Projective invariance and the kinetic depth effect.

Seven experiments test the assumption that, in the kinetic depth effect, observers have reliable and direct access to the equivalence of shapes in projective geometry. The assumption is implicit in 'inverse optics' approaches to visual form perception. Observers adjusted a comparison shape to match a standard shape; both standard and comparison were portrayed as in continuous rotation in space, using a graphics computer. The shapes were either plane quadrilaterals or solid prisms. The angular difference of the planes of the shapes was varied, as was the dot density of a texture in those planes. Departure from projective equivalence was measured in six studies by measuring the planar analogue of cross ratio, and in a seventh by measuring the cross ratio for points in space. Projective equivalence was not found to be perceived uniformly, except in one experiment that did not involve rotation in depth. Otherwise changes in orientation of up to 180 degrees about a single coordinate axis had no significant effect on matches in shape, while changes in orientation about more than one coordinate axis produced significant effects. The addition of texture and a change in rotation speed did not correct departures from projective equivalence.     

How to study the kinetic depth effect experimentally

Sperling, Landy, Dosher, and Perkins (1989) proposed an objective 3D shape identification task with 2D artifactual cues removed and with full feedback (FB) to the subjects to measure KDE and to circumvent algorithmically equivalent KDE-alternative computations and artifactual non-KDE processing. (1) The 2D velocity flow-field was necessary and sufficient for true KDE. (2) Only the first-order (Fourier-based) perceptual motion system could solve our task because the second-order (rectifying) system could not simultaneously process more than two locations. (3) To ensure first-order motion processing, KDE tasks must require simultaneous processing at more than two locations. (4) Practice with FB is essential to measure ultimate capacity (aptitude) and, thereby, to enable comparisons with ideal observers. Experiments without FB measure ecological achievement--the ability of subjects to extrapolate their past experience to the current stimuli.     

Early motion processes and the kinetic depth effect

It has been known for over 30 years that motion information alone is sufficient to yield a vivid impression of three-dimensional object structure. For example, a computer simulation of a transparent sphere, the surface of which is randomly speckled with dots, gives no impression of depth when presented as a stationary pattern on a visual display. As soon as the sphere is made to rotate in a series of discrete steps or frames, its 3-D structure becomes apparent. Three experiments are described which use this stimulus, and find that depth perception in these conditions depends crucially on the spatial and temporal properties of the display:

1. Depth is seen reliably only for between-frame rotations of less than 15°, using two-frame and four-frame sequences.

2. Parametric observations using a wide range of frame durations and inter-frame intervals reveal that depth is seen only for inter-frame intervals below 80 msec and is optimal when the stimulus can be sampled at intervals of about 40-60 msec.

3. Monoptic presentation of two frames of the stimulus is sufficient to yield depth, but the impression is destroyed by dichoptic presentation.

These data are in close agreement with the observed limits of direction perception in experiments using “short-range” stimuli. It is concluded that depth perception in the motion display used in these experiments depends on the outputs of low-level or “short-range” motion detectors.     

Stereokinetic effect and its relation to the kinetic depth effect.

The stereokinetic effect (SKE) has been defined and studied by nested circular patterns rotating on a turntable. Circles must appear not to rotate as they revolve, which in turn results in their appearing to translate relative to one another. A powerful illusion of object depth results even though the individual circles do not undergo an appropriate foreshortening consistent with their apparent changes in slant. It is suggested and tested that the SKE is based on the changing positions between the nested contours despite the absence of any change within each contour, whereas the kinetic depth effect (KDE) entails both kinds of change. It follows that a turntable method of presentation is not necessary, and between-contour transformations can be simulated by computer animation. Displays consisting of simple translations were shown to evoke robust depth impressions as were patterns consisting of contours of varying shapes. Comparisons of the depth, compellingness, and rigidity of matched SKE and KDE displays are reported. The SKE is taken to be paradigmatic for how the visual system perceives depth when observing small object rotations that occur in everyday situations.     

Rigid and non-rigid kinetic depth effect with rotating discrete helices

Summary To examine the conditions in which human observers fail to recover the rigid structure of a three-dimensional object in motion we used simulations of discrete helices with various pitches undergoing either pure rotation in depth (rigid stimuli) or rotation plus stretching (non-rigid stimuli). Subjects had either to rate stimuli on a rigidity scale (Experiments 1 and 2) or to judge the amount of rotation of the helices (Experiments 3 and 4). We found that perceived rigidity depended on the pitch of the helix rather than on objective non-rigidity. Furthermore, we found that helices with a large pitch/radius ratio were perceived as highly non-rigid and that their rotation was underestimated. Experiment 5 showed that the detection of a pair of dots rigidly related (located on. the helix) against a background of randomly moving dots is easier at small phases in which the change of orientation across frames is also small. We suggest that this is because at small phases the grouping of dots in virtual lines does occur and that this may be an important factor in the perceived nonrigidity of the helices.This research was supported by MPI 60% (1987, 1988) and CNR (1986), 1987, 1988) grants to Clara Casco and Sergio Roncato and Grant CNR 90.01603.PS93 to Giorgio Ganis.     

On the limits of perceptual complementarity in the kinetic depth effect

In a series of experiments, we have investigated the abilities of human observers to perceive geometric properties of moving three-dimensional objects as a function of their perspective and rotational complexities. The results indicate a decreasing ability of observers to extract metric, angular, and rigid motion as the perspectives and rotations depart from parallel projections and one-parameter central rotations. In this way, quantitative limits are suggested for the principle of perceptual complementarity suggested by Shepard (1981).     

Simple kinetic information for transparent depth

The present paper reports three investigations of new kinetic information for transparent depth using computer-generated dot patterns. An initial demonstration showed that separation in depth could be obtained by translating rectangular lattices of dots through one another like intersecting columns of marching soldiers. The first two experiments showed that diagonal interactions between lattices created significantly stronger separation than did horizontal or vertical interactions (horizontal was, in turn, stronger than vertical) and that patterns which translated through one another without any of the individual elements intersecting were better separated than those whose rows or columns intersected in register. The third experiment showed that random patterns interacting in any direction created the strongest separations of all the patterns observed. Results were taken to indicate that a unified theory of depth information, developed in the context of James Gibson’s ecological optics, must incorporate both spatial and kinetic structure in its specification of necessary and sufficient stimulus conditions.     

Ratings of kinetic depth in multidot displays

Subjects saw kinetic depth displays whose shape (sphere or cylinder) was defined by luminous dots distributed randomly on the surface or in the volume of the object. Subjects rated perceived 3-D depth, rigidity, and coherence. Despite individual differences, all 3 ratings increased with the number of dots. Dots in the volume yielded ratings equal to or greater than surface dots. Each rating varied with 3 of 4 factors (shape, distribution, numerosity, and perspective), but the ratings either between trials or between conditions were often uncorrelated. Object shape affected rigidity but not depth ratings. Veridically perceived polar displays had slightly lower rigidity but higher depth ratings than parallel projection displays. (Reversed polar displays were always grossly nonrigid.) The interaction of ratings and stimulus parameters requires theories and experiments in which different KDE ratings are not treated interchangeably.     

Seeing stereoscopic depth from disparity between kinetic edges

Traditionally, it is assumed that stereovision operates only on the positional difference (disparity) between luminance-defined features in the images in the left and the right eye. Here, I show that stereoscopic depth can be seen from disparity between edges created by relative motion of texture elements, and between edges created by correlated flicker of stationary texture elements. Luminance-based stereopsis was impossible since the texture was binocularly uncorrelated. Positional disparity of the centre of revolving patterns was not an efficient depth cue. Stereopsis from the stimuli presented here was possible even without binocular overlap of textured areas. The results provide evidence that positional disparity of kinetic edges, defined by correlated flicker or motion contrast alone, can be used as matching features to recover stereoscopic depth.     

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 role of perceptual organization in the depth perception of kinetic lattice displays

College student subjects were asked to judge perceived depth in computer-generated displays. In all displays, one lattice of points moved through a stationary lattice in either a rowwise or columnwise direction. No points of the two lattices ever touched. Two display variables, strain and shear, each had a significant effect on depth ratings. Shear, however, was only effective at the level of strain for which depth ratings were high. The results confirm earlier studies in which “topological breakage” information was found to affect depth perception. The outcome of this study suggests that principles of perceptual organization can influence the nature of effective breakage information.     

Linear vection in the central visual field facilitated by kinetic depth cues.

Illusory self-motion (vection) is thought to be determined by motion in the peripheral visual field, whereas stimulation of more central retinal areas results in object-motion perception. Recent data suggest that vection can be produced by stimulation of the central visual field provided it is configured as a more distant surface. In this study vection strength (tracking speed, onset latency, and the percentage of trials where vection was experienced) and the direction of self-motion produced by displays moving in the central visual field were investigated. Apparent depth, introduced by using kinetic occlusion information, influenced vection strength. Central displays perceived to be in the background elicited stronger vection than identical displays appearing in the foreground. Further, increasing the eccentricity of these displays from the central retina diminished vection strength. If the central and peripheral displays were moved in opposite directions, vection strength was unaffected, and the direction of vection was determined by motion of the central display on almost half of the trials when the centre was far. Near centres produced fewer centre-consistent responses. A complete understanding of linear vection requires that factors such as display size, retinal locus, and apparent depth plane are considered.     

Apparent depth of pictures reflected by a mirror: The plastic effect

We investigated the plastic effect in picture perception, in which the apparent depth of a picture is increased when it is reflected by a mirror. The plastic effect was well known in the mid-18th century, but very few studies have elucidated its nature. In Experiment 1, we examined how often the plastic effect occurs in different ocular conditions. A group of 22 observers compared directly observed pictures and their mirror-reflected images in each of free-binocular, free-monocular, and restrictive-monocular conditions. When the observers were forced to choose the picture that appeared greater in depth, 73?% of them chose the reflected pictures, regardless of oculomotor condition. In Experiment 2, we examined how often the plastic effect is detected as a function of observation time. When 22 observers compared a directly watched movie and its mirror-reflected movie for 5?min, the number of observers who judged the reflected movie to be greater in depth was about 55?% at the onset of the trial but was 86?% at the end. In Experiment 3, we examined transfer of the plastic effect. Ten observers judged the change in apparent depth of directly observed pictures after prolonged exposure to the same reflected or actual pictures. Transfer was confirmed and was greater for pictures that represented greater depth (r = .88). We suggested that the plastic effect is mainly induced by the double apparent locations of a reflected picture. From the long incubation time and the transfer to real pictures, we also suggested that it involves perceptual learning regarding visual skill.     

Kinetic depth effect and identification of shape

We introduce an objective shape-identification task for measuring the kinetic depth effect (KDE). A rigidly rotating surface consisting of hills and valleys on an otherwise flat ground was defined by 300 randomly positioned dots. On each trial, 1 of 53 shapes was presented; the observer's task was to identify the shape and its overall direction of rotation. Identification accuracy was an objective measure, with a low guessing base rate of the observer's perceptual ability to extract 3D structure from 2D motion via KDE. (1) Objective accuracy data were consistent with previously obtained subjective rating judgments of depth and coherence. (2) Along with motion cues, rotating real 3D dot-defined shapes inevitably produced a cue of changing dot density. By shortening dot lifetimes to control dot density, we showed that changing density was neither necessary nor sufficient to account for accuracy; motion alone sufficed. (3) Our shape task was solvable with motion cues from the 6 most relevant locations. We extracted the dots from these locations and used them in a simplified 2D direction-labeling motion task with 6 perceptually flat flow fields. Subjects' performance in the 2D and 3D tasks was equivalent, indicating that the information processing capacity of KDE is not unique. (4) Our proposed structure-from-motion algorithm for the shape task first finds relative minima and maxima of local velocity and then assigns 3D depths proportional to velocity.     

The effect of discourse structure on depth of semantic integration in reading

A coherent discourse exhibits certain structures in that subunits of discourses are related to one another in various ways and in that subunits that contribute to the same discourse purpose are joined to create a larger unit so as to produce an effect on the reader. To date, this crucial aspect of discourse has been largely neglected in the psycholinguistic literature. In two experiments, we examined whether semantic integration in discourse context was influenced by the difference of discourse structure. Readers read discourses in which the last sentence was locally congruent but either semantically congruent or incongruent when interpreted with the preceding sentence. Furthermore, the last sentence was either in the same discourse unit or not in the same discourse unit as the preceding sentence, depending on whether they shared the same discourse purpose. Results from self-paced reading (Experiment 1) and eye tracking (Experiment 2) showed that discourse-incongruous words were read longer than discourse-congruous words only when the critical sentence and the preceding sentence were in the same discourse unit, but not when they belonged to different discourse units. These results establish discourse structure as a new factor in semantic integration and suggest that discourse effects depend both on the content of what is being said and on the way that the contents are organized.