Factors influencing perceived angular velocity

The assumption that humans are able to perceive and process-angular kinematics is critical to many structure-from-motion and optical flow models. The current studies investigate this sensitivity, and examine several factors likely to influence angular velocity perception. In particular, three factors are considered: (1) the extent to which perceived angular velocity is determined by edge transitions of surface elements, (2) the extent to which angular velocity estimates are influenced by instantaneous linear velocities of surface elements, and (3) whether element-velocity effects are related to three-dimensional (3-D) tangential velocities or to two-dimensional (2-D) image velocities. Edge-transition rate biased angular velocity estimates only when edges were highly salient. Element velocities influenced perceived angular velocity; this bias was related to 2-D image velocity rather than 3-D tangential velocity. Despite these biases, however, judgments were most strongly determined by the true angular velocity. Sensitivity to this higher order motion parameter was surprisingly good, for rotations both in depth (y-axis) and parallel to the line of sight (z-axis).     

Angular velocity discrimination

Three experiments were designed to investigate naive observers' abilities at discriminating the rotational velocities of two simultaneously viewed objects. In Experiment 1, rotations could occur about parallel or orthogonal axes, with initial orientations in phase or out of phase, and (for parallel rotational axes) in the same or opposite direction. Differential thresholds were approximately 10%. In Experiment 2, stimulus objects differed in the number of faces revealed in rotation (three vs. four). Observers' response curves had no greater spread, but their PSEs (points of subjective equality) were shifted such that there was a partial compensation for faces revealed per unit time. In both Experiment 1 and Experiment 2, performance was consistent across rotational axis and directional conditions. In Experiment 3, the effect of object size was examined, in order to determine the extent to which angular velocity judgments are influenced by the tangential velocity of the faces. When the comparison cube's edges were half the length of the standard's, PSEs were elevated 18.5%. Taken together, these data suggest that observers are able to discriminate angular velocities with a competence near that for linear velocities. However, perceived angular rate is influenced by structural aspects of the stimuli.     

The interaction of oculomotor cues and stimulus size in stereoscopic death constancy.

In the natural world, observers perceive an object to have a relatively fixed size and depth over a wide range of distances. Retinal image size and binocular disparity are to some extent scaled with distance to give observers a measure of size constancy. The angle of convergence of the two eyes and their accommodative states are one source of scaling information, but even at close range this must be supplemented by other cues. We have investigated how angular size and oculomotor state interact in the perception of size and depth at different distances. Computer-generated images of planar and stereoscopically simulated 3-D surfaces covered with an irregular blobby texture were viewed on a computer monitor. The monitor rested on a movable sled running on rails within a darkened tunnel. An observer looking into the tunnel could see nothing but the simulated surface so that oculomotor signals provided the major potential cues to the distance of the image. Observers estimated the height of the surface, their distance from it, or the stereoscopically simulated depth within it over viewing distances which ranged from 45 cm to 130 cm. The angular width of the images lay between 2 deg and 10 deg. Estimates of the magnitude of a constant simulated depth dropped with increasing viewing distance when surfaces were of constant angular size. But with surfaces of constant physical size, estimates were more nearly independent of viewing distance. At any one distance, depths appeared to be greater, the smaller the angular size of the image. With most observers, the influence of angular size on perceived depth grew with increasing viewing distance. These findings suggest that there are two components to scaling. One is independent of angular size and related to viewing distance. The second component is related to angular size, and the weighting accorded to it grows with viewing distance. Control experiments indicate that in the tunnel, oculomotor state provides the principal cue to viewing distance. Thus, the contribution of oculomotor signals to depth scaling is gradually supplanted by other cues as viewing distance grows. Binocular estimates of the heights and distances of planar surfaces of different sizes revealed that angular size and viewing distance interact in a similar way to determine perceived size and perceived distance.     

Perceiving surface slant from deformation of optic flow

Perceived surface orientation and angular velocity were investigated for orthographic projections of 3-D rotating random-dot planes. It was found that (a) tilt was accurately perceived and (b) slant and angular velocity were systematically misperceived. It was hypothesized that these misperceptions are the product of a heuristic analysis based on the deformation, one of the differential invariants of the first-order optic flow. According to this heuristic, surface attitude and angular velocity are recovered by determining the magnitudes of these parameters that most likely produce the deformation of the velocity field, under the assumption that all slant and angular velocity magnitudes have the same a priori probability. The results of the present investigation support this hypothesis. Residual orientation anisotropies not accounted for by the proposed heuristic were also found.     

Perceiving shape from profiles

Four experiments related human perception of shape from profiles to current theoretical predictions. In Experiment 1, judgments of structure and motion were obtained for single- and dualellipsoid displays rotating about various axes. Ratings were highest when the axis of rotation was in the image plane and were influenced by the number of ellipsoids and the orientation of a single ellipsoid. The subsequent experiments explored the effect of orientation on shape judgments of a single ellipsoid. The results of Experiments 2 and 3 suggested that the effect of orientation found in Experiment 1 was not due to either the inability of certain orientations to be perceived as three-dimensional objects or to two-dimensional artifacts. It was thus argued that this effect of orientation was due to points of correspondence in relative motion that arise when the major axis is not perpendicular to the axis of rotation. In Experiment 4, subjects provided judgments of both shape and angular velocity. The elevated ellipsoids that were judged as larger were also judged as rotating more slowly. The inverse relationship between size and angular velocity is consistent with current theories. The connection between theory and data was further demonstrated by applying a shape-recovery algorithm to the stimuli used in Experiment 4 and finding a similar tradeoff between angular velocity and shape.     

Surface formation and depth in monocular scene perception

The visual perception of monocular stimuli perceived as 3-D objects has received considerable attention from researchers in human and machine vision. However, most previous research has focused on how individual 3-D objects are perceived. Here this is extended to a study of how the structure of 3-D scenes containing multiple, possibly disconnected objects and features is perceived. Da Vinci stereopsis, stereo capture, and other surface formation and interpolation phenomena in stereopsis and structure-from-motion suggest that small features having ambiguous depth may be assigned depth by interpolation with features having unambiguous depth. I investigated whether vision may use similar mechanisms to assign relative depth to multiple objects and features in sparse monocular images, such as line drawings, especially when other depth cues are absent. I propose that vision tends to organize disconnected objects and features into common surfaces to construct 3-D-scene interpretations. Interpolations that are too weak to generate a visible surface percept may still be strong enough to assign relative depth to objects within a scene. When there exists more than one possible surface interpolation in a scene, the visual system's preference for one interpolation over another seems to be influenced by a number of factors, including: (i) proximity, (ii) smoothness, (iii) a preference for roughly frontoparallel surfaces and 'ground' surfaces, (iv) attention and fixation, and (v) higher-level factors. I present a variety of demonstrations and an experiment to support this surface-formation hypothesis.     

Rapid processing of cast and attached shadows

We used a visual-search method to investigate the role of shadows in the rapid discrimination of scene properties. Targets and distractors were light or dark 2-D crescents of identical shape and size, on a mid-grey background. From the dark stimuli, illusory 3-D shapes can be created by blurring one arc of the crescent. If the inner arc is blurred, the stimulus is perceived as a curved surface with attached shadow. If the outer arc is blurred, the stimulus is perceived as a flat surface casting a shadow. In a series of five experiments, we used this simple stimulus to map out the shadow properties that the human visual system can rapidly detect and discriminate. To subtract out 2-D image factors, we compared search performance for dark-shadow stimuli with performance for light-shadow stimuli which generally do not elicit strong 3-D percepts. We found that the human visual system is capable of rapid discrimination based upon a number of different shadow properties, including the type of the shadow (cast or attached), the direction of the shadow, and the displacement of the shadow. While it is clear that shadows are not simply discounted in rapid search, it is unclear at this stage whether rapid discrimination is acting upon shadows per se or upon representations of 3-D object shape and position elicited by perceived shadows.     

Local and global mechanisms of one- and two-dimensional orientation illusions

One-dimensional (1-D) orientation illusions induced on a test grating by a tilted and-surrounding 1-D inducing grating have a well-known angular function that exhibits both repulsion and attraction effects. Two-dimensional (2-D) orientation illusions are those induced on a test grating by 2-D image modulation, such as a pair of superimposed inducing gratings at different orientations, usually orthogonal (a plaid). Given the known angular functions induced by the plaid component gratings, two hypotheses were developed that predicted different plaid-induced illusion functions. Hypothesis 1 states that the 1-D component-induced effects simply add linearly; Hypothesis 2 states that there is an additional mechanism that responds to the virtual axes of mirror symmetry of the plaid and adds to the effect. The data of two experiments were consistent with the predictions from the second hypothesis but not the first. Possible neural substrates of mechanisms that extract axes of symmetry are discussed; it is suggested that such global symmetry axes may underlie the perceived orientation of complex shapes.     

3-D processing in the Poggendorff illusion

In the Poggendorff illusion two collinear oblique lines, separated by two vertical lines, appear to be misaligned. 3-D processing of the oblique but not the vertical lines is considered to cause this apparent misalignment. We investigated whether more explicitly triggering 2-D versus 3-D interpretations of the different parts of Poggendorff-like displays would influence the apparent misalignment. In Experiment 1, we found that compared to 2-D controls, 3-D interpretations of the vertical parts did not influence apparent misalignment, while for the oblique parts 3-D processing resulted in more apparent misalignment than 2-D controls. In Experiment 2, the amount of contour convergence of the oblique parts was manipulated resulting in the 3-D blocks, but not the 2-D line patterns, to be perceived as receding in depth. Now, apparent misalignment increased the more the 3-D blocks were perceived as receding in depth. We conclude that apparent misalignment in Poggendorff-like displays can be influenced by different interpretations of its separate parts, while keeping the local junctions between the different elements the same.     

Discriminating constant from variable angular velocities in structure from motion

We investigated accuracy in discriminating between constant and variable angular velocities for orthographic projections of three-dimensional rotating objects. The reported judgments of “constant” or “variable” angular velocity were only slightly influenced by the projected angular velocities, but they were greatly affected by the variations of the deformation, a first-order component of the optic flow. When viewing either a rotating ellipsoidal volume or a planar surface that accelerated and decelerated over the course of rotation, observers’ tendencies to report a variable angular velocity were increased when the temporal phase of the acceleration pattern increased the range of variation of the median deformation; the tendencies were decreased when the same acceleration pattern was used to decrease the range of variation of the median deformation. These results provide evidence contrary to the hypothesis that the visual system performs a mathematically correct analysis of the optic flow.     

Local and global mechanisms of one- and two-dimensional orientation illusions.

One-dimensional (1-D) orientation illusions induced on a test grating by a tilted and surrounding 1-D inducing grating have a well-known angular function that exhibits both repulsion and attraction effects. Two-dimensional (2-D) orientation illusions are those induced on a test grating by 2-D image modulation, such as a pair of superimposed inducing gratings at different orientations, usually orthogonal (a plaid). Given the known angular functions induced by the plaid component gratings, two hypotheses were developed that predicted different plaid-induced illusion functions. Hypothesis 1 states that the 1-D component-induced effects simply add linearly; Hypothesis 2 states that there is an additional mechanism that responds to the virtual axes of mirror symmetry of the plaid and adds to the effect. The data of two experiments were consistent with the predictions from the second hypothesis but not the first. Possible neural substrates of mechanisms that extract axes of symmetry are discussed; it is suggested that such global symmetry axes may underlie the perceived orientation of complex shapes.     

Reference frame effects on shape perception in two versus three dimensions

Three experiments are reported in which it is tested whether the Gestalt effect of configural orientation on shape perception operates on two-dimensional (2-D) or three-dimensional (3-D) representations of space. It is known that gravitationally defined squares and diamonds take longer to discriminate in diagonal arrays than in horizontal or vertical arrays. In the first experiment it is shown that this interference effect decreases dramatically in magnitude when pictorial depth information is added so that subjects perceive the target shapes in different depth planes. In the second experiment this difference is shown not to be due to relative size of the target shapes or to occlusion of a background plane. It is also shown, in the final experiment, that this difference is not due to linear perspective information or merely to perception of the target figures in a 3-D scene. The overall pattern of results supports the position that this configural reference frame effect arises primarily when the elements of the configuration are coplanar, and that the principal organization underlying it is the structure of the perceived 3-D environment rather than that of the 2-D image. In all three experiments, however, there is also a small interference effect in the noncoplanar 3-D conditions. This might be due either to some aspect of reference frame selection operating on the 2-D image representation or to the failure of subjects to see depth in the 3-D stimuli on some proportion of the trials.     

PERCEIVED CONTINUITY OF OCCLUDED VISUAL OBJECTS

Abstract— The human visual system does not rigidly preserve the properties of the retinal image as neural signals are transmitted to higher areas of the brain Instead, it generates a representation that captures stable surface properties despite a retinal image that is often fragmented in space and time because of occlusion caused by object and observer motion The recovery of this coherent representation depends at least in part on input from an abstract representation of three-dimensional (3-D) surface layout In the two experiments reported, a stereoscopic apparent motion display was used to investigate the perceived continuity of a briefly interrupted visual object When a surface appeared in front of the object's location during the interruption, the object was more likely to be perceived as persisting through the interruption (behind an occluder) than when the surface appeared behind the object's location under otherwise identical stimulus conditions The results reveal the influence of 3-D surface-based representations even in very simple visual tasks.     

Overestimation of heights in virtual reality is influenced more by perceived distal size than by the 2-D versus 3-D dimensionality of the display

One important aspect of the pictorial representation of a scene is the depiction of object proportions. Yang, Dixon, and Proffitt (1999 Perception 28 445-467) recently reported that the magnitude of the vertical-horizontal illusion was greater for vertical extents presented in three-dimensional (3-D) environments compared to two-dimensional (2-D) displays. However, because all of the 3-D environments were large and all of the 2-D displays were small, the question remains whether the observed magnitude differences were due solely to the dimensionality of the displays (2-D versus 3-D) or to the perceived distal size of the extents (small versus large). We investigated this question by comparing observers' judgments of vertical relative to horizontal extents on a large but 2-D display compared to the large 3-D and the small 2-D displays used by Yang et al (1999). The results confirmed that the magnitude differences for vertical overestimation between display media are influenced more by the perceived distal object size rather than by the dimensionality of the display.     

The influence of structure from motion on motion correspondence

The visual system has a remarkable ability to reconstruct 3-D structure from moving 2-D features. The processing of structure from motion is generally thought to consist of two stages. First, the direction and speed of features is measured (2-D velocity measurement) and, second, 3-D structure is reconstructed from the measured 2-D velocities (3-D structure recovery). Most models have assumed that these stages occur in a bottom-up fashion. Here, however, we present evidence that the 3-D structure-recovery stage influences the 2-D velocity-measurement stage. We developed a stimulus in which two perceptual modes of motion correspondence (one-way translation versus oscillation), and two perceptual modes of 3-D surface structure (flat surface versus cylinder) could be achieved. We found that the likelihood of perceiving both one-way motion and cylindrical structure increased in similar ways with increasing frame duration. In subsequent experiments we found, first, that a higher likelihood of perceiving one-way motion did not affect the likelihood of perceiving cylindrical structure; and, second, that a higher likelihood of perceiving cylindrical structure increased the likelihood of perceiving one-way motion. These results suggest that the higher, 3-D structure-recovery stage may influence the lower, 2-D motion-correspondence stage. This result is not in accordance with most computational models that assume that there is only one-way, feedforward information processing from the 2-D velocity (energy)-measurement stage to the 3-D structure-recovery stage. Perhaps, one of the roles of feedback processing is to seek consensus of the information processed in different stages.     

Haptic perception of linear extent.

The perception of linear extent in haptic touch appears to be anisotropic, in that haptically perceived extents can depend on the spatial orientation and location of the object and, thus, on the direction of exploratory motion. Experiments 1 and 2 quantified how the haptic perception of linear extent depended on the type of motion (radial or tangential to the body) when subjects explored different stimulus objects (raised lines or solid blocks) varying in length and in relative spatial location. Relatively narrow, shallow, raised lines were judged to be longer, by magnitude estimation, than solid blocks. Consistent with earlier reports, stimuli explored with radial arm motions were judged to be longer than identical stimuli explored with tangential motions; this difference did not depend consistently on the lateral position of the stimulus object, the direction of movement (toward or away from the body), or the distance of the hand from the body but did depend slightly on the angular position of the shoulder. Experiment 3 showed that the radial-tangential effect could be explained by temporal differences in exploratory movements, implying that the apparent anisotropy is not intrinsic to the structure of haptic space.     

Haptic perception of linear extent

The perception of linear extent in haptic touch appears to be anisotropic, in that haptically perceived extents can depend on the spatial orientation and location of the object and, thus, on the direction of exploratory motion. Experiments 1 and 2 quantified how the haptic perception of linear extent depended on the type of motion (radial or tangential to the body) when subjects explored different stimulus objects (raised lines or solid blocks) varying in length and in relative spatial location. Relatively narrow, shallow, raised lines were judged to be longer, by magnitude estimation, than solid blocks. Consistent with earlier reports, stimuli explored with radial arm motions were judged to be longer than identical stimuli explored with tangential motions; this difference did not depend consistently on the lateral position of the stimulus object, the direction of movement (toward or away from the body), or the distance of the hand from the body but did depend slightly on the angular position of the shoulder. Experiment 3 showed that the radial-tangential effect could be explained by temporal differences in exploratory movements, implying that the apparent anisotropy is not intrinsic to the structure of haptic space.     

A simple but powerful theory of the moon illusion

Modification of Restle's theory (1970) explains the moon illusion and related phenomena on the basis of three principles: (1) The apparent sizes of objects are their perceived visual angles. (2) The apparent size of the moon is determined by the ratio of the angular extent of the moon relative to the extents subtended by objects composing the surrounding context, such as the sky and things on the ground. (3) The visual extents subtended by common objects of a constant physical size decrease systematically with increasing distance from the observer. Further development of this theory requires specification of both the components of the surrounding context and their relative importance in determining the apparent size and distance of the moon.     

Apparent depth with retinal image motion of expansion and contraction yoked to head movement

The two main questions addressed in this study were (a) what effect does yoking the relative expansion and contraction (EC) of retinal images to forward and backward head movements have on the resultant magnitude and stability of perceived depth, and (b) how does this relative EC image motion interact with the depth cues of motion parallax? Relative EC image motion was produced by moving a small CCD camera toward and away from the stimulus, two random-dot surfaces separated in depth, in synchrony with the observers' forward and backward head movements. Observers viewed the stimuli monocularly, on a helmet-mounted display, while moving their heads at various velocities, including zero velocity. The results showed that (a) the magnitude of perceived depth was smaller with smaller head velocities (< 10 cm s-1), including the zero-head-velocity condition, than with a larger velocity (10 cm s-1), and (b) perceived depth, when motion parallax and the EC image motion cues were simultaneously presented, is equal to the greater of the two possible perceived depths produced from either of these two cues alone. The results suggested the role of nonvisual information of self-motion on perceiving depth.     

Aging persons' estimates of vehicular motion.

Estimated arrival times of moving autos were examined in relation to viewer age, gender, motion trajectory, and velocity. Direct push-button judgments were compared with verbal estimates derived from velocity and distance, which were based on assumptions that perceivers compute arrival time from perceived distance and velocity. Experiment 1 showed that direct estimates of younger Ss were most accurate. Older women made the shortest (highly cautious) estimates of when cars would arrive. Verbal estimates were much lower than direct estimates, with little correlation between them. Experiment 2 extended target distances and velocities of targets, with the results replicating the main findings of Experiment 1. Judgment accuracy increased with target velocity, and verbal estimates were again poorer estimates of arrival time than direct ones, with different patterns of findings. Using verbal estimates to approximate judgments in traffic situations appears questionable.