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.     

The perception of 3-D structure from contradictory optical patterns

Two experiments investigated observers’ perceptions of 3-D structure when optical sources of information were contradictory. When motion and stereoscopic disparities specified different surfaces, the perceptual outcome depended strongly on the direction of curvature present within each modality. Previous research has shown that the perception of surface slant and curvature is anisotropic for both motion and stereo and that it depends on the direction in which it takes place. In the present experiments, the modality with the “effective” direction of curvature tended to dominate or suppress the perception of surfaces in the other modality with less effective curvatures. The results have implications for models which attempt to combine 3-D data from different optical sources.     

Using motor tasks to quantitatively judge 3-D surface curvatures.

The primary objective of this study was to quantitatively investigate the human perception of surface curvature by using virtual surfaces and motor tasks along with data analysis methods to estimate surface curvature from drawing movements. Three psychophysical experiments were conducted. In Experiment 1, we looked at subjects' sensitivity to the curvature of a curve lying on a surface and changes in the curvature as defined by Euler's formula, which relates maximum and minimum principal curvatures and their directions. Regardless of direction and surface shape (elliptic and hyperbolic), subjects could report the curvature of a curve lying on a surface through a drawing task. In addition, multiple curves drawn by subjects were used to reconstruct the surface. These reconstructed surfaces could be better accounted for by analysis that treated the drawing data as a set of curvatures rather than as a set of depths. A pointing task was utilized in Experiment 2, and subjects could report principal curvature directions of a surface rather precisely and consistently when the difference between principal curvatures was sufficiently large, but performance was poor for the direction of zero curvature (asymptotic direction) on a hyperbolic surface. In Experiment 3, it was discovered that sensitivity to the sign of curvature was different for perceptual judgments and motor responses, and there was also a difference for that of a curve itself and the same curve embedded in a surface. These findings suggest that humans are sensitive to relative changes in curvature and are able to comprehend quantitative surface curvature for some motor tasks.     

Using motor tasks to quantitatively judge 3-D surface curvatures

The primary objective of this study was to quantitatively investigate the human perception of surface curvature by using virtual surfaces and motor tasks along with data analysis methods to estimate surface curvature from drawing movements. Three psychophysical experiments were conducted. In Experiment 1, we looked at subjects’ sensitivity to the curvature of a curve lying on a surface and changes in the curvature as defined byEuler’s formula, which relates maximum and minimum principal curvatures and their directions. Regardless of direction and surface shape (elliptic and hyperbolic), subjects could report the curvature of a curve lying on a surface through a drawing task. In addition, multiple curves drawn by subjects were used to reconstruct the surface. These reconstructed surfaces could be better accounted for by analysis that treated the drawing data as a set of curvatures rather than as a set of depths. A pointing task was utilized in Experiment 2, and subjects could report principal curvature directions of a surface rather precisely and consistently when the difference between principal curvatures was sufficiently large, but performance was poor for the direction of zero curvature (asymptotic direction) on a hyperbolic surface. In Experiment 3, it was discovered that sensitivity to the sign of curvature was different for perceptual judgments and motor responses, and there was also a difference for that of a curve itself and the same curve embedded in a surface. These findings suggest that humans are sensitive to relative changes in curvature and are able to comprehend quantitative surface curvature for some motor tasks.     

Walking,looking to the side,and taking curved paths

In two experiments, viewers judged heading from displays simulating locomotion through tree-filled environments, with gaze off to the side. They marked their heading with a mouse-controlled probe at three different depths. When simulated eye or head rotation generally exceeded 0.5 deg/sec, there was reliable curvature in perceived paths toward the fixated object. This curvature, however, was slight even with rotation rates as great as 2.6 deg/sec. Best-fit paths to circular arcs had radii of 1.8 km or greater. In a third experiment, pedestrians walked with matched gaze to the side. Measured curvature in the direction of gaze corresponded to a circular radius of about 1.3 km. Thus, at minimum, vision scientists need not worry about perceived path curvature in this situation; real path curvatures are about the same. However, at present, we can make no claim that the same mechanisms necessarily govern the two results.     

Illusion of rotary motion reversal in a sphere is facilitated by increased rotational speed.

A rotating sphere with an artistically painted surface may appear to reverse its direction of rotation and at the same time reverse its curvature from convex to concave (the Termes Illusion). This study tested the effects of 4 rotational speeds (stationary, 1 rpm, 2.5 rpm, and 3.75 rpm) in producing this illusion. Analysis indicated that the number and duration of reversals increased with speed of rotation and successive viewing sessions. Latency of reversal decreased with successive sessions. Explanations in terms of satiation theory, learning theory, instructions, and perceptual bias were discussed.     

Influence of shape on haptic curvature perception

Curvature discrimination of hand-sized doubly curved surfaces by means of static touch was investigated. Stimuli consisted of hyperbolical, cylindrical, elliptical and spherical surfaces of various curvatures. In the first experiment subjects had to discriminate the curvature along a specified orientation (the discrimination orientation) of a doubly curved surface from a flat surface. The curvature to be discriminated was oriented either along the middle finger or across the middle finger of the right hand. Independent of the shape of the surface, thresholds were found to be about 1.6 times smaller along the middle finger than across the middle finger. Discrimination biases were found to be strongly influenced by the shape of the surface; subjects judged a curvature to be more convex when the perpendicular curvature was convex than when this curvature was concave. With the results of the second experiment it could be ruled out that the influence of shape on curvature perception was simply due to a systematic error made by the subject regarding the discrimination orientation.     

Haptic curvature comparison of convex and concave shapes

A sculpture and the mould in which it was formed are typical examples of objects with an identical, but opponent, surface shape: each convex (ie outward pointing) surface part of a sculpture has a concave counterpart in the mould. The question arises whether the object features of opponent shapes can be compared by touch. Therefore, we investigated whether human observers were able to discriminate the curvatures of convex and concave shapes, irrespective of whether the shape was convex or concave. Using a 2AFC procedure, subjects had to compare the curvature of a convex shape to the curvature of a concave shape. In addition, results were also obtained for congruent shapes, when the curvature of either only convex shapes or only concave shapes had to be compared. Psychometric curves were fitted to the data to obtain threshold and bias results. When subjects explored the stimuli with a single index finger, significantly higher thresholds were obtained for the opponent shapes than for the congruent shapes. However, when the stimuli were touched by two index fingers, one finger per surface, we found similar thresholds. Systematic biases were found when the curvature of opponent shapes was compared: the curvature of a more curved convex surface was judged equal to the curvature of a less curved concave surface. We conclude that human observers had the ability to compare the curvature of shapes with an opposite direction, but that their performance decreased when they sensed the opponent surfaces with the same finger. Moreover, they systematically underestimated the curvature of convex shapes compared to the curvature of concave shapes.     

Depth capture by kinetic depth and by stereopsis

The perceived depth of regions within a stereogram lacking explicit disparity information can be captured by the surface structure of regions where disparity is explicit: stereo capture. In two experiments, observers estimated surface curvature/depth of an untextured object (a 'ribbon') superimposed on a cylinder textured with dots, the cylinder curvature being defined by disparity (stereo depth) or by motion parallax (kinetic depth: KD). With the stereo-defined cylinder, depth capture was obtained under conditions where the disparity of the ribbon was ambiguous; with the KD, cylinder depth capture was obtained under conditions where the motion flow of the cylinder was in a direction parallel to that of the ribbon. These results demonstrate yet another similarity between KD and stereopsis.     

The effects of age upon the perception of depth and 3-D shape from differential motion and binocular disparity

The ability of younger and older adults to perceive the 3-D shape, depth, and curvature of smooth surfaces defined by differential motion and binocular disparity was evaluated in six experiments. The number of points defining the surfaces and their spatial and temporal correspondences were manipulated. For stereoscopic sinusoidal surfaces, the spatial frequency of the corrugations was also varied. For surfaces defined by motion, the lifetimes of the individual points in the patterns were varied, and comparisons were made between the perception of surfaces defined by points and that of more ecologically valid textured surfaces. In all experiments, the older observers were less sensitive to the depths and curvatures of the surfaces, although the deficits were much larger for motion-defined surfaces. The results demonstrate that older adults can extract depth and shape from optical patterns containing only differential motion or binocular disparity, but these abilities are often manifested at reduced levels of performance.     

Mental rotation, physical rotation, and surface media.

Subjects made mirror-normal discriminations on alphanumeric characters shown in different orientations in the picture plane. Either the characters or the background rotated during stimulus presentation in Experiments 1-3. Character rotation in the direction of mental rotation facilitated mental rotation, whereas rotation in the opposite direction inhibited it. In Experiment 4, characters were presented in different surface media so as to stimulate only one representation at a time. Mental rotation performance was similar whether the stimuli were defined by luminance, color, texture, relative motion, or binocular disparity, suggesting that mental rotation occurs at a level beyond that of the independent analyses of these different media. These results support those of Experiments 1-3 in excluding the participation of low-level motion analysis centers in the mental rotation processes.     

Effects of circular motion on judgment of rotation direction and depth order in visual motion

Abstract:  The rotation direction and depth order of a rotating sphere consisting of random dots often reverses while it is viewed under orthographic projection. However, if a short viewing distance is simulated under perspective projection, the correct rotation direction can be perceived. There are two motion cues for the rotation direction and depth order. One is the speed cue; points with higher velocities are closer to the observer. The other is the vertical motion cue; vertical motion is induced when the dots recede from or approach the observer. It was examined whether circular motion, which does not have any depth information but induces vertical velocities, masks the vertical motion cue. In Experiment 1, the effects of circular motion on the judgment of the rotation direction of a rotating sphere were examined. The magnitude of the two cues (the speed cue and the vertical velocity cue) as well as the angular speed of circular motion was varied. It was found that the performance improved as the vertical velocity increased and that the speed cue had slight effects on the judgment of the rotation direction. It was also found that the performance worsened as the angular speed of the circular motion was increased. In Experiment 2, the effects of circular motion on depth judgment of a rotating half sphere were investigated. The performance worsened as the angular speed of the circular motion increased, as in Experiment 1. These results suggest that the visual system cannot compensate perfectly for circular motion for the judgment of the rotation direction and depth order.     

The interplay between stereopsis and structure from motion

In a series of psychophysical experiments, an adaptation paradigm was employed to study the influence of stereopsis on perception of rotation in an ambiguous kinetic depth (KD) display. Without prior adaptation or stereopsis, a rotating globe undergoes spontaneous reversals in perceived direction of rotation, with successive durations of perceived rotation being random variables. Following 90 sec of viewing a stereoscopic globe undergoing unambiguous rotation, the KD globe appeared to rotate in a direction opposite that experienced during the stereoscopic adaptation period. This adaptation aftereffect was short-lived, and it occurred only when the adaptation and test figures stimulated the same retinal areas, and only when the adaptation and test figures rotated about the same axis. The aftereffect was just as strong when the test and adaptation figures had different shapes, as long as the adaptation figure contained multiple directions of motion imaged at different retinal disparities. Nonstereoscopic adaptation figures had no effect on the perceived direction of rotation of the ambiguous KD figure. These results imply that stereopsis and motion strongly interact in the specification of structure from motion, a result that complements earlier work on this problem.     

Short-term visual memory for contour curvature in a delayed discrimination task

Abstract: A two-interval forced-choice of constant stimuli was used to measure the point of subjective equality (PSE) and discrimination threshold for standard contour curvature (1.91, 3.24 deg⁻¹) held in short-term visual memory (STVM). At both standard curvatures, the PSE for remembered curvature was nearly constant for standard curvature from 2 s to 16 s retention intervals, while the discrimination threshold increased as a linear function of retention interval. These results show that the decay in STVM for contour curvature is due to the noisy representation of curvature, neither to fading of the represented curvature nor to converging to the constant curvature. Furthermore, the Weber fraction was nearly constant for both standard curvatures at any delay from 2 to 16 s.     

Stereo-motion cooperation and the use ofmotion disparity in the visual perception of 3-D structure

When an observer views a moving scene binocularly, both motion parallax and binocular disparity provide depth information. In Experiments lA-1C, we measured sensitivity to surface curvature when these depth cues were available either individually or simultaneously. When the depth cues yielded comparable sensitivity to surface curvature, we found that curvature detection was easier with the cues present simultaneously, rather than individually. For 2 of the 6 subjects, this effect was stronger when the component of frontal translation of the surface was vertical, rather than horizontal. No such anisotropy was found for the 4 other subjects. If a moving object is observed binocularly, the patterns of optic flow are different on the left and right retinae. We have suggested elsewhere (Cornilleau-Pérès & Droulez, in press) that this motion disparity might be used as avisual cue for the perception of a 3-D structure. Our model consisted in deriving binocular disparity from the left and right distributions of vertical velocities, rather than from luminous intensities, as has been done in classical studies on stereoscopic vision. The model led to some predictions concerning the detection of surface curvature from motion disparity in the presence or absence of intensity-based disparity (classically termedbinocular disparity). In a second set of experiments, we attempted to test these predictions, and we failed to validate our theoretical scheme from a physiological point of view.     

Similar mechanisms underlie curvature comparison by static and dynamic touch

In four experiments, we tested whether haptic comparison of curvature ranging from ?41m to +41m is qualitatively the same for static and for dynamic touch. In Experiments 1 and 3, we tested whether static and dynamic curvature discrimination are based on height differences, attitude (slope) differences, curvature differences, or a combination of these geometrical variables. It was found that both static and dynamic haptic curvature discrimination are based on attitude differences. In Experiments 2 and 4, we tested whether this mechanism leads to errors in the comparison of stimuli with different lengths for static and dynamic touch, respectively. If the judgments are based on attitude differences, subjects will make systematic errors in these comparisons. In both experiments, we found that subjects compared the curvatures of strips of the same length veridically, whereas they made systematic errors if they were required to compare the curvatures of strips of different lengths. Longer stimuli were judged to be more curved than shorter stimuli with the same curvature. We conclude that similar mechanisms underlie static and dynamic haptic curvature comparison. Moreover, additional data comparison showed that static and dynamic curvature comparison is not only qualitatively, but also quantitatively similar.     

Similar mechanisms underlie curvature comparison by static and dynamic touch.

In four experiments, we tested whether haptic comparison of curvature ranging from -4/m to +4/m is qualitatively the same for static and for dynamic touch. In Experiments 1 and 3, we tested whether static and dynamic curvature discrimination are based on height differences, attitude (slope) differences, curvature differences, or a combination of these geometrical variables. It was found that both static and dynamic hepatic curvature discrimination are based on attitude differences. In Experiments 2 and 4, we tested whether this mechanism leads to errors in the comparison of stimuli with different lengths for static and dynamic touch, respectively. If the judgments are based on attitude differences, subjects will make systematic errors in these comparisons. In both experiments, we found that subjects compared the curvatures of strips of the same length vertically, whereas they made systematic errors if they were required to compare the curvatures of strips of different lengths. Longer stimuli were judged to be more curved than shorter stimuli with the same curvature. We conclude that similar mechanisms underlie static and dynamic haptic curvature comparison. Moreover, additional data comparison showed that static and dynamic curvature comparison is not only qualitatively, but also quantitatively similar.     

Rapid volitional control of apparent motion during percept generation

How rapidly can one voluntarily influence percept generation? The time course of voluntary visual–spatial attention is well studied, but the time course of intentional control over percept generation is relatively unknown. We investigated the latter question using “one-shot” apparent motion. When a vertical or horizontal pair of squares is replaced by its 90º-rotated version, the bottom-up signal is ambiguous. From this ambiguous signal, it is known that people can intentionally generate a percept of rotation in a desired direction (clockwise or counterclockwise). To determine the time course of this intentional control, we instructed participants to voluntarily induce rotation in a precued direction (clockwise rotation when a high-pitched tone was heard, and counterclockwise rotation when a low-pitched tone was heard), and then to report the direction of rotation that was actually perceived. We varied the delay between the instructional cue and the rotated frame (cue-lead time) from 0 to 1,067 ms. Intentional control became more effective with longer cue-lead times (asymptotically effective at 533 ms). Notably, intentional control was reliable even with a zero cue-lead time; control experiments ruled out response bias and the development of an auditory–visual association as explanations. This demonstrates that people can interpret an auditory cue and intentionally generate a desired motion percept surprisingly rapidly, entirely within the subjectively instantaneous moment in which the visual system constructs a percept of apparent motion.     

Consciousness mediated by neural transition states: How invisibly rapid motions can become visible

When observers view a rapidly moving stimulus they may see only a static streak. We report that there can be a transient percept of motion if such a moving stimulus is preceded or followed by a stationary image of that stimulus. A ring of dots was rotated so rapidly observers only saw a continuous outline circle and could not report its rotation direction. When an objectively stationary ring of dots preceded or followed this rotating ring, the stationary ring appeared to visibly launch into motion from a standstill or visibly rotate to a halt, principally in the same direction as the actual rapid rotation. Thus, motions too rapid to be consciously perceived as motion can nonetheless be processed by the visual system, and generate neural transition states that are consciously experienced as motion percepts. We suggest such transition states might serve a unifying function by bridging discontinuous motion states.     

Priming by motion too rapid to be consciously seen

When a rapidly rotating ring of dots was briefly flashed, observers saw only a solid ring with no discriminable rotation. However, when this stimulus served as a prime that was followed by a target that consisted of a clearly rotating ring of dots, response times (RTs) to report the target's rotation were shorter when the prime and target directions were congruent than when they were incongruent. In accord with shape priming data, this priming effect increased monotonically with the prime-target stimulus-onset asynchrony (SOA). The prime also biased the perceived direction of an ambiguous apparent motion target, but only at an intermediate SOA. At the same SOA, we also found that target presentations enabled above-chance discrimination of prime's rotation direction. These outcomes demonstrate the processing of motion direction information that is not phenomenally represented. They suggest a common mechanism may mediate the priming of RTs by shape and motion, whereas a different mechanism mediates perceptual measures of motion priming.