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Visual perception involves spatially and temporally coordinated variations in diverse physical systems: environmental surfaces and symbols, optical images, electro-chemical activity in neural networks, muscles, and bodily movements-each with a distinctly different material structure and energy. The fundamental problem in the theory of perception is to characterize the information that enables both perceptual awareness and real-time dynamic coordination of these diverse physical systems. Gibson's psychophysical and ecological conception of this problem differed from that of mainstream science both then and now. The present article aims to incorporate Gibson's ideas within a general conception of information for visual perception. We emphasize the essential role of spatiotemporal form, in contrast with symbolic information. We consider contemporary understanding of surface structure, optical images, and optic flow. Finally, we consider recent evidence about capacity limitations on the rate of visual perception and implications for the ecology of vision., Competing Interests: Declaration of Conflicting Interests: The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article., (© The Author(s) 2021.)

This study investigated effects of divided attention on the temporal processes of perception. During continuous watch periods, observers responded to sudden changes in the color or direction of any one of a set of moving objects. The set size of moving objects was a primary variable. A simple detection task required responses to any display change, and a selective task required responses to a subset of the changes. Detection rates at successive points in time were measured by response time (RT) hazard functions.The principal finding was that increasing the set size divided the detection rates-and these divisive effects were essentially constant over time and over the time-varying influence of the target signals and response tasks. The set size, visual target signal, and response task exerted mutually invariant influence on detection rates at given times, indicating independent joint contributions of parallel component processes. The lawful structure of these effects was measured by RT hazard functions but not by RTs as such. The results generalized the time-invariant divisive effects of set size on visual process rates found by Lappin, Morse, & Seiffert (Attention, Perception, & Psychophysics, 78, 2469-2493, 2016). These findings suggest that the rate of visual perception has a limiting channel capacity.

In some cases, people overestimate how much they can see. This can produce a metacognitive blind spot that may lead participants to devote fewer cognitive resources than a visual task demands. However, little research has tested whether individuals who are particularly optimistic about their visual capabilities are susceptible to poor visual performance. We tested whether optimistic metacognitive judgments would predict poor performance in a visual task, especially when it placed a large attentional load on the participant, and when it required balancing between multiple sources of information. We tested participants in a simplified battle command simulation in which they were asked to detect visual changes. Participants who predicted spatially expansive visual attention performance performed more poorly in the change detection task when the task required tracking larger numbers of aircraft, and when it included a secondary change-list display., (Copyright © 2019. Published by Elsevier Inc.)

Segregation of objects from their backgrounds is a fundamental visual function and one that is particularly effective when objects are in motion. Theoretically, suppressive center-surround mechanisms are well suited for accomplishing motion segregation. This longstanding hypothesis, however, has received limited empirical support. We report converging correlational and causal evidence that spatial suppression of background motion signals is critical for rapid segmentation of moving objects. Motion segregation ability is strongly predicted by both individual and stimulus-driven variations in spatial suppression strength. Moreover, aging-related superiority in perceiving background motion is associated with profound impairments in motion segregation. This segregation deficit is alleviated via perceptual learning, but only when motion segregation training also causes decreased sensitivity to background motion. We argue that perceptual insensitivity to large moving stimuli effectively implements background subtraction, which, in turn, enhances the visibility of moving objects and accounts for the observed link between spatial suppression and motion segregation.

Under optimal conditions, just 3-6 ms of visual stimulation suffices for humans to see motion. Motion perception on this timescale implies that the visual system under these conditions reliably encodes, transmits, and processes neural signals with near-millisecond precision. Motivated by in vitro evidence for high temporal precision of motion signals in the primate retina, we investigated how neuronal and perceptual limits of motion encoding relate. Specifically, we examined the correspondence between the time scale at which cat retinal ganglion cells in vivo represent motion information and temporal thresholds for human motion discrimination. The timescale for motion encoding by ganglion cells ranged from 4.6 to 91 ms, and depended non-linearly on temporal frequency, but not on contrast. Human psychophysics revealed that minimal stimulus durations required for perceiving motion direction were similarly brief, 5.6-65 ms, and similarly depended on temporal frequency but, above ~10%, not on contrast. Notably, physiological and psychophysical measurements corresponded closely throughout ( r = 0.99), despite more than a 20-fold variation in both human thresholds and optimal timescales for motion encoding in the retina. The match in absolute values of the neurophysiological and psychophysical data may be taken to indicate that from the lateral geniculate nucleus (LGN) through to the level of perception little temporal precision is lost. However, we also show that integrating responses from multiple neurons can improve temporal resolution, and this potential trade-off between spatial and temporal resolution would allow for loss of temporal resolution after the LGN. While the extent of neuronal integration cannot be determined from either our human psychophysical or neurophysiological experiments and its contribution to the measured temporal resolution is unknown, our results demonstrate a striking similarity in stimulus dependence between the temporal fidelity established in the retina and the temporal limits of human motion discrimination.

A towering figure in experimental psychology, Charles W. Eriksen, passed away in February this year. "Erik" made extensive original and lasting contributions to both research methods and theories in several areas of psychology, especially involving visual information processing. His research exhibited consistent concerns with experimental methods for distinguishing among alternative explanations and distinguishing perception from behavior. Erik pioneered many research methods now in common use-including converging operations, visual search, rapid serial presentations, the stop-signal paradigm, temporal integration in form perception, spatial cues for guiding selective attention, and the flankers task. He also introduced and tested many theories of selective attention. Erik was the founding editor of Perception & Psychophysics, and served for 23 years as its principal editor. An impressive and unforgettable person, Erik was a compelling personification of "the greatest generation."

Visual function demands coordinated responses to information over a wide field of view, involving both central and peripheral vision. Visually impaired individuals often seem to underutilize peripheral vision, even in absence of obvious peripheral deficits. Motivated by perceptual training studies with typically sighted adults, we examined the effectiveness of perceptual training in improving peripheral perception of visually impaired youth. Here, we evaluated the effectiveness of three training regimens: (1) an action video game, (2) a psychophysical task that combined attentional tracking with a spatially and temporally unpredictable motion discrimination task, and (3) a control video game. Training with both the action video game and modified attentional tracking yielded improvements in visual performance. Training effects were generally larger in the far periphery and appear to be stable 12 months after training. These results indicate that peripheral perception might be under-utilized by visually impaired youth and that this underutilization can be improved with only ~8 hours of perceptual training. Moreover, the similarity of improvements following attentional tracking and action video-game training suggest that well-documented effects of action video-game training might be due to the sustained deployment of attention to multiple dynamic targets while concurrently requiring rapid attending and perception of unpredictable events., Competing Interests: J.N. is the founder of Neurotrainer. D.T. is an uncompensated scientific advisor for Neurotrainer. R.Z. and J. L. declare no competing financial interests.

If attention is distributed among multiple moving objects, how does this divided attention affect the temporal process for detecting a specific target motion? Well-trained observers in three experiments monitored ongoing random motions of multiple objects, trying to rapidly detect non-random target motions. Response time hazard rates revealed a simple lawful structure of the detection processes. Target detection rates (hazard rates, in bits /s) were inversely proportional to the number of observed objects. Detection rates at any response time and in any condition equaled a product of two parallel (functionally independent and concurrent) visual processes: visual awareness and motion integration. The rate of visual awareness was inversely proportional to Set Size (n = 1-12), constant over time, and invariant with integrated motion information. Thus, a single rate parameter, indicating a constant channel capacity of visual awareness, described detection rates over a wide range of conditions and response times. During an initial interval of roughly 0.5 s, detection rates increased proportionally with the duration and length of motion; but after this initial integration, detection rates were constant, independent of the time the target remained undetected. The relationship between the quantity of visual information and detection rates was simpler than anticipated by contemporary theories of attention, perception, and performance.

What are the geometric primitives of binocular disparity? The Venetian blind effect and other converging lines of evidence indicate that stereoscopic depth perception derives from disparities of higher-order structure in images of surfaces. Image structure entails spatial variations of intensity, texture, and motion, jointly structured by observed surfaces. The spatial structure of binocular disparity corresponds to the spatial structure of surfaces. Independent spatial coordinates are not necessary for stereoscopic vision. Stereopsis is highly sensitive to structural disparities associated with local surface shape. Disparate positions on retinal anatomy are neither necessary nor sufficient for stereopsis.

Purpose: Effects of low vision on peripheral visual function are poorly understood, especially in children whose visual skills are still developing. The aim of this study was to measure both central and peripheral visual functions in youths with typical and low vision. Of specific interest was the extent to which measures of foveal function predict performance of peripheral tasks., Methods: We assessed central and peripheral visual functions in youths with typical vision (n = 7, ages 10-17) and low vision (n = 24, ages 9-18). Experimental measures used both static and moving stimuli and included visual crowding, visual search, motion acuity, motion direction discrimination, and multitarget motion comparison., Results: In most tasks, visual function was impaired in youths with low vision. Substantial differences, however, were found both between participant groups and, importantly, across different tasks within participant groups. Foveal visual acuity was a modest predictor of peripheral form vision and motion sensitivity in either the central or peripheral field. Despite exhibiting normal motion discriminations in fovea, motion sensitivity of youths with low vision deteriorated in the periphery. This contrasted with typically sighted participants, who showed improved motion sensitivity with increasing eccentricity. Visual search was greatly impaired in youths with low vision., Conclusions: Our results reveal a complex pattern of visual deficits in peripheral vision and indicate a significant role of attentional mechanisms in observed impairments. These deficits were not adequately captured by measures of foveal function, arguing for the importance of independently assessing peripheral visual function.

How do retinal images lead to perceived environmental objects? Vision involves a series of spatial and material transformations--from environmental objects to retinal images, to neurophysiological patterns, and finally to perceptual experience and action. A rationale for understanding functional relations among these physically different systems occurred to Gustav Fechner: Differences in sensation correspond to differences in physical stimulation. The concept of information is similar: Relationships in one system may correspond to, and thus represent, those in another. Criteria for identifying and evaluating information include (a) resolution, or the precision of correspondence; (b) uncertainty about which input (output) produced a given output (input); and (c) invariance, or the preservation of correspondence under transformations of input and output. We apply this framework to psychophysical evidence to identify visual information for perceiving surfaces. The elementary spatial structure shared by objects and images is the second-order differential structure of local surface shape. Experiments have shown that human vision is directly sensitive to this higher-order spatial information from interimage disparities (stereopsis and motion parallax), boundary contours, texture, shading, and combined variables. Psychophysical evidence contradicts other common ideas about retinal information for spatial vision and object perception.

Characterizing the temporal limits of the human visual system has long been a central goal of vision research. Spanning three centuries of research, temporal order judgments have been used to estimate the temporal precision of visual processing, with nearly all the research focusing on onset asynchrony discriminations. Recent neurophysiological work, however, demonstrated that neural latencies for stimulus offsets are shorter and less variable than those following event onsets, suggesting that event offsets might provide more reliable timing cues to the visual system than event onsets. Here, we tested this hypothesis by measuring psychophysical thresholds for discriminating onset and offset asynchronies for both stationary and moving stimuli. In three experiments, we showed that offset asynchrony thresholds were indeed consistently lower and were less affected by stimulus variations than onset asynchrony thresholds. These findings are consistent with neurophysiology and suggest a possible role of offset signals as reliable timing references for visual events., (Copyright 2010 Elsevier Ltd. All rights reserved.)

The issue of the existence of planes-understood as the carriers of a nexus of straight lines-in the monocular visual space of a stationary human observer has never been addressed. The most recent empirical data apply to binocular visual space and date from the 1960s (Foley, 1964). This appears to be both the first and the last time this basic issue was addressed empirically. Yet the question is of considerable conceptual interest. Here we report on a direct empirical test of the existence of planes in monocular visual space for a group of sixteen experienced observers. For the majority of these observers monocular visual space lacks a projective structure, albeit in qualitatively different ways. This greatly reduces the set of viable geometrical models. For example, it rules out all the classical homogeneous spaces (the Cayley-Klein geometries) such as the familiar Luneburg model. The qualitatively different behavior of experienced observers implies that the generic population might well be inhomogeneous with respect to the structure of visual space., (Copyright 2009 Elsevier B.V. All rights reserved.)

We evaluated spatial displacement and temporal duration thresholds for discriminating the motion direction of gratings for a broad range of speeds (0.06 degrees/s to 30 degrees/s) in fovea and at +/-30 degrees eccentricity. In general, increased speed yielded lower duration thresholds but higher displacement thresholds. In most conditions, these effects of speed were comparable in fovea and periphery, yielding relatively similar thresholds not correlated with decreased peripheral acuity. The noteworthy exceptions were interactive effects at slow speeds: (1) Displacement thresholds for peripheral motion were affected by acuity limits for speeds below 0.5 degrees/s. (2) Low-vision observers with congenital nystagmus had elevated thresholds for peripheral motion and slow foveal motion but resembled typically sighted observers for foveal motions at speeds above 1 degree/s. (3) Suppressive center-surround interactions were absent below 0.5 degrees/s and their strength increased with speed. Overall, these results indicate qualitatively different sensitivities to slow and fast motions. Thresholds for very slow motion are limited by spatial resolution, while thresholds for fast motion are probably limited by temporal resolution.

Segregation of objects from their backgrounds is one of vision's most important tasks and one that is accomplished with ease. It is often hypothesized that suppressive center-surround receptive field interactions represent a key neural substrate underlying efficient figure-ground segregation, yet this intuitively appealing hypothesis has received very little experimental support. Using the motion aftereffect as an experimental tool, we explored this hypothesis by examining how surround suppression was affected by contextual manipulations that altered the perceived figure-ground relations but kept local motion signals unchanged. The results demonstrated that surround suppression was strong when the visual context implied a large moving field. On the other hand, when the contextual interpretation was consistent with a smaller moving object, surround suppression was greatly reduced. These findings are consistent with the notion that center-surround interactions play a role in segregating moving objects from backgrounds.

Schizophrenia is often accompanied by a range of visual perception deficits, with many involving impairments in motion perception. The presence of perceptual abnormalities may impair neural processes that depend on normal visual analysis, which in turn may affect overall functioning in dynamic visual environments. Here, we examine the integrity of suppressive center-surround mechanisms in motion perception of schizophrenic patients. Center-surround suppression has been implicated in a range of visual functions, including figure-ground segregation and pursuit eye movements, visual functions that are impaired in schizophrenia. In control subjects, evidence of center-surround suppression is found in a reduced ability to perceive motion of a high-contrast stimulus as its size increases. This counterintuitive finding is likely a perceptual correlate of center-surround mechanisms in cortical area MT. We now show that schizophrenic patients exhibit abnormally weak center-surround suppression in motion, an abnormality that is most pronounced in patients with severe negative symptoms. Interestingly, patients with the weakest surround suppression outperformed control subjects in motion discriminations of large high-contrast stimuli. This enhanced motion perception of large high-contrast stimuli is consistent with an MT abnormality in schizophrenia and has a potential to disrupt smooth pursuit eye movements and other visual functions that depend on unimpaired center-surround interactions in motion.

What properties determine visually perceived space? We discovered that the perceived relative distances of familiar objects in natural settings depended in unexpected ways onthe surrounding visual field. Observers bisected egocentric distances in a lobby, in a hallway, and on an open lawn. Three key findings were the following: (1) Perceived midpoints were too far from the observer, which is the opposite of the common foreshortening effect. (2) This antiforeshortening constant error depended on the environmental setting--greatest in the lobby and hall but nonsignificant on the lawn. (3) Context also affected distance discrimination; variability was greater in the hall than in the lobby or on the lawn. A second experiment replicated these findings, using a method of constant stimuli. Evidently, both the accuracy and the precision of perceived distance depend on subtle properties of the surrounding environment.

Center-surround interactions are a key property of visual motion mechanisms. Using a temporal reverse correlation method with human observers, we investigated perceptual interactions between a brief center motion (approximately 20 ms) and a surround that moved up-down with a new direction chosen randomly every 5 ms. The aim was to reveal interactions between center and surround motions and their dependency on relative direction, contrast, and timing. Hypothesizing that surround computation involves different neural circuitry than the center response, we manipulated surround contrast to affect the relative timing of center and surround signals. The reverse correlation analysis yielded temporal profiles of surround influence indicating, in 5 ms steps, the time course of the effect of the surround on the discriminability of center motion. The resulting temporal profiles varied systematically with contrast: as surround contrast decreased, both the latency and duration of its influence increased. This finding, consistent with longer and variable neural response latencies at low contrast, psychophysically reveals fine-scale temporal interactions between center and surround signals. Additionally, the strength of surround influence was correlated with psychophysical thresholds for discriminating center motion. The directionality of this relationship, however, depended only on center contrast. When center motion was high contrast, poor direction discrimination was associated with an increased probability of same-direction surround motions. Low-contrast center motion, however, was more discriminable when surrounded by motion in the same direction, regardless of surround contrast. This suggests that the previously reported adaptive nature of center-surround interactions in motion is driven primarily by the visibility of the center motion signals.

Visual patterns have widely varying contrasts and elicit local signals of varying reliability, ranging from noisy to relatively noise-free. One way to deal efficiently with the variable visual input is to employ flexible neural mechanisms that adapt to changing conditions. We investigated whether the spatial properties of motion mechanisms change with stimulus contrast and found that the optimal size for perceiving motion decreases with increasing contrast. These data were well-described by a model in which spatial summation increases with decreasing contrast.

The ability of observers to perceive three-dimensional (3-D) distances or lengths along intrinsically curved surfaces was investigated in three experiments. Three physically curved surfaces were used: convex and/or concave hemispheres (Experiments 1 and 3) and a hyperbolic paraboloid (Experiment 2). The first two experiments employed a visual length-matching task, but in the final experiment the observers estimated the surface lengths motorically by varying the separation between their two index fingers. In general, the observers' judgments of surface length in both tasks (perceptual vs. motoric matching) were very precise but were not necessarily accurate. Large individual differences (overestimation, underestimation, etc.) in the perception of length occurred. There were also significant effects of viewing distance, type of surface, and orientation of the spatial intervals on the observers' judgments of surface length. The individual differences and failures of perceptual constancy that were obtained indicate that there is no single relationship between physical and perceived distances on 3-D surfaces that is consistent across observers.

Centre-surround receptive field organization is a ubiquitous property in mammalian visual systems, presumably tailored for extracting image features that are differentially distributed over space. In visual motion, this is evident as antagonistic interactions between centre and surround regions of the receptive fields of many direction-selective neurons in visual cortex. In a series of psychophysical experiments we make the counterintuitive observation that increasing the size of a high-contrast moving pattern renders its direction of motion more difficult to perceive and reduces its effectiveness as an adaptation stimulus. We propose that this is a perceptual correlate of centre-surround antagonism, possibly within a population of neurons in the middle temporal visual area. The spatial antagonism of motion signals observed at high contrast gives way to spatial summation as contrast decreases. Evidently, integration of motion signals over space depends crucially on the visibility of those signals, thereby allowing the visual system to register motion information efficiently and adaptively.

We use an exocentric pointing task to study exocentric visual directions to targets that are opposite to a pointer relative to the observer. (The apparent distance between the target and the pointer always exceeded 90 degrees of visual angle.) All pointing takes place in the horizontal plane at eye height. Observers could not see both target and pointer at a single glance. They had to look back and forth between them, using combinations of eye movements, head turns, twists at the waist and turning on the feet. In the limit of diametrically opposite targets we find that the observers pick either one of two distinct orientations of the pointer as equally "visually correct". Which one results depends on the stance assumed by the observer. The difference between the two equally acceptable pointings is between 5 degrees and 10 degrees. Such a result is predicted from earlier measurements in the context of a model that describes the geometry of the horizon as a Riemannian space with varying intrinsic curvature. The present results thus fit--perhaps surprisingly--very well in such a picture., (Copyright 2002 Elsevier Science B.V.)

Vision requires a reference frame. To what extent does this reference frame depend on the structure of the visual input, rather than just on retinal landmarks? This question is particularly relevant to the perception of dynamic scenes, when keeping track of external motion relative to the retina is difficult. We tested human subjects' ability to discriminate the motion and temporal coherence of changing elements that were embedded in global patterns and whose perceptual organization was manipulated in a way that caused only minor changes to the retinal image. Coherence discriminations were always better when local elements were perceived to be organized as a global moving form than when they were perceived to be unorganized, individually moving entities. Our results indicate that perceived form influences the neural representation of its component features, and from this, we propose a new method for studying perceptual organization.

Detection thresholds were compared for moving and stationary oscillations with equivalent contrast changes. Motion was more detectable than stationary oscillation, and the difference increased with size of the feature (a Gaussian blob). Phase discriminations between a center and two flanking features were much better for motion than for stationary oscillation. Motion phase discriminations were similar to motion detection and were robust over increases in spatial separation and temporal frequency, but not so for stationary oscillations. Separate visual motion signals were positively correlated, but visual signals for stationary oscillation were negatively correlated. Evidently, motion produces visually coherent changes in image structure, but stationary contrast oscillation does not.

We determined the curvature of apparent frontoparallels in a natural scene (a large lawn in broad daylight). Data on frontoparallels in these conditions are very sparse and reveal idiosyncratic curvatures of frontoparallels and irregular variation with distance. We used a method of bisection of linear segments indicated through pairs of stakes at angular separations (from the vantage point) of up to 120 deg. Distances of 2 m and 10 m (in the forward direction) were used. The bisection was carried out by the observer through maneuvering a radio-controlled vehicle carrying a third stake. Four observers participated in the experiment; they had no problems with the task and yielded mutually consistent results. We found that the frontoparallels are significantly curved and are concave towards the observer. Surprisingly, the sign of the curvature is opposite to that found when the frontoparallels are defined through an exocentric pointing task. Available theory (Luneburg's) does not predict this, but the theory is hardly applicable to the case of vision in natural scenes. This interesting discrepancy has not been reported before.

Oscillation thresholds were evaluated for detecting motion and discriminating relative motion. Three horizontally aligned Gaussian blobs oscillated horizontally, with the center in-phase or out-of-phase with the two flankers. Motion thresholds were well below those for static bisection, and involved small contrast changes (<0.25%). Remarkably, acuity was better for discriminating phase relations than for detecting rigid motion, averaging 8.7 and 11.0 arcsec, respectively, for 100 arcmin between blobs. Phase discrimination acuities were robust over separations of 20-320 arcmin and temporal frequencies of 1.5-6 Hz. Motion phase relations must be coherent among spatially separate retinal signals, carrying information about intrinsic image structure.

In three experiments, observers judged the apparent extents of spatial intervals along the surface of a curved cylinder or a flat plane that was binocularly viewed in a natural, indoor environment. The observers' judgments of surface lengths were precise and reliable but were also inaccurate and subject to relatively large constant errors. These distortions differed among the observers, but they tended to perceive lengths oriented along the curved dimension of the cylinder as being longer than physically equivalent lengths in the noncurved dimension. This phenomenon did not occur when the observers judged curved and noncurved paths on the flat surface. In addition, some observers' judgments of length were affected by changes in the distance to the cylinder, whereas others were affected by the cylinder's orientation in space. These results demonstrate that the perception of length on surfaces is highly dependent on the particular context in which the length occurs.

We consider the horizontal plane at eye height, that is all objects seen at the horizon. Although this plane visually degenerates into a line in the visual field, the 'depth' dimension nevertheless gives it a two-dimensional structure. We address the problem of intrinsic curvature of this plane. The classical geometric method is based on Gauss's original definition: The angular excess in a triangle equals the integral curvature over the area of the triangle. Angles were directly measured by a novel method of exocentric pointing. Experiments were performed outside, in the natural environment, under natural viewing conditions. The observers were instructed not to move from a set location and to maintain eye height, but were otherwise free to perform eye, head, and body movements. We measured the angular excess for equilateral triangles with sides of 2-20 m, the vantage position at the barycenter. We found angular excesses and deficits of up to 30 degrees. From these data we constructed the metric. The curvature changes from elliptic in near space to hyperbolic in far space. At very large distances the plane becomes parabolic.

Vision is based on spatial correspondences between physically different structures--in environment, retina, brain, and perception. An examination of the correspondence between environmental surfaces and their retinal images showed that this consists of 2-dimensional 2nd-order differential structure (effectively 4th-order) associated with local surface shape, suggesting that this might be a primitive form of spatial information. Next, experiments on hyperacuities for detecting relative motion and binocular disparity among separated image features showed that spatial positions are visually specified by the surrounding optical pattern rather than by retinal coordinates, minimally affected by random image perturbations produced by 3-D object motions. Retinal image space, therefore, involves 4th-order differential structure. This primitive spatial structure constitutes information about local surface shape.

Observers viewed the optical flow field of a rotating quadric surface patch and were required to match its perceived structure by adjusting the shape of a stereoscopically presented surface. In Experiment 1, the flow fields included rigid object rotations and constant flow fields with patterns of image acceleration that had no possible rigid interpretation. In performing their matches, observers had independent control of two parameters that determined the surface shape. One of these, called the shape characteristic, is defined as the ratio of the two principle curvatures and is independent of object size. The other, called curvedness, is defined as the sum of the squared principle curvatures and depends on the size of the object. Adjustments of shape characteristic were almost perfectly accurate for both motion conditions. Adjustments of curvedness, on the other hand, were systematically over-estimated and were not highly correlated with the simulated curvedness of the depicted surface patch. In Experiment 2, the same flow fields were masked with a global pattern of curl, divergence, or shear, which disrupted the first-order spatial derivatives of the image velocity field, while leaving the second-order spatial derivatives invariant. The addition of these masks had only negligible effects on observers' performance. These findings suggest that observers' judgments of three-dimensional surface shape from motion are primarily determined by the second-order spatial derivatives of the instantaneous field of image displacements.

Stereoacuity experiments tested definitions of binocularly disparate spatial positions by perturbing the binocular correspondence of the two half-images. Dichoptic translations perturbed zero-order retinal positions; expansions perturbed first-order horizontal separations; rotations perturbed first-order orientations; and anisotropic expansions deformed first-order two-dimensional (2D) structure. Each transformation perturbed relative positions in the two half-images by more than 100 arcsec, but stereoacuity thresholds remained about 10 arcsec. Binocular disparity involves second-order 2D differential structure of the monocular half-images, specifying local surface shape. Stereoacuity is much better than nonstereo acuity, suggesting that monocular spatial signals are binocularly correlated.

Pictorial relief was measured for a series of pictures of a smooth solid object. The scene was geometrically identical (ie the perspective of the three-dimensional scene remained the same) for all pictures, the rendering different. Some of the pictures were monochrome full-scale photographs taken under different illumination of the scene. Also included were a silhouette (uniform black on uniform white) and a 'cartoon'-style rendering (visual contour and key linear features rendered in thin black line on a uniform white ground). Two subjects were naive and started with the silhouette, saw the cartoon next, and finally the full-scale photographs. Another subject had seen the object and did the experiment in the opposite sequence. The silhouette rendering is impoverished, but has considerable relief with much of the basic shape. The cartoon rendering yields well-developed pictorial relief, even for the naive subjects. Shading adds only small local details, but different illumination produces significant alterations of relief. It is concluded that shape constancy under changes in illumination is dominant throughout, but that the (small) deviations from true constancy reveal the effect of cues such as shading in a natural setting. Such a ¿perturbation analysis' appears more promising than either stimulus-reduction or cue-conflict paradigms.

Pizlo and Salach-Golyska (1994) have raised an important question about the validity of the interpretation of experiments reported by Lappin and Love (1992)--based on the fact that alternative cues in the image plane might have supported the shape discriminations in those experiments. The meaning of the hypothesis that visual space may be scaled by congruence under motion is clarified, pertinent evidence is reviewed, and new experimental evidence is reported. We conclude that visual space can be metrically scaled by congruence of moving shapes.

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 surface curvatures defined by optical motion was evaluated in three experiments. Observers accurately detected very small amounts of curvature in a direction perpendicular to the direction of rotation, but they were less sensitive to curvatures along the direction of rotation. Variations in either the number of points (between 91 and 9) or the number of views (from 15 to 2) had little or no effect on discrimination accuracy. The results of this study demonstrate impressive visual sensitivity to surface curvature. Several characteristics of this sensitivity to curvature are inconsistent with many computational models for deriving three-dimensional structure from motion.

A fundamental problem in the study of spatial perception concerns whether and how vision might acquire information about the metric structure of surfaces in three-dimensional space from motion and from stereopsis. Theoretical analyses have indicated that stereoscopic perceptions of metric relations in depth require additional information about egocentric viewing distance; and recent experiments by James Todd and his colleagues have indicated that vision acquires only affine but not metric structure from motion--that is, spatial relations ambiguous with regard to scale in depth. The purpose of the present study was to determine whether the metric shape of planar stereoscopic forms might be perceived from congruence under planar rotation. In Experiment 1, observers discriminated between similar planar shapes (ellipses) rotating in a plane with varying slant from the frontal-parallel plane. Experimental conditions varied the presence versus absence of binocular disparities, magnification of the disparity scale, and moving versus stationary patterns. Shape discriminations were accurate in all conditions with moving patterns and were near chance in conditions with stationary patterns; neither the presence nor the magnification of binocular disparities had any reliable effect. In Experiment 2, accuracy decreased as the range of rotation decreased from 80 degrees to 10 degrees. In Experiment 3, small deviations from planarity of the motion produced large decrements in accuracy. In contrast with the critical role of motion in shape discrimination, motion hindered discriminations of the binocular disparity scale in Experiment 4. In general, planar motion provides an intrinsic metric scale that is independent of slant in depth and of the scale of binocular disparities. Vision is sensitive to this intrinsic optical metric.

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.

In this study the sensitivity of human vision to the smoothness of stereoscopic surface structure was investigated. In experiments 1 and 2 random-dot stereograms were used to evaluate the discrimination of smooth versus 'noisy' sinusoidal surfaces differing in the percentages of points on a single smooth surface. Fully coherent smooth surfaces were found to be much more discriminable than other less smooth randomly perturbed surfaces. In experiment 3 the discrimination between discontinuous triangle-wave surfaces and similarly shaped smoothly curved surfaces obtained from the addition of the fundamental and the third harmonic of the corresponding triangle-wave surface was evaluated. The triangle-wave surfaces were found to be more accurately discriminated from the smoothly curved surfaces than would be predicted from the detectability of the difference in their Fourier power spectra. This superior discriminability was attributed to differences between the curvature and/or discontinuity of the two surfaces. In experiment 3 the effects of incoherent 'noise' points on the discrimination between the two surface types were also evaluated. These randomly positioned noise points had a relatively small effect on the discrimination between the two surfaces. In general, the results of these experiments indicate that smooth surfaces are salient for stereopsis and that isolated local violations of smoothness are highly discriminable.

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.

Three experiments examined parameters affecting human observers' ability to detect the global three-dimensional (3D) organization of a random-dot display corresponding to the polar projection of a rotating sphere. Results indicate that the detection of 3D structure is critically dependent on the detectability of motion, is disrupted by increased redundant information specifying the two-dimensional location of points in the display, and undergoes a rapidly increasing resistance to the disruptive effects of noise with increasing numbers of frames. These results, in conjunction with earlier findings, are inconsistent with existing theories concerning the perception of three-dimensionality in moving displays, in that they indicate a high degree of visual sensitivity to stimulus organizations with unique topological representations.

Human observers detected the global three-dimensional organization of visual patterns consisting of only two successive frames of randomly positioned dots, corresponding to projections of a rotating sphere. A perfectly coherent sphere yielded a stable perceptual organization that was detected more accurately than other slightly less organized patterns.

Stationary and moving target forms were composed of 5 equally spaced dots embedded in a background of 600 noise dots; the spatial and temporal separations between the target dots were varied independently. Target detectability decreased linearly with both spatial and temporal separations between the target dots. Detectability of both stationary and moving targets obeyed the same quantitative dependence on total separations, invariant under orientation in space-time. Detection also depended primarily on the relative density of the target and noise rather than on the absolute spatial or temporal separations between target dots. Thus, space and time had interchangeable effects on the detection of both stationary and moving targets.

Is the perception of velocity determined by the prior discrimination of spatial and temporal distances? Two experiments sought to answer this question by comparing the discriminabilities of moving stimuli varied in spatial extent, temporal duration, or in redundant combinations of both variables. The subject's task was to identify which of two alternative stimuli was presented on each trial. A set of four stimuli was constructed from two values of spatial extent and two values of temporal duration. Separate conditions required discrimination of each of the six possible pairs of these stimuli. Experiment 1 examined continuous motion and Experiment 2 examined apparent motion for stimuli with short (50 versus 65 msec) and with long (500 versus 650 msec) interstimulus intervals. With continuous motion and with good apparent motion (short intervals), the discrimination between the different-velocity bivariate pairs was too accurate to be attributed only to discriminations of the spatial and temporal extents of the motion. This did not occur with poor apparent motion. Evidently, time and space are perceptually related.