Stereokinesis with moving visual phantoms

When a flat pattern composed of a solid ellipse with two symmetrical semirings (corresponding to the visible parts of a contour ellipse whose major axis is perpendicular to that of the solid ellipse) is slowly rotated in the frontoparallel plane, a compelling three-dimensional impression occurs. Subjects report seeing an egg-shaped object that is inserted into a circular ring: the two objects move solidly into three-dimensional space and a moving visual phantom is generated so that the ring appears completed by an illusory curved bar in the region closest to the observer during rotation. A number of variations of this illusion are presented. It is shown that stereokinetic phantoms (i) maintain the shape of the inducing elements; (ii) appear only after the stereokinetic transformation has taken place; and (iii) depend on the organization of the three-dimensional percept as a whole. Relations between stereokinetic phantoms and other completion phenomena are presented and discussed.     

Subjective contours can produce stereokinetic effects

When a pattern of interrupted concentric circles drawn so as to produce an anomalous contour ellipse is slowly rotated in the frontoparallel plane, the subjective figure appears first to deform and then to tilt as a ring in 3-D space over motionless circles. Also, Benussi's floating cone can be obtained by placing an eccentric gray dot upon an anomalous solid ellipse and setting this figure into rotation. These patterns provide strong evidence that subjective contours can produce stereokinetic effects as effectively as real contours can. Implications for current explanations of stereokinetic effects are presented and discussed.     

Attentional distribution in the visual field duringsame-different judgments as assessed by response competition

Judgments ofsame anddifferent on a comparison task have been found to be subject to response competition if an irrelevant stimulus is presented in the display along with the target stimuli. For example, the reaction time for judging two letters the same is markedly increased if a different but irrelevant letter is also present in the display (C. W. Eriksen, O’Hara, & B. [A.] Eriksen, 1982). We have made use of this competition effect to map the visual attentional field in two dimensions. In two experiments, we varied the size of the attended area by varying the separation of the comparison stimuli. The boundaries of the attended area were mapped by varying the location of a response-competitive irrelevant noise letter. On this task, the attended area was found to be elliptical in shape, with the location of the target stimuli defining the major axis. The minor axis of the ellipse increased in direct proportion to increases in the major axis. Rather than interpret these field effects in terms of areas of enhanced processing, we propose that instead they represent the limits or failures in inhibition of competing stimulation.     

On the minimal relative motion principle—the oscillating tilted bar

Beghi, Xausa, Tomat, and Zanforlin (J. Math. Psychol. 41(1997) 11) present a visual stereokinetic illusion. In the image plane, one end of an oblique bar moves horizontally back and forth, while the other end is stationary. Perceptually, this becomes a bar of a constant length rotating in depth around a vertical axis that passes through the stationary end of the bar. Beghi et al. (1997) provide a mathematical model of minimal relative motion to account for this percept. Here we show that the minimal relative motion principle cannot explain the perceptual phenomenon. Specifically, we raise two objections. (1) It is necessary to consider not only the length, but also the direction, of a vector when comparing vector fields. In fact, when directions are taken into consideration, Beghi et al.'s mathematical result diverges from their perceptual experimental result. (2) There is a mathematical inconsistency in Beghi et al. (1997): mixing absolute and relative velocities in their minimization is unwarranted, and does not lead to correct minimization.     

Learning to see stereokinetic effects

The Saturn illusion is a stereokinetic effect that occurs when a flat pattern composed of a full ellipse with two symmetrical semirings is rotated slowly in the frontoparallel plane. Subjects report seeing an egg-shaped object inserted into a circular ring, and the two objects move solidly into 3-D space as a single rigid body. Inexperienced observers show a conspicuous delay before reaching this percept. Two experiments are reported in which it is shown that this incubation time progressively decreases with repeated exposures to the stimulus pattern. A certain amount of time (14 s on average) is, however, required to obtain the effect, even after six successive exposures. It is argued that this time, which is independent of the speed of rotation and is not further reducible, is a fixed entity and is needed to compute the most rigid 3-D solution from deformations in the 2-D image. The results are discussed in relation to current theories of perception of structure from motion.     

Stereokinetic phenomena revisited: The oscillating tilted bar, the swinging gate and the vertical contracting bar

We present here a revised version of our mathematical modelling of the stereokinetic phenomena known as the “oscillating tilted bar”, the “swinging gate” and the stereokinetic phenomenon elicited by a vertical, periodically contracting line segment simultaneously undergoing a lateral displacement from left to right and conversely in the frontal plane of an observer. The criticisms of Liu, Z. [(2004). On the minimal relative motion principle—The oscillating tilted bar. Journal of Mathematical Psychology, 48, 196-198] and Rokers and Liu [(2004). On the minimal relative motion principle—Lateral displacement of a contracting bar. Journal of Mathematical Psychology, 48, 292-295.] helped us in reformulating our models, eliminating discrepancies and ambiguities. Characteristic of the present modelling is the clear definition of a multi-stage mathematical procedure matching different requirements posed by the Visual System, as we know them from our experimental observations.     

Shape effects on memory for location

The participants were 40 students who were briefly presented 32 dot locations, one at a time, and attempted to reproduce each location after a short delay. Half of the participants completed the task with the surrounding shapes being a circle, a horizontal ellipse, and a vertical ellipse; for the other half, the surrounding shapes were a square, a triangle, and a pentagon. Elongation of the task field along an axis led to exaggerated bias along that axis, but the pattern of bias was fairly constant across the shapes. The data were modeled by assuming that bias in estimation was due to the weighting of spatial category prototypes. Modeling indicated that shape affected spacing of prototypes, but there was no evidence that it affected the number of prototypes. These results were consistent with use of a viewer-based frame of reference, with prototypes reflecting four spatial quadrants generated by left—right and up—down distinctions from the viewer’s perspective.     

Visual binding in the standing wave illusion

When two video frames are alternated at the appropriate rate, one with a central bar and the other with two flanking bars, the central bar becomes invisible. Competing explanations for this standing wave illusion are examined, with the results showing an influence of higher level shape representations on lower level edge processes. In Experiment 1, flanking bar duration was found to be more important to masking than central bar duration. Experiment 2 showed strong nonlocal effects in that masking of the central bar depended critically on whether it appeared in the same video frame as other visible bars. Experiments 3 and 4 showed that the contour shared by bars in separate frames was a less important factor than shape and surface similarity. This illusion is therefore an excellent tool for studying recursive interactions between higher level object representations and lower level contour processes.     

The height of a stereokinetic cone: A quantitative determination of a 3-D effect from 2-D moving patterns without a “rigidity assumption”

Summary When a circular disc with an eccentric dot painted on it is set in slow circular motion, a three-dimensional solid object appears to the observer: the stereokinetic cone. The cone shows a well-defined height and tilt. All current theories of how the visual system can extract 3-D percepts from 2-D moving patterns, are based on a rigidity assumption hypothesis. But this assumption cannot explain why the stereokinetic cone appears to have a well-defined height. An alternative hypothesis is proposed here, which avoids the rigidity assumption and is based on a minimization process of the relative velocity differences between all the points of the rotating pattern. The hypothesis allows a quantitative prediction of the stereokinetic cone height both when the rotating disc is circular and when it is elliptical. The predictions are in good agreement with previously reported experimental results and with our own observations.     

Perception of the stereokinetic illusion by the common marmoset (<Emphasis Type="Italic">Callithrix jacchus</Emphasis>)

Stereokinetic illusions have never been investigated in non-human primates, nor in other mammalian species. These illusions consist in the perception of a 3D solid object when certain 2D stimuli are rotated slowly in the plane perpendicular to the line of sight. The ability to perceive the stereokinetic illusion was investigated in the common marmoset (Callithrix jacchus). Four adult marmosets were trained to discriminate between a solid cylinder and a solid cone for food reward. Once learning criterion was reached, the marmosets were tested in sets of eight probe trials in which the two solid objects used at training were replaced by two rotating 2D stimuli. Only one of these stimuli produced, at least to the human observer, the stereokinetic illusion corresponding to the solid object previously reinforced. At test, the general behaviour and the total time spent by the marmosets observing each stimulus were recorded. The subjects stayed longer near the stimulus producing the stereokinetic illusion corresponding to the solid object reinforced at training than they did near the illusion corresponding to the previously non-rewarded stimulus. Hence, the common marmosets behaved as if they could perceive stereokinetic illusions.     

“Octave illusion” or “Deutsch’s illusion”?

The “Deutsch’s illusion” occurs in most people when a dichotic pair of tones spaced an octave apart is presented repeatedly in alternation, so that when the right ear receives the high tone, the left ear receives the low tone, and vice versa. The illusory percept consists typically in a single low tone heard at one ear alternating with a single high tone heard at the other ear. Here, we investigate whether the frequency interval between the tones and their duration play a role in the perception of the illusion. By testing 74 subjects we demonstrate that the illusion is not confined to tones spaced an octave apart but it is perceivable also with tones separated by a major seventh, a minor ninth, a major ninth, and a minor tenth. Regarding duration, the present results show that the illusion is stronger with tones lasting 500 than 200 ms. The present results suggest that the perceptual mechanisms at the basis of the illusion are not strictly linked to the frequency relationships between the dichotic tones.     

Domestic chicks perceive stereokinetic illusions

Stereokinetic illusions occur when certain 2-D patterns are set in slow rotation in a plane perpendicular to the line of sight. Such phenomena have never been investigated in animal species other than our own. We used the domestic chick (Gallus gallus) to check whether these illusions are experienced by non-human species, taking advantage of filial imprinting. Newly hatched visually naive chicks were individually exposed for 4 h to 2-D stimuli producing, to a human observer, the perception of a stereokinetic cone (experiment 1) or of a stereokinetic cylinder (experiment 2). Thereafter, each chick underwent a free-choice test between a solid 3-D cone and a solid 3-D cylinder. A control group of newly hatched but not imprinted chicks underwent the same testing procedure, to check for the presence of any spontaneous preference for one or other of the two solid objects. Imprinted chicks approached the 3-D stimulus closely resembling the stimulus they had been exposed to during imprinting (the cone in experiment 1 and the cylinder in experiment 2). Non-imprinted chicks did not show any preference. These results suggest that domestic chicks experience stereokinetic illusions.     

On the nature of the decision axis in signal-detection-based models of recognition memory

Most models of recognition memory involve a signal-detection component in which a criterion is placed along a decision axis. Older models generally assume a familiarity-decision axis, but newer models often assume a likelihood ratio axis instead because it allows for a more natural account of the ubiquitous mirror effect. In 3 experiments reported here, item strength was differentially manipulated to see whether a mirror effect would occur. Within a list, the items from 1 category were strengthened by repetition, but the items from another category were not. On the subsequent recognition test, the hit rate was higher for the strong category, but the false-alarm rates for the weak and strong categories were the same (i.e., no mirror effect was observed). This result suggests that the decision axis represents a familiarity scale and that participants adopt a single decision criterion that they maintain throughout the recognition test.     

The role of vision in the on-line correction of illusion effects on action.

In this study, participants reached out and picked up a bar placed on a background grating that induced an illusion in the perceived orientation of the bar. The illusion had a large effect on the orientation of the hand early in the reaches, but this effect decreased continuously as the hand approached the target. This pattern occurred whether or not participants were allowed vision of the hand and target while reaching. These results are consistent with a "planning/control" model of action, in which actions are planned using a context-dependent visual representation but monitored and corrected on-line using a context-independent visual representation. The hypothesized neural bases of these representations are discussed.     

Stereokinetic shapes and their shadows

The visual space of phenomenal appearances has a complex geometry which cannot be reduced strictly to Euclidean or projective geometry. The distinctive nature of this space and its objects is evidenced paradigmatically by stereokinetic phenomena, which are perceptual objects in actual three-dimensional coming into being. Stereokinetic phenomena produce the appearance not only of corporeality but also, in certain circumstances, of shadows. By altering certain components of his experiments on the three-dimensional appearance of a truncated cone, in fact, Musatti discovered that on its white base floats some sort of shadow obscuring stretches of the white lines. These shadows are connected to phenomena of amodal presentations successively analysed by Kanizsa. The continuity of the unfolding in visual space of stereokinetic transformations produces a diversified series of percepts coming into being, shadows included, and highlights the role of configurational movement as a factor of formal unification, thereby proposing once again the hypothesis of assimilative factors as responsible for the field organisation of past experience.     

The effect of movement velocity on form perception: geometric illusions in dynamic displays

We investigated the effects of movement velocity on the perception of simple geometric trajectories. We show that when an ellipse is traced by the continuous displacement of a spot against an empty background, the subjective aspect ratio (R = vertical axis/horizontal axis) of the figure depends on the law of motion of the spot. If the tangential velocity of the spot is constant, very large and subject-specific biases emerge in the perception of the aspect ratio. If the tangential velocity of the spot is made equal to that of an elliptic motion with aspect ratio R less than 1, and resulting from the vectorial composition of two harmonic functions (Lissajous motion) there is a general trend to perceive the ellipse as being flatter than in reality. The effect, however, is not symmetric: when the velocity follows a Lissajous modulation with R greater than 1, highly significant biases are still present in most subjects, but no common trend emerges from the experimental population. The results are discussed in the context of recent findings on the relationship between form and kinematics in spontaneous human movements.     

Adventures with gelatinous ellipses--constraints on models of human motion analysis

An ellipse rotating rigidly about its center may appear to rotate rigidly or to deform nonrigidly so that it appears gelatinous. We use this ambiguous stimulus to study how motion information is propagated across space. We find that features that are quite far from the contour of the ellipse may have a strong influence on the percept of the ellipse, provided they move in a way consistent with the motion of the ellipse. We show that the percept cannot be accounted for by computational models that pool constraints over a local area only, or by models that propagate information along contours, or by models that indiscriminately propagate information across space. However, the percept can be accounted for by a class of models that assume smoothness in a layered representation.     

Multiple 3-D interpretations in a classic stereokinetic effect

It is known that a flat ellipse rotating in the frontoparallel plane sooner or later appears as a rigid circular disc tilting in 3-D space. An experiment is reported in which prolonged exposure to the same flat pattern produces a second previously unnoticed 3-D percept: an elongated egg slanted in 3-D space, which points towards the observer and the end parts of which describe a circular trajectory in the frontal plane. It is shown that the achievement of this alternative percept is not affected by the particular shape of the ellipse, although the time needed to reach it increases with an ellipse with a 2:3 axis ratio.     

The luminance conditions of Fuchs's transparency in two-dimensional patterns

Fuchs's transparency occurs when the contour of a transparent surface encloses the contour of another surface located on an underlying homogeneous background. The luminance conditions of Fuchs's transparency have not yet been determined. Six experiments were designed to study this problem with achromatic two-dimensional patterns. An ellipse enclosing a coplanar square was briefly presented. It simulated the cast of an elliptical spotlight or shadow on the square. The duration of the ellipse, the luminance of the square before the ellipse appeared, and the luminance of two squares outside the ellipse did not substantially affect the probability of perceiving the ellipse as transparent. However, this probability varied largely with the single values of the stimulus luminance differences and with the order relations of the stimulus luminances. It is concluded that this local and global luminance information conditioned the occurrence of Fuchs's transparency in two-dimensional patterns.     

Rats (Rattus norvegicus) encode the shape of an array of discrete objects

To navigate efficiently, a traveler must establish a heading using a frame of reference. A large body of evidence has indicated that humans and a variety of nonhuman animals utilize the geometry, or shape, of enclosed spaces as a frame of reference to determine their heading. An important and yet unresolved question is whether shape information from arrays of discrete objects and enclosed environments are represented, and utilized, in the same way. In the present study, rats were presented with a reference memory task in which they had to find water that was hidden in 1 of 4 discrete and unique objects placed at the vertices of a rectangle. The results indicate that rats could utilize both feature and geometry cues to locate the hidden goal. The rats' performance declined during transformation tests using a triangular array, indicating that the rats may have encoded the primary axis of the object array, rather than local cues, to direct their search.