Coherence of early motion signals.

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.

The perception of length on curved and flat surfaces.

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.

Direct measurement of the curvature of visual space.

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.

Foundations of spatial vision: from retinal images to perceived shapes.

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.

The perception of surface curvature from optical motion.

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.

Definition and detection of binocular disparity.

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.

Shape constancy in pictorial relief.

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.

On the scaling of visual space from motion--in response to Pizlo and Salach-Golyska.

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.

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 detection of surface curvatures defined by optical motion.

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.

Planar motion permits perception of metric structure in stereopsis.

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.

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 discriminability of smooth stereoscopic surfaces.

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.

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.

Detection of three-dimensional structure in moving optical patterns.

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.

Accurate visual measurement of three-dimensional moving patterns.

Human observers discriminated relative three-dimensional distances in simple patterns of motion parallax with an acuity similar to vernier acuity under comparable conditions. Accurate visual measures of three-dimensional distance can be derived from the structural invariance of patterns undergoing perspective transformations.

Detection of visual forms in space and time.

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.

Visual detection of multi-letter patterns.

This study addressed two basic questions about the detection of multi-letter patterns: (a) How is the detection of a multi-letter pattern related to the detection of its individual components? (b) How is the detection of a sequence of letters influenced by the observer's familiarity with that sequence? In three experiments observers searched for one-, two-, or three letter patterns embedded in a rapid series of multiple six-letter frames. In Experiment 1, unfamiliar two-letter patterns were detected more accurately than their one-letter components. This two-letter advantage reflects the fact that in an array of fixed size, larger target stimuli contain more information and are easier to discriminate from nontarget alternatives. Quantitative analyses indicated that observers combine information not decisions, about the component letters in a pattern. In Experiment 2, with statistical and physical properties equated, a familiar three-letter pattern (i.e., CAT) was detected more accurately than its unfamiliar anagram (i.e., TCA). This word advantage in word (not letter) detection persisted even after extensive practice and was uninfluenced by the lexical character of distractor items. In Experiment 3, words (e.g., FIB), pronounceable non words (e.g., FIF(, and familiar acronyms (e.g., FBI) were detected more readily than unfamiliar items (e.g., IBF). Thus both orthographic knowledge and familiarity with specific sequences can facilitate perceptual processing in "word" detection.