March 2009
Volume 9, Issue 3
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Research Article  |   March 2009
Shape distortions and Gestalt grouping in anorthoscopic perception
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Journal of Vision March 2009, Vol.9, 8. doi:10.1167/9.3.8
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      Murat Aydın, Michael H. Herzog, Haluk Öğmen; Shape distortions and Gestalt grouping in anorthoscopic perception. Journal of Vision 2009;9(3):8. doi: 10.1167/9.3.8.

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When a figure moves behind a stationary narrow slit, observers often report seeing the figure as a whole, a phenomenon called slit viewing or anorthoscopic perception. Interestingly, in slit viewing, the figure is perceived compressed along the axis of motion. As with other perceptual distortions, it is unclear whether the perceptual space in the vicinity of the slit or the representation of the figure itself undergoes compression. In a psychophysical experiment, we tested these two hypotheses. We found that the percept of a stationary bar, presented within the slit, was not distorted even when at the same time a circle underwent compression by moving through the slit. This result suggests that the compression of form results from figural rather than from space compression. In support of this hypothesis, we found that when the bar was perceptually grouped with the circle, the bar appeared compressed. Our results show that, in slit viewing, the distortion occurs at a non-retinotopic level where grouped objects are jointly represented.

Introduction
When a figure moves behind a stationary narrow slit, observers often report seeing the figure as a spatially extended whole although each slice of the figure excites the same retinotopic area (i.e., there is no spatially extended retinotopic image), a paradigm known as anorthoscopic perception or slit viewing (Helmholtz, 1867/1962; Parks, 1965; Zöllner, 1862). 
One intriguing aspect in anorthoscopic perception is the apparent compression of objects along the axis of motion, e.g., a circle is perceived as an ellipse (Anstis & Atkinson, 1967; Haber & Nathanson, 1968; Helmholtz, 1867/1962; McCloskey & Watkins, 1978; Morgan, Findlay, & Watt, 1982; Parks, 1965; Rock, 1981; Zöllner, 1862). Advocates of the retinal painting hypothesis have suggested that the distortion results from a failure of observers to move their eyes in perfect synchrony with the figure (Anstis & Atkinson, 1967; Haber & Nathanson, 1968; Helmholtz, 1867/1962). According to this argument, if these involuntary eye movements are slower than the actual speed of the figure, a compressed version of the figure will be painted onto the retina. However, recent studies questioned this hypothesis showing that under free viewing conditions, the apparent figure compression is neither related to pursuit nor saccadic eye movements (Rieger, Grüschow, Heinze, & Fendrich, 2007; also see Fendrich & Mack, 1980, 1981; Fendrich, Rieger, & Heinze, 2005; Fujita, 1990; McCloskey & Watkins, 1978; Morgan et al., 1982; Nishida, 2004; Rock, 1981; Sohmiya & Sohmiya, 1992, 1994). 
Another explanation for the apparent compression was proposed by Rock (1981). According to his argument, the speed and the direction of the figure are ambiguous (Shimojo & Richards, 1986). He argued that the perceived length of the figure depends entirely on its perceived speed and the apparent compression results from the underestimation of the actual physical speed (also see Palmer & Kellman, 2001, 2002, 2003 for a similar argument). 
A third explanation for the apparent compression in anorthoscopic perception is based on the compression of the space within the slit (“space compression” hypothesis). Space compression has been previously reported in the literature under a variety of viewing conditions. For example, during saccades, targets are mislocalized toward the saccade goal point as if the visual space around the saccade goal point were compressed (i.e., saccadic compression; Honda, 1999; Lappe, Awater, & Krekelberg, 2000; Ross, Morrone, & Burr, 1997). Moreover, other research suggests that space compression can also occur during fixation. For example, Watanabe and Yokoi (2006) recently proposed that, during fixation, flashes, which are briefly presented in the spatial vicinity of a moving object, are attracted toward a common point behind the moving object as if the space around the moving stimulus were compressed. Sheth and Shimojo (2001) presented evidence indicating that space undergoes compression in visual memory. 
In a recent study (Aydın, Herzog, & Öğmen, 2008), we tested directly the speed underestimation hypothesis by measuring the perceived speed in anorthoscopic perception. Our results provided evidence against the speed underestimation hypothesis by showing that the perceived speed of the figure is always faster, not slower, than the physical speed. Our data supported an alternative hypothesis, which states that the apparent compression of a figure in anorthoscopic perception results from differential perceived speeds of its parts (Aydın et al., 2008). More specifically, the trailing parts of the figure are perceived to move faster than the leading parts. Assuming that the perceived width of the figure is determined by the relative speeds of its leading and trailing parts, this speed difference predicts compression. The hypothesis that the perceived size of an object depends on the perceived speeds of its components is consistent with a recent theory of dynamic form perception (Öğmen, 2007). The goal of the current study was to test this “dynamic form” hypothesis along with the aforementioned “space compression” hypothesis. A fundamental difference between these two hypotheses is that the “space compression” hypothesis is relatively low level and predicts that any stimulus presented in the compressed space should be perceived as compressed. On the other hand, the “dynamic form” hypothesis is relatively high level because it relies on perceptual grouping operations (Öğmen, 2007; details will be discussed in the Discussion section). Accordingly, it predicts that the compression of stimuli presented behind the slit should depend on how different stimuli are grouped into coherent Gestalts. To test these contrasting predictions, we presented two stimuli, a bar and a circle, behind the slit. According to the “space compression” hypothesis, these two stimuli should undergo similar compression irrespective of whether they are grouped together into a single Gestalt. On the other hand, according to the “dynamic form” hypothesis, the compression of the two stimuli should depend strongly on the outcome of grouping operations. 
Methods
Apparatus
Visual stimuli were generated via the visual stimulus generator card (VSG 2/3; Cambridge Research Systems). Stimuli were displayed on a 19-in. color monitor set at a resolution of 656 × 492 with a refresh rate of 160 Hz. The distance between the monitor and the observer was 182 cm at which the screen covered a 12.5 deg by 9.5 deg visual area. The room in which the experiments were conducted was dimly illuminated by the light coming from the image on the screen. Behavioral responses were recorded for off-line analysis via a joystick connected to the computer, which drives the VSG card. 
Stimuli and procedures
Measuring the compression of the bar
A test bar was presented in a vertical slit (21.3 arcmin wide and 3.2 deg tall) and a comparison bar in a horizontal slit (7.1 deg wide and 0.9 deg tall; Figure 1). Both slits were centered at an eccentricity of 1.8 deg in the lower and upper visual fields, respectively. In all conditions, the comparison bar was flashed for 75 ms at the center of the horizontal slit. 
Figure 1
 
Stimulus display. The perceived width of a bar was determined under different conditions. In each panel, the width of the lower bar (test bar) was fixed and the width of the upper bar (comparison bar) was changed according to the method of constant stimuli. The flashed objects are denoted by oblique line segments around them (not shown in the actual stimulus display). The moving objects (and their direction of motion) are denoted by an arrow. The dashed parts of the circle are not visible to the observer due to the slit. The task of the observer was to report whether the test or the comparison bar appeared wider.
Figure 1
 
Stimulus display. The perceived width of a bar was determined under different conditions. In each panel, the width of the lower bar (test bar) was fixed and the width of the upper bar (comparison bar) was changed according to the method of constant stimuli. The flashed objects are denoted by oblique line segments around them (not shown in the actual stimulus display). The moving objects (and their direction of motion) are denoted by an arrow. The dashed parts of the circle are not visible to the observer due to the slit. The task of the observer was to report whether the test or the comparison bar appeared wider.
The perceived width of the test bar was measured by using the method of constant stimuli. The width of the test bar was always 17 arcmin. To map a psychometric function, the width of the comparison bar took one of the following six values: 10.7, 12.8, 14.9, 17, 19.2, and 21.3 arcmin. The height of the test and the comparison bars was 4.3 arcmin. Under some conditions, the test bar moved horizontally (randomly rightward or leftward) with a speed of 8.5 deg/sec. Otherwise, the test and the comparison bars were stationary. 
In some conditions, a circle with a diameter of 1.8 deg moved horizontally (randomly rightward or leftward) with a speed of 8.5 deg/sec through the vertical slit. The bars and the circle were black (4 cd/m 2) on a white background (40 cd/m 2). The luminance of the background on which the slits were cut was 20 cd/m 2
There were five different conditions ( Figure 1): 
Condition 1: The test bar was flashed for 75 ms at the center of the vertical slit. 
Condition 2: The test bar was flashed for 75 ms at the center of the vertical slit and the circle moved horizontally with a speed of 8.5 deg/sec behind the vertical slit. 
Condition 3: The test bar moved horizontally with a speed of 8.5 deg/sec behind the vertical slit. This condition serves as a baseline for Conditions 4 and 5. 
Condition 4: The test bar and the circle moved horizontally in tandem with a speed of 8.5 deg/sec behind the vertical slit. 
Condition 5: The test bar and the circle moved horizontally in opposite directions, both with a speed of 8.5 deg/sec behind the vertical slit. 
The task of the observer was to report whether the test or the comparison bar appeared wider. After mapping the psychometric function, the width of the comparison bar that yields 50% wider-or-narrower response level was calculated and taken as a point of subjective equality. Different conditions were run in separate sessions. In a given session, there were 20 trials for each value of the width of the comparison bar yielding a total of 120 trials per session. Each observer participated in a single session for each condition. Observers were required to fixate on a fixation point provided halfway between the centers of the two slits. 
Comparison of Conditions 1 and 2 will determine whether the space, in the vicinity of the slit, or the figure itself is compressed in anorthoscopic perception. If space is compressed by slit motion, we expect the width of the bar to be perceived smaller in Condition 2 than in Condition 1 provided that the circle is perceptually compressed. Comparison of Conditions 3, 4, and 5 will reveal the role of perceptual grouping in slit viewing. When the moving bar is perceptually grouped with the moving circle, i.e., Condition 4, we expect the bar to inherit the compression of the circle. Hence, the perceived width of the bar should be smaller in Condition 4 than in Condition 3. On the other hand, when the moving bar and the circle are not perceptually grouped, i.e., Condition 5, we expect that the perceived width of the bar should be similar to that in Condition 3. 
Measuring the compression of the circle
Since, in the experiment discussed above, our hypotheses regarding the compression of the bar depends entirely on the assumption that the circle is perceived as compressed, we need to make sure that the circle is indeed perceived compressed. To this end, in separate sessions, the perceived width of the circle was measured by using the method of adjustment. All stimulus parameters and the display were the same as in the previous experiment except that, after the stimulus display, the slit disappeared and a comparison ellipse, with an adjustable width and the same height as the original one, was presented 1.8 deg below the fixation point. The initial width of the comparison ellipse was random. The task of the observer was to adjust the width of the comparison ellipse to the perceived width of the original one. Each observer participated in two sessions for each of Conditions 2, 4, and 5. In a given session, there were 18 trials. 
Subjects
Participants were one of the authors (MA) and three volunteers who were unaware of the purpose of the experiments. The age of the participants ranged from 25 to 27 years. All participants had normal or corrected-to-normal vision. The experiments were undertaken with the permission of The University of Houston Committee for the Protection of Human Subjects and informed consent was obtained from the participants before the experiments started. 
Results
A comparison of Conditions 1 and 2 reveals that the perceived width of the bar is virtually identical in both conditions [ t(3) = 0.199, p = 0.855], which suggests figural rather than space compression ( Figure 2). If the space were compressed, we would expect the width of the bar to be perceived smaller in Condition 2 than in Condition 1. Analysis of the data for the compression of the circle in Figure 3 confirms that the circle in Condition 2 was indeed perceived as compressed in the horizontal direction by about 15% [ t(2) = 5.728, p = 0.029]. It should also be noted that the width of the bar in Condition 1 is consistently [and significantly, t(3) = 5.290, p = 0.013] underestimated by 5–10% (across observers) with respect to its veridical value (dotted horizontal line in Figure 2). We speculate that this bias possibly results from lateral inhibitory interactions between the lateral edges of the bar and the slit due to their spatial proximity. However, additional experiments are needed to pinpoint the exact source of this bias. 
Figure 2
 
Perceived width of the bar in different conditions. The horizontal dotted line denotes the physical width of the bar (17 arcmin). Data points below this line represent compression. Error bars represent ±1 SEM across observers ( N = 4).
Figure 2
 
Perceived width of the bar in different conditions. The horizontal dotted line denotes the physical width of the bar (17 arcmin). Data points below this line represent compression. Error bars represent ±1 SEM across observers ( N = 4).
Figure 3
 
(Top) Percent compression of the bar and the circle in different conditions. Error bars represent ±1 SEM across observers ( N = 3). Percent compression was calculated by the following formula: 100 * (Physical width − Perceived width) / Physical width. (Bottom) Absolute values (in arcmin) of the perceived widths of the bar and the circle in different conditions. The physical widths of the bar and the circle were 17 and 108 arcmin, respectively.
Figure 3
 
(Top) Percent compression of the bar and the circle in different conditions. Error bars represent ±1 SEM across observers ( N = 3). Percent compression was calculated by the following formula: 100 * (Physical width − Perceived width) / Physical width. (Bottom) Absolute values (in arcmin) of the perceived widths of the bar and the circle in different conditions. The physical widths of the bar and the circle were 17 and 108 arcmin, respectively.
In Condition 3, since the moving bar was briefly fully visible through the slit, the width of the bar was, as expected, not significantly different than its baseline value in Condition 1 [Condition 1 vs. Condition 3: t(3) = 0.826, p = 0.469]. More importantly, comparison of Conditions 3 and 4 reveals that the moving bar is more compressed in the presence of a moving circle [11.4% and 25.6% compression in Conditions 3 and 4, respectively, t(3) = 4.314, p = 0.023]. However, the presence of the compressed circle is not sufficient for increased compression of the bar, since in Condition 5, in which the bar and the circle move in opposite directions, the perceived width of the bar is similar to that in Condition 3 [ t(3) = 1.599, p = 0.208]. Analysis of the data for the compression of the circle in Figure 3 shows that, as expected, the circle is perceived as compressed both in Condition 4 [14.6% compression, t(2) = 7.905, p = 0.016] and in Condition 5 [15.6% compression, t(2) = 5.428, p = 0.032] and the magnitude of compression was not significantly different between the two conditions [ t(2) = 0.545, p = 0.640]. That the magnitudes of the circle's perceived compression in Conditions 4 and 5 were not significantly different rules out the possibility that the difference in the perceived width of the bar in Conditions 4 and 5 ( Figure 2) is due to the difference in the magnitude of perceived compression of the circle in those conditions. 
Discussion
In a psychophysical experiment, we showed that the compression of an anorthoscopic percept is not caused by perceptual compression of space in the slit. Such a compression would predict that any stimulus displayed in this space would also undergo a compression. However, this is not the case because performance in Conditions 1 and 2 is very similar ( Figure 2). This result is similar to the recent findings on presaccadic space compression. It was shown that during presaccadic compression of visual space, the apparent size of a solid object (Matsumiya & Uchikawa, 2001) or illusory Kanizsa rectangle (Sogo & Osaka, 2005) remains uncompressed. Similarly, Watanabe and Yokoi (2006) found no shape distortion of a dumbbell-like figure while the representation of space was distorted due to a moving target. 
Additionally, we showed that a moving bar is more compressed in the presence of a perceptually compressed circle moving in the same but not in the opposite direction ( Figure 2). We suggest that the additional compression that occurs in Condition 4 results from the perceptual grouping of the circle and the bar. When the bar and the circle move in the same direction with the same speed as in Condition 4, they are perceptually grouped based on the Gestalt principle of “common fate” (Wertheimer, 1923/1950). Indeed, when we removed the slit and asked observers to report the perceived grouping of the stimuli, they indicated that the bar and the circle appeared as one group when they moved in the same direction. Processed as one group, the compression of the circle transferred to the bar. On the other hand, when the bar and the circle moved in opposite directions as in Condition 5, they were not perceptually grouped and the compression of the circle did not transfer to the bar. 
These results can also be discussed in a recently introduced theoretical framework for moving form perception (Öğmen, 2007). According to this framework, when the bar and the circle are grouped, they are mapped to the same non-retinotopic space with correlated velocity vectors (Figure 4, left). More specifically, for parts of the bar and the circle that are crossing the slit simultaneously, the assigned velocity vectors should be correlated (dotted arrows in Figure 4, left). Because the trailing parts of the circle are assigned larger velocity vectors than the leading parts (solid arrows in Figure 4, left; Aydın et al., 2008), grouping assigns a larger velocity vector to the trailing edge of the bar with respect to its leading edge and induces a compression of the bar (Figure 4, left, Perception). Hence, the compression of the circle transfers to the bar via grouping relations. This argument is further supported by the fact that, compared to the baseline Condition 3, the additional compression of the bar by 14.2% in Condition 4 is almost identical to the 14.6% compression of the circle in that condition. The equality of the compression ratios for the bar and the circle suggests that the increase in perceived velocity, as one progresses from the leading to the trailing part of the figure, is linear. However, given the relatively large error bars in the data shown in Figure 3, deviations from linearity are possible. A deviation from linearity will predict that the compressed bar will appear displaced with respect to the center of the circle (Figure 4, left, Perception). In a pilot experiment (data not shown here), we found that the bar is perceived closer to the trailing edge of the circle by a shift of about 25% of the physical radius of the circle. Additional experiments wherein perceived speeds are measured at multiple positions between the leading and trailing edges can clarify the morphology of the perceived speed gradient. 
Figure 4
 
The explanation of the results in the framework of Öğmen (2007). (Left) The bar and the circle move in the same direction with the same speed as in Condition 4. (Right) The bar and the circle move in opposite directions as in Condition 5. Figure is not drawn to scale and the relative magnitude of the bar with respect to the circle is exaggerated for clarity.
Figure 4
 
The explanation of the results in the framework of Öğmen (2007). (Left) The bar and the circle move in the same direction with the same speed as in Condition 4. (Right) The bar and the circle move in opposite directions as in Condition 5. Figure is not drawn to scale and the relative magnitude of the bar with respect to the circle is exaggerated for clarity.
On the other hand, when the bar and the circle move in opposite directions as in Condition 5, they are not perceptually grouped and the bar is mapped to the non-retinotopic space independently from the circle with an independent estimation of velocity ( Figure 4, right). Since assigned velocity vectors are not correlated, the compression of the circle does not transfer to the bar ( Figure 4, right, Perception). In other words, according to this theory, compression occurs in the non-retinotopic space whose contents are determined by grouping operations. 
While we emphasize the importance of grouping in the coordination of velocity vectors, the exact mechanisms whereby such a coordination occurs remains an open question. Several experiments support the idea that the assignment of velocities to objects depends on the nature of prevailing grouping relations (e.g., Adelson & Movshon, 1982; Anstis, 1990; Lorenceau & Alais, 2001; Stoner, Albright, & Ramachandran, 1990; Wallach, 1935) and some researchers suggested interactions between spatial frequency mechanisms to explain the phenomena of “motion capture” (Ramachandran & Cavanagh, 1987) and “coherence capture” (Yo & Wilson, 1992). Whether these phenomena and their putative mechanisms are related to the findings reported here needs further investigation. It also remains to be investigated whether other grouping factors, such as similarity, are equally effective as common fate in transferring velocity vectors. 
Overall, our results provide further evidence for the involvement of perceptual grouping operations in the form analysis of moving objects (Öğmen, Otto, & Herzog, 2006; Otto, Öğmen, & Herzog, 2006). Recently, for example, by using a stimulus known as the “Ternus-Pikler display” (e.g., Pantle & Picciano, 1976; Ternus, 1926), Öğmen et al. (2006) showed a new illusion where attribution of features of moving objects obeys rules of perceptual grouping. Importantly, they showed that the visual system violates low level retinotopic relations in order to maintain spatiotemporal contiguity of object identities in the perceptual space. 
Although, in this study, our emphasis is on the role of perceptual grouping relations in the form analysis of moving objects, the same principles may play a role in the form, as well as surface, analysis of static objects (van Lier & Wagemans, 1997; Xian & Shevell, 2004). All these reports, along with the current one, point to the possible role of perceptual grouping operations in guiding the form and/or surface analysis of moving and/or static objects. 
Acknowledgments
The authors would like to thank two anonymous reviewers for their comments. 
Commercial relationships: none. 
Corresponding author: Murat Aydın. 
Email: aydmurat2002@yahoo.com. 
Address: Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77024-4005 USA. 
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Figure 1
 
Stimulus display. The perceived width of a bar was determined under different conditions. In each panel, the width of the lower bar (test bar) was fixed and the width of the upper bar (comparison bar) was changed according to the method of constant stimuli. The flashed objects are denoted by oblique line segments around them (not shown in the actual stimulus display). The moving objects (and their direction of motion) are denoted by an arrow. The dashed parts of the circle are not visible to the observer due to the slit. The task of the observer was to report whether the test or the comparison bar appeared wider.
Figure 1
 
Stimulus display. The perceived width of a bar was determined under different conditions. In each panel, the width of the lower bar (test bar) was fixed and the width of the upper bar (comparison bar) was changed according to the method of constant stimuli. The flashed objects are denoted by oblique line segments around them (not shown in the actual stimulus display). The moving objects (and their direction of motion) are denoted by an arrow. The dashed parts of the circle are not visible to the observer due to the slit. The task of the observer was to report whether the test or the comparison bar appeared wider.
Figure 2
 
Perceived width of the bar in different conditions. The horizontal dotted line denotes the physical width of the bar (17 arcmin). Data points below this line represent compression. Error bars represent ±1 SEM across observers ( N = 4).
Figure 2
 
Perceived width of the bar in different conditions. The horizontal dotted line denotes the physical width of the bar (17 arcmin). Data points below this line represent compression. Error bars represent ±1 SEM across observers ( N = 4).
Figure 3
 
(Top) Percent compression of the bar and the circle in different conditions. Error bars represent ±1 SEM across observers ( N = 3). Percent compression was calculated by the following formula: 100 * (Physical width − Perceived width) / Physical width. (Bottom) Absolute values (in arcmin) of the perceived widths of the bar and the circle in different conditions. The physical widths of the bar and the circle were 17 and 108 arcmin, respectively.
Figure 3
 
(Top) Percent compression of the bar and the circle in different conditions. Error bars represent ±1 SEM across observers ( N = 3). Percent compression was calculated by the following formula: 100 * (Physical width − Perceived width) / Physical width. (Bottom) Absolute values (in arcmin) of the perceived widths of the bar and the circle in different conditions. The physical widths of the bar and the circle were 17 and 108 arcmin, respectively.
Figure 4
 
The explanation of the results in the framework of Öğmen (2007). (Left) The bar and the circle move in the same direction with the same speed as in Condition 4. (Right) The bar and the circle move in opposite directions as in Condition 5. Figure is not drawn to scale and the relative magnitude of the bar with respect to the circle is exaggerated for clarity.
Figure 4
 
The explanation of the results in the framework of Öğmen (2007). (Left) The bar and the circle move in the same direction with the same speed as in Condition 4. (Right) The bar and the circle move in opposite directions as in Condition 5. Figure is not drawn to scale and the relative magnitude of the bar with respect to the circle is exaggerated for clarity.
© 2009 ARVO
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