually interrelated. In experiments 2 and 3 the visual independence of these four groups of transformations was tested by comparing the accuracy of coherence discrimination of each of the transformations presented alone with that when added to background motions produced by each of the four transformations. Coherence discriminations were less accurate when the target transformation was added to another background transformation, indicating that these transformations are not visually independent. Rotations and expansions, however, were visually independent. In experiment 3 qualitatively similar effects for patterns of several different sizes and dot densities were found. In general, an impressive visual sensitivity to globally coherent structure and motion under several different geometric transformations was observed in these experiments. A basic theoretical issue concerns the local visual mechanisms underlying this sensitivity.

The perception of mirror-reflected objects.

In what ways and under what conditions does an object appear to differ from its enantiomorph (its mirror reflection)? This 'mirror question' or its popular counterpart, "Why does a mirror reverse left and right but not up and down?" is frequently encountered, but an acceptable answer is not to be found in the literature. The question is approached as an experimental problem in visual psychophysics. A mirror optically reverses the axis perpendicular to its surface. What are the perceptual consequences of this stimulus transformation? This question is examined in four experiments by using stimuli of varying complexity and familiarity. Apparent reversals are demonstrated along right-left, front-back, top-bottom, and oblique axes, depending on the perceived asymmetries of the stimulus object. Perceived asymmetry is shown to depend both on structural asymmetries and on canonical axes and orientations defined by social convention. It is concluded that an object appears to differ from its enantiomorph by an apparent reversal along the axis of least perceived asymmetry. Implications for perceptual frames of reference and for the perception of symmetry are discussed.

Detection and discrimination of coherent motion.

When viewing a pair of bars defined by the difference of spatial Gaussian functions (DOGs), human observers can discriminate accurately the relative movements of the bars, even when they differ in spatial frequency. On each trial, observers viewed two brief presentation intervals in which a pair of vertically oriented DOGs moved randomly back and forth within a restricted range. During one interval, both bars moved in the same horizontal direction and by the same magnitude (correlated movements); in the other interval, their movements were uncorrelated. When discrimination accuracy is related to the simultaneous detection of two independent movements, it was found that, if observers can detect the movements of spatially separated bars, they can tell whether their relative movements are correlated. Performance remained remarkably accurate even when the two bars differed in spatial frequency by more than two octaves or were presented separately to the two eyes. Apparently, the accurate discrimination of coherent motion involves an efficient spatial integration of optical motion information over multiple spatial locations and multiple spatial scales.

Static depth cues do affect the perceived direction of motion.

Models of motion perception usually assume that the visual system references spatial displacements to retinal coordinates, and not to three-dimensional coordinates recovered by a parallel process. The present studies investigated whether moving elements viewed in the context of a static random-dot stereogram could lead to the appearance of motion in depth. Observers judged the velocity of a monocular element translating horizontally in the stereo context as 'same as' or 'different to' that of a standard. Based on velocity constancy, if there was apparent motion in depth, the relative velocity judgments would yield a predictable pattern of errors. The first experiment compared two stereo contexts: a sloped surface versus a fronto-parallel plane at zero disparity. The results indicated an overall increase in the perceived velocity of the element moving in the sloped surface context. A similar pattern of results was found when surfaces differing in incline were compared. Experiment 2 explored the case of fronto-parallel planes at crossed and uncrossed disparities. Here depth differences did not systematically affect observers' judgments. It was concluded that in some cases motion analysis can be affected by three-dimensional disparity information and not by angular displacement alone.