August 2004
Volume 45, Issue 8
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Visual Psychophysics and Physiological Optics  |   August 2004
The Duncker Illusion: Intersubject Variability, Brief Exposure, and the Role of Eye Movements in Its Generation
Author Affiliations
  • Ari Z. Zivotofsky
    From the 1Brain Science Program, Bar Ilan University, Ramat Gan, Israel; and the 2Laboratory of Sensorimotor Research, National Eye Institute, National Institutes of Health, Bethesda, Maryland.
Investigative Ophthalmology & Visual Science August 2004, Vol.45, 2867-2872. doi:10.1167/iovs.04-0031
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      Ari Z. Zivotofsky; The Duncker Illusion: Intersubject Variability, Brief Exposure, and the Role of Eye Movements in Its Generation. Invest. Ophthalmol. Vis. Sci. 2004;45(8):2867-2872. doi: 10.1167/iovs.04-0031.

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Abstract

purpose. The Duncker illusion, also known as induced motion, is the illusory component of an object’s motion that results from background movement. The origins of this robust phenomenon are still subject to debate. The goal of this study was to examine the role eye movements play in its generation.

methods. The Duncker illusion was generated by rear-projecting an LED target and a random-dot background onto a semitranslucent screen. Each moved under independent control of mirror galvanometers. The background was either stationary or moved vertically, whereas the target moved horizontally with various degrees of a vertical component. Using a two-alternative, forced-choice cancellation paradigm involving multiple interleaved staircases, seven human subjects quantified the illusion under a variety of conditions. These conditions included varying the exposure time from 50 to 200 ms.

results. The strength of the illusion did not decrease, even when exposures too brief to generate eye movement were used. Four of the subjects showed no difference between long and short exposures (P > 0.12). In two the illusion was stronger for short exposures (P < 0.05), and in one the illusion was not quantifiable. There was little intrasubject variability across trial types, yet there was a large intersubject variability in the strength of the illusion.

conclusions. The illusion is robust in that it is perceived under a wide variety of conditions by all observers. By varying the parameters, it was possible to demonstrate that eye movements do not play a role in generating the illusion and that this robust illusion is most likely caused by the visual system attributing relative motion between target and background to target motion and ignoring any true background movement. The mechanism by which this occurs varies in degree between individuals.

Under normal circumstances, the visual background is generally large, distant, and stationary, with smaller, nearer objects moving across it. These moving objects can induce a variety of visual percepts. If an object moves while the observer fixates a stationary point in the background, the object’s retinal image mirrors the object’s true motion, and the observer accurately perceives the object’s motion across the stationary background. If the observer tracks such an object with his or her eyes, the retinal image of the background moves, while the retinal image of the object is roughly stationary, yet the observer still perceives the object to be moving across a stationary background, presumably because the brain has access to information indicating that the eyes, and not the background, are moving. 
If, however, the background moves, that adds an additional, unnatural source of relative motion between the target and background. Duncker 1 demonstrated that background motion induces an erroneous perception of motion of a stationary foreground object. The induced illusory motion of the object is in the direction opposite that of the background motion. 
A more complex variant of the Duncker illusion is when both the object and the background move—a situation easily arranged in the laboratory—and the observer perceives (illusory) motion of the object in addition to the actual motion. For example, if the object moves horizontally, and the background moves vertically, then the object is perceived to have an illusory vertical component resulting in a perceived diagonal trajectory, as though the background was assumed to be stationary and the relative motion between the object and background was attributed to motion of the object. 2  
When an observer’s gaze moves in a natural environment, retinal images of the large stable background move in the opposite direction across the retina. It has long been recognized that uniform motion of a large visual stimulus can induce illusory self-motion in the opposite direction. 3 4 This phenomenon is known as vection and has been attributed to the fact that in natural circumstances retinal motion of the background is probably due to motion of the observer. 
The visual system thus seems to rely on an assumption of a background that is a stable, reliable frame of reference, and this assumption can lead to illusory motion of a foreground target and/or the observer. In a previous study, 5 the magnitude of errors induced by this illusion in saccades to remembered targets was quantified. Previous studies of this extremely robust illusion have quantified it using the slant-matching method. 6 7 This is a subjective method in which the participant draws his percept on a piece of paper after exposure to the stimulus. An alternative method to quantify the illusion is that of cancellation of the illusion (described later), and that is what is used herein. In addition, the previous studies were performed over periods of seconds to minutes, rather than shorter durations during which the illusion is first perceived. No investigators in previous studies have used qualitative methods in subsecond durations to quantify the illusion, to measure its intersubject variability, or to determine how various stimulus parameters affect the illusion. Those questions are addressed in the present study. 
Another question concerns the possible role of eye movements in the generation of the illusion: Could the illusory motion of the object result from slippage of its retinal image due to involuntary tracking of the background motion? The “dragging” of the eye by the background yields retinal motion that can be (mis)interpreted as target motion in the opposite direction. Eye movements have been implicated in other illusions of motion and have been suggested as the cause of this illusion. Eye movement information can at times be used to influence illusory judgments of direction of self-motion, 8 9 and it has been suggested that eye movements play a role in vection. 10 We provide herein evidence that eye movements are not necessary to generate the Duncker Illusion, by showing that the illusion is still apparent, even when the exposure to the stimulus conditions is too brief for any eye movements to have occurred while the stimuli were visible. 
Some of these results have been reported in abstract form (Zivotofsky AZ, et al. IOVS 1997;38:ARVO Abstract 932). 
Methods
Subjects
Data were collected from seven human subjects. All procedures adhered to the tenets of the Declaration of Helsinki and were approved by the Institutional Review Committee concerned with the use of humans. All subjects gave informed consent. Two of the subjects assisted in the experiments and were aware of the hypotheses (FM, RK); the others were unaware of the purpose of the experiments. All subjects had normal or corrected-to-normal vision. 
Stimulus and Recording Procedures
The presentation of stimuli, and the acquisition, display, and storage of data were controlled by a computer (Vectra 486; Hewlett Packard, Palo Alto, CA), using a Real-time EXperimentation software package developed by Hays et al. 11 During recording sessions, subjects sat facing a translucent tangent screen (distance, 33.3 cm; subtend, 85° × 85°) onto which a target (high-brightness red LED projector; 0.3°) and background (a random-dot pattern of black dots on a white background, 50% density) that subtended 20° × 20° were separately back projected. Mirror galvanometers (model CX-660; drivers with MG350DT motors; General Scanning, Watertown, MA), in an x/y configuration positioned in each of the two light paths, were used to control the horizontal and vertical positions of the images. The galvanometers were driven by digital-to analog converter (DAC) outputs of the computer at a rate of 1 kHZ with a resolution of 12 bits. Subjects’ heads were secured in place by means of a chin rest, a forehead rest, and a headband. In most experiments the target and background were both seen by both eyes. In selected experiments it was arranged that the target was seen by only one eye and the background by only the other eye. For this, polarizing filters were placed in the two projection paths along with matching filters in front of each eye. The screen was constructed of material specially designed to retain polarization (Yamaboshi, Tokyo, Japan). 
Experimental Paradigms
In all experiments the target always moved horizontally, to either the right or the left, with various degrees of a vertical component added, as explained later, while the background moved either up or down (experimental) or was stationary (controls). The moving background induced an illusory vertical component to the target motion, which was in the direction opposite that of the background motion, causing the target to appear to be moving obliquely. To quantify the illusory vertical movement, we gave the target a real vertical component, the direction and magnitude of which were varied systematically to determine how much true vertical target motion was necessary to cancel the illusory effect induced by the background motion. A two-alternative, forced-choice (2AFC) procedure was used to find the point of subjective equivalence (i.e., the point where the subject reported vertical motion to be up or down 50% of the time). For this multiple, randomly interleaved, adaptive staircases (one-down/one-up) were used to adjust the vertical component of target motion progressively in accordance with the subject’s reported percept of motion. Each staircase started with the target moving at a random angle of up to 10° off the horizontal. For each trial (i.e., level of a staircase), the subject indicated with a button press whether the target’s vertical component was up or down. If the subject indicated that the target appeared to be moving with an upward (or downward) component, the true upward component was reduced (or increased) for the next step in that staircase. The vertical component was altered initially in steps of 20°, and each time it reversed direction (signaling overshoot), the step size was reduced by a factor of 1.5 until the step was changing by 2° each time, at which rate it continued until the end of the staircase. Rather than a fixed number of reversals in a staircase, each staircase had a fixed number of total steps. Thus, after 12 steps, a new block of interleaved staircases was started together. This technique maximized the data collected within the important transition zone around the trajectory angle that gave subjective equivalence. 
For most of the experiments a standard paradigm was used in which the speed of both the target and the background was 20°/sec, and the images were viewed binocularly. The subject initially fixated a stationary target against a stationary background. After a variable period, the target and the background began moving. The primary direction of the target motion (i.e., right or left), was randomized. After 200 ms, all visual stimuli were turned off, and the subject pressed a button to indicate the perceived vertical direction of the target motion. To establish some degree of uniform behavior, the subjects were instructed to track the target as best as they could, although eye movements were not monitored. For all subjects the effect of shortening the stimulus duration to 50 ms (at which point the target and background were both extinguished) was examined, and for some of the subjects, the effect of varying the target speed (20°, 28°, or 40°/sec) and of restricting the subject’s view with orthogonal polarizing filters so that the target and the background were seen by different eyes (dichoptic presentation) were also considered. 
Data Analysis
The raw psychophysical data consisted of the true direction of target motion (expressed as the angle of trajectory with respect to the horizontal, with zero defined as right and 90° as up) and the subject’s response indicating whether the target was perceived to have an upward or downward component. The data were sorted based on trial type (i.e., the direction of background motion and the direction of target motion at the start of the staircase). Frequency histograms were constructed of the number of trials in which the subject indicated that he or she perceived upward or downward trajectories for the range of true target trajectories. Within each trial type, the range of target trajectories was divided into 20 bins of equal size. 
A quantitative estimate of the strength of the illusory movement was obtained by fitting a psychometric function to plots of the percentage of trials in which motion was perceived to be upward against the direction of true target motion. There were two requirements in the selection of the function we used. It had to be a symmetric function—that is, it had to yield the same value for the inflection point irrespective of whether the relationship between angle and “percent up” or angle and “percent down” was calculated. There is nothing intrinsically special about either direction, and the results therefore had to be identical. The function also had to provide a slope parameter that was insensitive to the location of the sigmoid on the x-axis to leave open the possibility of comparing slopes across experimental conditions. 
A two-parameter exponential function of the form, f(x)=1/{1+exp[b · (xc)]}, where b is the slope coefficient and c is the value at the inflection point, was used. This function is symmetric about the inflection point and insensitive to position on the x-axis. The function was fit on computer (SigmaPlot for Windows; SPSS, Chicago, IL) and used the target trajectory at the function’s inflection point as an estimate of the point of subjective equality (PSE). 
Results
When the target moved with purely horizontal motion, all subjects reported the target to have a vertical component in the direction opposite the background motion. When the target’s motion had a large (>30°) vertical component in the direction of background motion, subjects generally reported that the perceived vertical component of target motion was now in the true direction. In other words, the real vertical motion of the target had overcome the illusory component induced by the background motion. Figure 1 shows the distribution of upward perception as a function of the true target trajectory for one subject when the background motion was down and the target moved to the right. When the target was moving purely horizontally, the subject reported that the target’s motion had an upward component, and when the target’s trajectory had a downward component exceeding 23°, the subject invariably reported that the target’s motion had a downward component. For target trajectories with a downward component of 14° to 20°, the subject sometimes reported an upward component and other times a downward component. Over this zone of uncertainty, the imposed vertical component of target motion came close to balancing the illusory vertical component due to the background motion. 
A psychometric function (see the Methods section) was fitted to the data (curve in Fig. 1 ) and was used to estimate the trajectory for which there was subjective equality between the real and illusory motion—that is, when the ordinate was 50%. For the data shown, this criterion yielded a trajectory of −17.7° (r 2 = 0.955). 
Six of the seven subjects showed the same general effect, their psychometric functions indicating that the trajectories associated with subjective equality were invariably deviated in the direction of background motion consistent with an (illusory) shift of the perceived trajectory in the opposite direction to the background motion. In 23 of the 24 cases (six subjects times four experimental conditions) the PSE was significantly different from zero. It was not possible to fit the psychometric function to the data for the seventh subject, because this subject always reported target motion in the opposite direction to background motion, even in the case of our largest deviations of the true target direction from horizontal. In other words, there was no reversal in the direction of perceived target motion. This phenomenon will be further explored later in Results. 
The data for the other six subjects are summarized in the histograms of Figure 2 , which show the estimates of the direction of subjective equality for the two directions of background motion (up, down) and target motion (horizontal component, right and left). There was considerable intersubject variability, and all the data in Figure 2 are ordered in accordance with the magnitude of the direction of subjective equality when the background motion was upward and the horizontal component of target motion was rightward. It is clear from Figure 2 that the rank ordering of subjects was often similar across all four conditions, thus revealing a good deal of intrasubject consistency across trials. (Spearman rank-order correlation shows that between conditions 1 and 2 the significance was at the 0.01 level and between conditions 2 and 3 it was at the 0.05 level.) Also shown in Figure 2 , with the same ordinal scale, are the data for the control conditions (background stationary), which indicate that all subjects estimated the target’s trajectory quite accurately when there was no background motion. The average absolute deviation from horizontal in the controls was 2.3° ± 1.6° (SD). The absolute perception of horizontal was thus reliable and close to ideal. Furthermore, this demonstrates that all subjects understood the task and performed it correctly. The seventh subject similarly performed the controls accurately, indicating that she too understood the task. 
As a means of assessing the role of eye movements in generating the illusion, the strength of the illusion (as measured by the PSE) was compared during 50- and 200-ms exposures. It is evident from Figure 3 , which plots the direction of subjective equality for the 50-ms against that for 200-ms exposures, that the magnitude of subjective equality was often similar in the two cases, though sometimes actually stronger with the shorter exposure. In four of the six subjects, there was no significant difference in the two conditions (P > 0.12, paired t-test). For the remaining two subjects the illusion was significantly stronger with the 50-ms exposure (P < 0.05). Thus, for all subjects, the illusory shift was still evident when the exposure time was reduced to 50 ms, which is significant because there was not sufficient time for any tracking eye movements to occur during this brief exposure period. This indicates that tracking during exposure to the stimuli is not necessary for the illusion. 
For these experiments, the speed of the target was always the same as that of the background (20°/sec). To two of the six subjects whose 20°/sec data could be fitted with psychometric functions, in a separate session a higher target speed (40°/sec) was presented while keeping the background velocity at 20°/sec, and in both cases the effect of the background motion was weaker, on average, by 56%. This decrease was statistically significant (P < 0.05, t-test) in three of four tests for subject 1, and in four of four tests for subject 2. This experiment was also tried on the subject who showed no reversal on the earlier experiment. With the higher speed, she now regularly showed a normal psychometric function. This is significant for two reasons. It means that she understood and was capable of performing the task, and thus her lack of reversals in the initial experiment was a real phenomenon. Second, it indicates that with a higher target speed she, too, showed a reduced effect of the background motion, enabling her to perceive a point at which the target reverses direction. Her initial lack of reversals was due to her ascribing a disproportionate weight to the background motion. 
In four of the six subjects, we also examined the effect of polarizing the display so that subjects saw the images either dioptically (as before) or dichoptically (the background being seen by one eye and the target being seen only by the other eye). The strength of the illusion in the dichoptic condition was no different from in the dioptic condition for all four subjects in all four permutations of the illusion (background up and down, target right and left; P > 0.05, t-test). 
Discussion
The Duncker illusion was found to be an extremely robust phenomenon. It is amenable to straightforward quantification using psychometric functions that reveal a good deal of intrasubject consistency across trials, but show an unanticipated high level of intersubject variability. The point of subjective equality was measured to provide an estimate of the perceived direction of the target motion and thus of the effect of the background movement. The amount of compensation required by each subject varied and is a measure of the magnitude of the component added by the background movement. Various methods have been used in the past to quantify both static 12 13 14 and moving 15 16 illusions. By quantifying the illusion under various conditions, it is possible to understand better the underlying mechanism used in generating the percept. In the present study, the quantification was also used to examine what role, if any, eye movements play in generating the illusion and to a lesser extent to examine other factors contributing to the generation of the illusion. 
Do Eye Movements Contribute to the Duncker Illusion?
Could the illusory motion of the object result from slippage of its retinal image due to involuntary tracking of the background motion? The role of eye movements in other illusions, both static and dynamic, has been investigated. Eye movement information can at times be used to influence illusory judgments of direction of self-motion, 9 and it has been suggested that eye movements play a role in vection. 10 Eye movements of some form seem to be required to generate the scintillating grid illusion on a Hermann grid. 17 In non-Duncker conditions it is well recognized that when a moving object is observed with stationary eyes it appears to move significantly faster than when the observer tracks the object. This is known as the Aubert-Fleischl Illusion or paradox. A similar phenomenon exists in estimating the speed of illusory motion in circular vection. 18 Thus, eye movements influence the percept of that illusion. 
Based on the finding that the illusory strength was little affected by shortening the period of exposure to 50 ms, it is clear that eye movements are not necessary for the Duncker Illusion: 50 ms does not allow enough time for any tracking to have occurred during the exposure period. As a matter of fact, it does not allow time for any eye movements. It is generally accepted that the eye movements with the shortest latencies are short-latency ocular following, which in humans has a latency of 70 to 75 ms. 19 An early study 20 in which eye movements were measured using the electro-oculogram (EOG) and in which subjects were instructed to fixate a point attached to a large moveable frame that caused induced motion, similarly concluded, based on different reasoning, that induced motion was not caused by those eye movements. However, their inconsistent, small findings, and less sophisticated methods raised doubts about the lack of relevant, causative eye movements. It seemed it was still possible that eye movements were necessary for the generation of the illusion. Our data with the 50-ms exposure rule out any role of eye movements in generating the illusion. 
A potentially confounding factor is the effect of anticipatory slow eye movements. The randomization of target direction as well as the random variation in time before target motion commenced minimized the possibility that anticipatory slow eye movements occurred. In addition, had they occurred, it is unlikely they would have correlated with the actual direction of target motion, and thus their influence would have been random and would not have contributed to the strength of the illusion. 
Perceived motion in cross-modal stimuli has also been demonstrated. Visual motion can “capture” a stationary sound source and elicit subjective motion 21 or can influence the motion of a moving sound source. 22 It has been demonstrated that ocular tracking of the visual target is not necessary to generate illusory motion. 
So What Does Generate the Duncker Illusion?
Several theories exist to explain the Duncker Illusion. One theory 5 6 7 suggests that the moving background activates the OKN system that is then suppressed by the smooth pursuit system. This nonactuated smooth pursuit in the direction opposite background motion causes the percept of target motion in the direction opposite background motion. 23 A problem with this theory is that during induced motion paradigms OKN is not suppressed. Typical OKN responses in the appropriate direction can be seen in previous works. 2 Supporters of this theory 7 have also noted the presence of OKN during the Duncker Illusion and view a correlation between the OKN strength and the magnitude of the illusion as supportive of this theory. An alternative hypothesis 24 about which the present study sheds no new light, suggests that the background movement alters the subject’s apparent straight-ahead (ASA). 
Based on the current findings, we hypothesize, as did Duncker in 1929, 1 that the visual system is accustomed to observing a world in which small objects always move against a larger, stationary background and thus attributes relative motion between a target and the background to target (or observer) motion. In general the assumption is accurate, and relative motion is in fact due to target motion. In these experiments there was both a vertical and a horizontal component to the relative motion and hence the visual system assumed, erroneously in this case, that the target had a diagonal trajectory. 
We found considerable intersubject variability in the strength of the illusion. It appears that different people weigh the effect of the background motion differently. One subject (RJK) at times behaved as though uninfluenced by the background motion and showed no statistical difference from the control task. Another subject (JM) often responded as though all relative motion were judged relative to a stationary background, so that when the target and background both moved down, but the target at a slower velocity, she reported the target as moving up. It may be possible to relate this individual response pattern to how subjects allocate visual attention. That is, it may be that RJK was more focused on the target with a “spotlight” of attention, while JM’s attention was more spatially distributed and included more of the background. 
The foregoing hypothesis explains the finding that increasing the target speed (while maintaining the same background speed) decreased the apparent strength of the illusion. When the vertical speeds of two targets traveling to the right with the same angle off of the horizontal are compared, the one with the overall higher velocity has a greater vertical component. Thus, the angle at which a particular target’s vertical speed “overtakes” the vertical motion of the background varies directly with the target’s velocity. As the target velocity is increased, this overtaking happens at a smaller angle, leading to an earlier percept of a reversal of the direction of the vertical component of the target motion. 
This also explains the unusual results of the seventh subject, which are a strong proof of this hypothesis. Her visual system seemed to treat all relative motion between the target and background as attributable to the target. Thus, when the target and background were moving with the same velocity she did not perceive a vertical component of the target that was sufficient to overtake the background motion, and thus she always reported an illusory component. This was true even at the extreme. When the background was moving down at 20°/sec and the target was moving almost perfectly vertically down at 20°/sec, there is a small upward relative motion and thus, despite the fact that the target was moving almost straight down, she perceived the target as moving up. However, if the target was moving at 40°/sec, its vertical component eventually overtook the illusory vertical component, and she finally saw the target moving in its veridical direction. 
In conclusion, the evidence presented in this study points to an explanation of the Duncker Illusion in which the visual system is seen as attributing relative motion between target and background inappropriately to target motion. Eye movements do not seem to play a role in the genesis of this illusion. 
 
Figure 1.
 
The percentage of trials in which the subject reported upward target motion: dependence on the true target trajectory. Sample data for one subject (MAB) in one experiment (background motion downward, target rightward, 200 ms exposure). On the abscissa, 0° signifies target motion to the right, 90° is up, and −90° is down. Because of the downward background motion, small negative angles are always perceived as having an upward component. The data is the percentage of trials in which the subject reported upward target motion (symbols). A symmetric exponential curve was fit to the data (r 2 = 0.955) and the 50% point (the inflection point) was used as the point of subjective equality.
Figure 1.
 
The percentage of trials in which the subject reported upward target motion: dependence on the true target trajectory. Sample data for one subject (MAB) in one experiment (background motion downward, target rightward, 200 ms exposure). On the abscissa, 0° signifies target motion to the right, 90° is up, and −90° is down. Because of the downward background motion, small negative angles are always perceived as having an upward component. The data is the percentage of trials in which the subject reported upward target motion (symbols). A symmetric exponential curve was fit to the data (r 2 = 0.955) and the 50% point (the inflection point) was used as the point of subjective equality.
Figure 2.
 
Histograms showing the point of subjective equality (and SD) in six subjects in four test and two control conditions.
Figure 2.
 
Histograms showing the point of subjective equality (and SD) in six subjects in four test and two control conditions.
Figure 3.
 
A comparison in six subjects of the direction of subjective equality with exposures of 50 and 200 ms. The dashed line has a slope of 1. Each subject is represented by a different number, and there are four experimental conditions for each subject. The correlation coefficient = 0.78 (for 22° of freedom, the 1% significance = 0.515).
Figure 3.
 
A comparison in six subjects of the direction of subjective equality with exposures of 50 and 200 ms. The dashed line has a slope of 1. Each subject is represented by a different number, and there are four experimental conditions for each subject. The correlation coefficient = 0.78 (for 22° of freedom, the 1% significance = 0.515).
The author thanks Fred A. Miles, Rich J. Krauzlis, and Claudio Busettini of the Laboratory of Sensorimotor Research for help in designing and running the experiments and Karen Pettigrew, PhD, for statistical assistance. 
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Figure 1.
 
The percentage of trials in which the subject reported upward target motion: dependence on the true target trajectory. Sample data for one subject (MAB) in one experiment (background motion downward, target rightward, 200 ms exposure). On the abscissa, 0° signifies target motion to the right, 90° is up, and −90° is down. Because of the downward background motion, small negative angles are always perceived as having an upward component. The data is the percentage of trials in which the subject reported upward target motion (symbols). A symmetric exponential curve was fit to the data (r 2 = 0.955) and the 50% point (the inflection point) was used as the point of subjective equality.
Figure 1.
 
The percentage of trials in which the subject reported upward target motion: dependence on the true target trajectory. Sample data for one subject (MAB) in one experiment (background motion downward, target rightward, 200 ms exposure). On the abscissa, 0° signifies target motion to the right, 90° is up, and −90° is down. Because of the downward background motion, small negative angles are always perceived as having an upward component. The data is the percentage of trials in which the subject reported upward target motion (symbols). A symmetric exponential curve was fit to the data (r 2 = 0.955) and the 50% point (the inflection point) was used as the point of subjective equality.
Figure 2.
 
Histograms showing the point of subjective equality (and SD) in six subjects in four test and two control conditions.
Figure 2.
 
Histograms showing the point of subjective equality (and SD) in six subjects in four test and two control conditions.
Figure 3.
 
A comparison in six subjects of the direction of subjective equality with exposures of 50 and 200 ms. The dashed line has a slope of 1. Each subject is represented by a different number, and there are four experimental conditions for each subject. The correlation coefficient = 0.78 (for 22° of freedom, the 1% significance = 0.515).
Figure 3.
 
A comparison in six subjects of the direction of subjective equality with exposures of 50 and 200 ms. The dashed line has a slope of 1. Each subject is represented by a different number, and there are four experimental conditions for each subject. The correlation coefficient = 0.78 (for 22° of freedom, the 1% significance = 0.515).
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