Illusory position shift induced by motion within a moving envelope during smooth-pursuit eye movements

Abstract

Abstract

Abstract:

Abstract  The static envelope of a Gabor patch with a moving carrier appears to shift in the direction of the carrier motion; this phenomenon is known as the motion-induced position shift (De Valois & De Valois, 1991; Ramachandran & Anstis, 1990). This conventional stimulus configuration contains at least three covarying factors: the retinal carrier velocity, the environmental carrier velocity, and the carrier velocity relative to the envelope velocity, which happens to be zero. We manipulated these velocities independently to identify which is critical, and we measured the perceived position of the moving Gabor patch relative to a reference stimulus moving in the same direction at the same speed. In the first experiment, the position of the moving envelope observed with fixation appeared to shift in the direction of the carrier velocity relative to the envelope velocity. Furthermore, the illusion was more pronounced when the carrier moved in a direction opposite to that of the envelope. In the second and third experiments, we measured the illusion during smooth-pursuit eye movement in which the envelope was either static or moving, thereby dissociating retinal and environmental velocities. Under all conditions, the illusion occurred according to the envelope-relative velocity of the carrier. Additionally, the illusion was more pronounced when the carrier and envelope moved in opposite directions. We conclude that the carrier's envelope-relative velocity is the primary determinant of the motion-induced position shift.

Introduction

The ability to estimate the position of an object in the world is among the most basic functions of our visual system. Object-position processing involves higher integrative stages of visual processing because it requires spatial information, recognition of object shape and its figure–ground relationship, and an observer's ability to monitor his or her own eye and bodily movements. De Valois and De Valois (1991) have shown that a statically positioned Gabor patch containing a moving sinusoidal carrier shifts its apparent position in the direction of carrier motion. This phenomenon, hereafter termed the motion-induced position shift, is induced by several kinds of motion, including second-order motion, global motion, binocularly defined motion, and the motion after-effect (e.g., Bressler & Whitney, 2006; Durant & Johnston, 2004; Hisakata & Murakami, 2009; Murakami & Kashiwabara, 2009; Nishida & Johnston, 1999; Ramachandran & Anstis, 1990). This phenomenon demonstrates that motion processing strongly affects estimates of position. 

Previous studies investigated the motion-induced position shift under laboratory conditions: the observer judged the position of a stimulus that moves within a static contour while fixating on a point located elsewhere. When observers move their eyes, motion velocity is defined in at least two ways: the velocity according to retinal coordinates and that according to environmental coordinates. For example, during smooth-pursuit eye movement, the retinal image of an object slips according to the eye movements, and we must estimate the actual velocity of the object in the world by subtracting the eye velocity from the retinal velocity of the object (for review, see Goldstein, 2007; Furman & Gur, 2012). Moreover, in addition to these velocities, the velocity relative to another object can be defined independently. For example, if one object moves at 5 deg/s and another object moves at 3 deg/s, the resulting relative velocity is 2 deg/s. Therefore, when the carrier and the envelope of a Gabor patch move independently in the environment, the velocity of the carrier can be defined in terms of the retinal, environmental, or envelope-relative velocity. If the motion-induced position shift occurs during movement of the envelope caused by the experimenter's manipulation, the observer's eye movement, or both, it is unclear which velocity determines the phenomenon. 

To address this issue, we independently manipulated three kinds of movement: the motion of the envelope, the motion of the carrier, and the subject's eye movement. We measured the illusory horizontal displacement between two vertically aligned Gabor patches. Carrier velocity was described in three ways: 

• 1.  
  Display-relative velocity (the velocity in the environment),
• 2.  
  Retina-relative velocity (the velocity on the retina), and
• 3.  
  Envelope-relative velocity (the velocity relative to movement of the envelope)

We had two primary foci: whether the motion-induced position shift would occur with a moving envelope and moving eyes and, if it did, which carrier motion induced the shift. 

In Experiment 1, the envelope was moved at a constant velocity, and fixation was maintained. In this case, the display-relative and the retina-relative velocities were the same, but the envelope-relative velocity of the carrier differed. In Experiment 2, the envelope was static, and the subject's eyes moved at a constant velocity. In this case, the display-relative and the envelope-relative velocities were the same, but the retina-relative velocity differed. In Experiment 3, both the envelope and the eyes moved in the same direction at the same speed. In this case, the retina-relative and the envelope-relative velocities were the same, but the display-relative velocity differed (Figure 1). 

Figure 1

 

The 2 × 2 table illustrates the experimental setup. Conventional experiments examining the motion-induced position shift measure the position shift with a static envelope during fixation. In Experiment 1, we measured the position shift with a moving envelope during fixation. In Experiment 2, we measured the position shift with a static envelope during smooth-pursuit eye movement. In Experiment 3, we measured the position shift with a moving envelope during smooth-pursuit eye movement.

Experiments

Experiment 1: Position shift with a moving envelope during fixation

In Experiment 1, the envelope moved at a constant velocities, but the carrier of the Gabor patch moved independently. Subjects observed the stimulus while maintaining fixation (Figure 2). We examined whether the position shift was induced by the carrier when the Gabor patch itself moved and, if so, which of the aforementioned velocities determined this shift. 

Figure 2

 

Rationale for Experiment 1. The envelope moved on the display, and the carrier moved independently. The observer fixated on a stationary fixation point. The display-relative and retina-relative velocities of the carrier were identical, and its envelope-relative velocity differed. The table presents the eye velocity, the envelope velocity on the display, and the envelope velocity on the retina as well as the carrier's display-relative, retina-relative, and envelope-relative velocities in the leftward panel. Positive values indicate rightward motions.

Methods

Subjects:

One of the authors (RH) and five subjects with normal or corrected-to-normal vision participated in the experiment. The stimuli were viewed binocularly from a distance of 107.3 cm. 

Apparatus:

Stimuli were generated by a computer (Apple MacPro with OS 10.4.11; Apple, Inc., Cupertino, CA) and were displayed on a CRT monitor (Mitsubishi Electric RDF223H, 1600 × 1200 pixels, 1 min/pix, refresh rate 100 Hz, mean luminance 48 cd/m²; Mitsubishi Electric Corporation, Tokyo, Japan). The videocard color look-up table was linearized. 

Stimuli:

We used one vertical and one horizontal Gabor patch with an envelope standard deviation of 30 min, a carrier spatial frequency of 1.5 cycle/deg, and a Michelson contrast of 50%. The envelope for and carrier of the vertical Gabor patch moved independently. The velocity of the envelope was always −2.5 deg/s (leftward on the display) or 2.5 deg/s (rightward). When the envelope moved leftward at −2.5 deg/s, the following five display-relative carrier velocities were used: 0.5, 0, −2.5, −5, and −5.5 deg/s (rightward is positive). When the envelope moved rightward at 2.5 deg/s, the following five display-relative carrier velocities were used: −0.5, 0, 2.5, 5, and 5.5 deg/s (rightward is positive). Therefore, in both cases, the envelope-relative carrier velocities were −3, −2.5, 0, 2.5, and 3 deg/s, with the positive velocity values indicating that the carrier was moving in the same direction as the envelope (Table in Figure 2). 

Procedure:

Along a horizontal path 8 deg below a fixation point, a vertical Gabor patch moved at a constant speed (Figure 3); its duration was 1 s. At 750 ms after the onset of this movement, a horizontal Gabor patch with a static carrier appeared 3 deg above the vertical Gabor patch and moved in the same direction at the same speed for 250 ms. The subject was asked to judge the vertical alignment of these patches in a two-alternative forced-choice paradigm. We used the method of constant stimuli (±30 min in five steps with 30 trials per point) to determine the point of subjective equality as the strength of the illusory position shift of the vertical Gabor patch. The carrier velocities were presented in a random order within each session. 

Figure 3

 

Time course of each trial in Experiment 1. The fixation point was presented above the stimulus. The vertical Gabor patch moved horizontally for 1 s; 750 ms after the onset of movement, the horizontal Gabor patch appeared and moved horizontally for 250 ms. The carrier of the vertical Gabor patch was always moving at one of five velocities, whereas the carrier of the horizontal Gabor patch was static. The envelopes of both the vertical and the horizontal Gabor patches moved at 2.5 deg/s. Their horizontal positional offset was systematically varied from trial to trial according to the method of constant stimuli used to reach the point of subjective alignment.

In addition to the aforementioned conditions related to carrier velocity, we also measured the mislocalization of the Gabor patch with a moving envelope and a static horizontal carrier to control any baseline position shift that may have occurred independent of carrier motion. If it occurred, such a shift may have been due to the flash-lag effect (Nijhawan, 1994, 1997), in which a briefly presented stimulus appears to lag behind a moving stimulus even when they are physically aligned. Under this control condition, the moving vertical Gabor patch was simply replaced by the moving horizontal Gabor patch, and its vertical alignment with another moving horizontal Gabor patch 3 deg above was judged in the same way. We subtracted the baseline mislocalization under the control condition from all mislocalizations under the vertical Gabor conditions to exclude any biases derived from the current experimental setup. 

Results

The results are presented in Figure 4. The upper abscissa indicates the carrier's display-relative velocity (which was identical to its retina-relative velocity); the lower abscissa indicates the envelope-relative velocity. Although the envelope moved either rightward or leftward, we flipped the data for leftward movement and merged the data to present the results as if the envelope always moved rightward. In this format, positive values for the position shift and the carrier velocity indicate the rightward direction, and negative values indicate the leftward direction. 

Figure 4

 

Results of Experiment 1. Magnitude of position shift averaged for the six subjects is plotted under the five velocity conditions. Error bars indicate the standard errors. Although the envelope moved either rightward or leftward, we flipped data for the leftward movement and merged the data to show the results as if the envelope always moved rightward. In this flipped–merged format, positive values for position shift indicate that the envelope apparently shifted rightward, and positive values for carrier velocity indicate that the carrier moved rightward.

This experiment yielded three major findings. First, a motion-induced position shift occurred with the moving envelope, ANOVA, F(4, 20) = 28.62, p < 0.01. The extent of the position shift corresponded to the perceptual misalignment between the lower vertical and upper horizontal Gabor patches whose envelopes were moving in the same direction at the same speed. The vertical Gabor patch appeared as spatially offset to the right when its carrier was moving rightward and as spatially offset to the left when its carrier was moving leftward. Second, the position shift increased with the carrier's envelope-relative velocity rather than with its display-relative or retina-relative velocity. The illusory shift occurred rightward and leftward when the carrier moved rightward and leftward, respectively, relative to the envelope motion, −3 deg/s < 0 deg/s, t(20) = 5.89, p < 0.01; −2.5 deg/s < 0 deg/s, t(20) = 3.19, p < 0.01; 2.5 deg/s > 0 deg/s, t(20) = 2.57, p < 0.05; 3 deg/s > 0 deg/s, t(20) = 2.9, p < 0.01. The illusory shift was indistinguishable from zero when the envelope-relative velocity was 0 deg/s, t(5) = −0.47, p > .05. Third, the magnitude of the position shift was smaller when the carrier moved in the same direction as the envelope than when it moved in the opposite direction. The absolute values at −3 deg/s and −2.5 deg/s were significantly different from those at 3 deg/s and 2.5 deg/s, t(22) = −2.41, p < 0.05. 

Experiment 2: Position shift with a static envelope during smooth-pursuit eye movement

The results of Experiment 1 revealed that envelope-relative velocity was the major determinant of illusion strength. To examine this phenomenon irrespective of eye movement, Experiment 2 was designed to observe the Gabor patches with static envelopes while smooth-pursuit eye movements were used to track a horizontally moving spot. In this situation, the vertical envelope moved on the retina due to eye movement even though the envelope was actually static on the display (Figure 5). As a result, the carrier's display-relative and envelope-relative velocities were identical to each other when tracking was perfect, and only the retina-relative velocity differed. We examined whether the illusion was induced by the envelope-relative velocity even when subjects moved their eyes, adding retinal image motions to the carrier as well as to the envelope. 

Figure 5

 

Rationale for Experiment 2. Each subject made smooth-pursuit eye movements to keep foveating the tracking target moving horizontally; the envelope was static on the display. The conventions are otherwise the same as in Figure 2.

Methods

Subjects and apparatus:

We used a video-based eye tracker (SR Research Eyelink II; Cambridge Research System, Cambridge, UK) to measure the subjects' eye positions during stimulus observation. The mean luminance of the display was 33 cd/m². Otherwise, the subjects and apparatus were identical to those used in Experiment 1. 

Analysis of eye movements:

We measured each subject's horizontal and vertical eye movements binocularly at a sampling rate of 250 Hz. We removed trials that contained saccades (eye movements over 30 deg/s) or blinks as well as trials in which the eye speed during the 250 ms in which both patches were present deviated from ±0.625 deg/s around the tracking target speed, which was always 2.5 deg/s. The median eye velocities of the trials used for analyses are presented in Figure 6. The median pursuit gain ranged from 0.88 to 0.96 across subjects. We ensured that there were no within-subject statistically significant differences in eye velocity across the different carrier-velocity conditions. 

Figure 6

 

Median eye velocity measured for each subject under each velocity condition in Experiment 2. Under the “horizontal” condition, the carrier's orientation was horizontal. The error bar indicates quartile deviations. The target speed was 2.5 deg/s. Trials in which the eye velocity was faster than 3.125 deg/s or slower than 1.875 deg/s were excluded from the analysis.

Stimuli and procedure:

The stimuli were the same as those employed in Experiment 1 with the exceptions that the envelopes of all Gabor patches were static and the fixation point was now a tracking target that actually moved at a constant velocity of −2.5 deg/s (leftward on the display) or 2.5 deg/s (rightward on the display) (Figure 7). Each subject made a smooth-pursuit eye movement in response to the moving target and was asked to judge the vertical alignment of the two static Gabor patches presented in the lower visual hemifield. The carrier velocities of the vertical Gabor patches on the display were −3, −2.5, 0, 2.5, and 3 deg/s. The carrier of the horizontal Gabor patch was static. Because the envelopes of the Gabor patches were static on the display, the carrier's envelope-relative velocity was the same as its display-relative velocity. On the other hand, the retina-relative velocity differed because the envelope moved on the retina at either −2.5 deg/s or 2.5 deg/s due to eye movement. The retina-relative velocities were therefore −5.5, −5, −2.5, 0, and 0.5 deg/s, with the positive velocity values indicating that the carrier was moving in the same direction on the retina as was the envelope (Table in Figure 5). 

Figure 7

 

Time course of each trial in Experiment 2. The pursuit target was presented above the stimulus and moved at 2.5 deg/s. The pursuit target alone initially moved for 1 s. During the pursuit, the vertical Gabor patch was presented for 1 s; 750 ms after the onset of the vertical Gabor patch, the horizontal Gabor patch was presented for 250 ms. The carrier of the vertical Gabor patch moved at one of five velocities, whereas the carrier of the horizontal Gabor patch was static. The envelopes of both the vertical and the horizontal Gabor patches were static on the display.

We used the method of constant stimuli employed in Experiment 1. However, the number of trials per point was not equal across points due to the exclusion of trials with eye-movement errors. The total numbers of accepted trials were 1,198 for RH, 896 for TF, 1,430 for YK, 1,100 for KS, 821 for HO, and 1,184 for YM. 

Results

Figure 8 shows the results of this experiment. We flipped and merged the data to present the results as if the eyes always moved leftward (i.e., as if the envelope always moved rightward in the retinal coordinates). The lower abscissa indicates the envelope-relative disparity, which was identical to the display-relative velocity, whereas the upper abscissa indicates the retina-relative velocity. 

Figure 8

 

Results of Experiment 2. Conventions are identical to those used in Figure 5.

As in Experiment 1, the magnitude of the position shift was significantly modulated across velocity conditions, F(4,20) = 39.21, p < 0.01. Furthermore, the illusion occurrence was more compatible with the speed values along the lower than along the upper abscissa, −3 deg/s < 3 deg/s, t(20) = 9.80, p < 0.01; −3 deg/s < 2.5 deg/s, t(20) = 10.22, p < 0.01; −3 deg/s < 0 deg/s, t(20) = 7.68, p < 0.01; −2.5 deg/s < 3 deg/s, t(20) = 6.54, p < 0.01; −2.5 deg/s < 2.5 deg/s, t(20) = 6.96, p < 0.01; −2.5 deg/s < 0 deg/s, t(20) = 4.42, p < 0.01. If the carrier's retina-relative velocity had been important for the phenomenon, no illusion should have occurred when the retina-relative velocity was zero. Actually, however, a strong illusion occurred at 0 deg/s retina-relative velocity, t(5) = −4.13, p < 0.01. As in Experiment 1, the illusion favored the envelope-relative velocity. That is, even when the carrier created no motion signals on the retina, the illusory position shift occurred in the direction compatible with the carrier's motion relative to the environmentally stationary envelope. In contrast, the illusion strength was not significantly different from zero at 0 deg/s envelope-relative velocity, t(5) = 1.84, p > 0.05. 

We found a strong asymmetry in the illusion strength between the same and opposite directions with respect to the retinal motion of the envelope. The illusion was robust when the carrier moved in the direction opposite that of the envelope but was absent when the carrier moved in the same direction as the envelope. The absolute values at −3 deg/s and −2.5 deg/s were significantly different from those at 3 deg/s and 2.5 deg/s, respectively, t(22) = −4.94, p < 0.001. 

Experiment 3: Position shift with a moving envelope during smooth-pursuit eye movement

The results of Experiments 1 and 2 indicated that the envelope-relative velocity was the major determinant of the strength of the motion-induced position shift in the envelope, whose movement on the retina was caused by either the stimulus motion on the display or the subject's own eye movement. Thus, in both experiments, the envelope always moved on the retina. We were interested in whether our finding could be generalized to a situation in which the envelope was retinally static despite eye movement. To address this question, Experiment 3 involved moving the envelope in the same direction and at the same speed as the tracking target, thereby creating a situation in which the envelope was static on the retina (Figure 9). In this case, the retina-relative velocity would be equivalent to the envelope-relative velocity, given perfect tracking, and only the display-relative velocity would differ. 

Figure 9

 

Rationale for Experiment 3. Each subject made smooth-pursuit eye movement; the tracking target and the stimulus envelope moved in the same direction and at the same speed on the display. As a result, the envelope was static on the retina. The conventions are otherwise the same as in Figure 2.

Methods

The stimuli were the same as those used in Experiment 2 with the exception that the envelopes of the vertical and horizontal Gabor patches and the tracking target moved horizontally at −2.5 deg/s (leftward on the display) or at 2.5 deg/s (rightward on the display) (Figure 10). Each subject made a smooth-pursuit eye movement in response to the tracking target and was asked to judge the vertical alignment of the two Gabor patches moving along with the pursuit target. When the envelope and tracking target moved leftward at −2.5 deg/s, the carrier velocities of the vertical Gabor patch were −5.5, −5, −2.5, 0, or 0.5 deg/s on the display. When the envelope and tracking target moved rightward at 2.5 deg/s, the carrier velocities of the vertical Gabor patch were −0.5, 0, 2.5, 5, or 5.5 deg/s on the display. Therefore, in both cases, the envelope-relative carrier velocities were −3, −2.5, 0, 2.5, or 3 deg/s, with positive velocity values indicating that the carrier was moving in the same direction on the retina as the envelope (Table in Figure 9). 

Figure 10

 

Time course of each trial in Experiment 3. The pursuit target moved at 2.5 deg/s. The pursuit target alone initially moved for 1 s. During the pursuit, the vertical Gabor patch was presented for 1 s; 750 ms after the onset of the vertical Gabor, the horizontal Gabor patch was presented for 250 ms. The carrier of the vertical Gabor patch moved at one of five velocities, whereas the carrier of the horizontal Gabor patch was static. The envelopes of both the vertical and the horizontal Gabor patches moved at 2.5 deg/s on the display.

Otherwise, the experimental setup, including subjects, apparatus, psychophysical procedure, and recording and analysis of eye movements, was identical to that of Experiment 2. The median eye velocities of the accepted trials are shown in Figure 11. All subjects made under pursuit, and the pursuit gain ranged from 0.88 to 0.96 across subjects. We ensured that there were no intrasubject differences in eye velocities across the different carrier-velocity conditions. The total numbers of accepted trials were 1,132 for RH, 998 for TF, 1,397 for YK, 1,532 for KS, 1,189 for HO, and 1,068 for YM. 

Figure 11

 

Median and quartile deviations in eye velocity measured for each subject under each velocity condition in Experiment 3.

Results

As in Experiments 1 and 2, we flipped and merged the data to present the results as if both the eyes and the envelope always moved leftward on the display. In Figure 12, the lower abscissa indicates the envelope-relative velocity (which was identical to the retina-relative velocity), and the upper abscissa indicates the display-relative velocity. Again, the magnitude of the position shift differed across conditions, F(4, 20) = 74.88, p < 0.01, in favor of the lower abscissa, −3 deg/s < 0 deg/s, t(20) = 5.83, p < 0.01; −2.5 deg/s < 0 deg/s, t(20) = 6.19, p < 0.01; 2.5 deg/s > 0 deg/s, t(20) = 5.83, p < 0.01; and 3 deg/s > 0 deg/s, t(20) = 6.60, p < 0.01. 

Figure 12

 

Results of Experiment 3. Conventions are identical to those used in Figure 5.

Unlike Experiments 1 and 2, however, we did not observe any asymmetry between positive and negative velocities, t(22) = 0.29, p > 0.05. 

In a pilot experiment, we measured the illusion strength using a conventional stimulus setup (i.e., with a static envelope and with static eyes). We found that the magnitude of misalignment for such a conventional Gabor patch was saturated at 2.5 deg/s (Figure 13), which is presumably why we found no difference between the illusion strengths at ±2.5 deg/s and ±3 deg/s in Experiment 3. 

Figure 13

 

Results of the pilot experiment. Only carrier velocities were manipulated, whereas both the envelope and the eye were static.

Discussion

Why does the motion-induced position shift occur during envelope motion?

In this study, we found that motion within a stimulus envelope can induce an illusory position shift of the envelope, even when the envelope itself is moving, when the observer's eyes are moving or when both the envelope and the observer's eyes are moving. The velocity of the carrier was defined in three ways when either the envelope or the eyes moved: relative to the display, relative to the retina, and relative to the envelope. The results demonstrated that the envelope-relative velocity was the primary determinant of the magnitude of the position shift. That is, in all experiments, the motion-induced position shift occurred consistently in the direction of the envelope-relative carrier motion and disappeared when the envelope-relative velocity was zero. On the other hand, neither the display-relative nor the retina-relative velocity of the carrier was a valid predictor of the illusion because a robust illusion occurred even when either velocity was zero. 

The carrier that was static on the retina still produced the motion-induced position shift, indicating that neural registration of low-level retinal motion signals within the carrier location is not a necessary condition for the illusion to occur. Additionally, the carrier that was static in the world still produced the motion-induced position shift. This indicates that neural construction of high-level environmental motion representations within the carrier location is not a necessary condition for the illusion to occur. Rather, the relative relationship between the velocity of the inducing carrier and that of the induced envelope is critical for the generation of the phenomenon. When only the carrier is moving within a static envelope, it is subjectively dragged in the direction of the carrier. When the envelope itself is retinally moving, it is subjectively shifted less than predicted by the envelope's velocity when the carrier is retinally moving more slowly, creating relative motion in reference to the envelope; this is the case both when the environmentally moving envelope is viewed with fixation (Experiment 1) and when the environmentally static envelope is viewed during pursuit (Experiment 2). When both the envelope and eye are moving in the same direction at the same speed, the envelope is subjectively shifted farther than predicted by its velocity when the carrier is moving faster, and it is subjectively shifted less than predicted by the envelope's velocity when the carrier is moving more slowly (Experiment 3). 

The present experiments, however, do not identify the stage at which this relativity is explicitly calculated. Indeed, relative motion can be extracted in either low-level motion processing, in which velocity is simply represented by the retinal coordinates, or in high-level processing, in which all velocities have been remapped to the environmental coordinates. Our experimental finding that the envelope-relative velocity determines the illusion strength indicates that the perceptual organization of a pattern or a texture delineated by a closed contour may affect the perceived position of the stimulus. Similar to the position and motion of the contour, the position and motion of the pattern inside the contour would be also important in determinations by the visual system of the position of a unified object. Because the pattern of an object will probably move in the same direction and at the same speed as the object itself in a natural environment, use of both contour and texture information would yield a more accurate and rapid estimation of perceived position (De Valois & De Valois, 1991; Nijhawan, 1994). This strategy requires perceptual organization to determine what belongs to what prior to position estimation. Future research should examine if and how the type of perceptual organization influences the perceived position of organized objects. 

Asymmetry of the position shift for the retinally moving envelope

We also found that the position shift decreased when the carrier's envelope-relative velocity was in the same direction as the retinally moving envelope. In contrast, we did not find such an asymmetry in Experiment 3, in which the envelope was moving on the display, but the eye was also moving in the same direction, thereby canceling the retinal motion of the envelope. 

We hypothesize that the visual system regards the motion-induced position shift suggested by the carrier as less reliable when it suggests a shift toward the future direction of the envelope's retinal position. Although the visual system may be able to predict the future position of a moving object by using its history, there is no way to know for sure what happens next. In a study of the flash-lag effect, Whitney and Murakami (1998) demonstrated that the effect was reversed when the flash was presented at the onset of a sudden reversal of the moving stimulus, suggesting that the visual system does not treat a motion extrapolation as a valid candidate for the moving object's perceived position. Similarly, the position shift in the present study was not great when it would place the contour farther along its future motion trajectory on the retina. A Bayesian perspective may help to explain why this happens. Whereas the sensory evidence originating from the carrier motion relative to the envelope would suggest an equal amount of position shift if it is ahead of or behind the current position along the motion trajectory, knowledge differs from suggestion. That is, the prior probability of the envelope's being somewhere along the previous trajectory should be higher than the probability of the envelope's being somewhere along the path extrapolated for the future. This imbalance in the prior distribution may tend to pull back the perceived position of the envelope given equivalent sensory evidence. 

Previous studies suggest that the early visual areas are involved in the illusory position shift. For example, Whitney et al. (2003) demonstrated that activation in V1 correlated with the direction of the illusory position shift. Additionally, Roach, McGraw, and Johnston (2011) found a modulation in contrast sensitivity only at the side of the leading edge but not at the side of the trailing edge. Chung, Patel, Bedell, and Yilmaz (2007) and Arnold, Thompson, and Johnston (2007) proposed that the sensitivity modulation at the leading edge elicits a centroid shift, which biases position estimation toward the motion direction. The current dataset is not incompatible with these hypotheses but, if correct, our results would indicate that such modulation occurs not only within a retinally static envelope, as is the case for conventional stimuli for the motion-induced position shift, but also for a retinally moving stimulus. It should be noted that sensitivity enhancement could not occur at the leading edge of the retinally moving envelope itself as our data indicated that the position shift decreased asymmetrically at that side. Moreover, the present results are compatible with the predictive forward model, which has been proposed to account for the illusion in the computational framework of estimation (Arnold et al., 2007; Chung et al., 2007), the carrier motion inside plays a predictive role in estimating the envelope position in favor of the direction of the carrier motion. As discussed above, a Bayesian framework might better capture all aspects of the position-shift illusion, since we found that carrier motion is not the sole determinant of the illusion, and its interaction with the retinal velocity of the envelope should also be considered. 

Ceiling effect

In Experiment 3, the position shift was saturated at ±2.5 deg/s and we found no significant differences in illusion strength between ±2.5 and ±3 deg/s. The same saturation was confirmed in a pilot experiment in which the illusion strength was flat across a carrier velocity range of 2.5–5 deg/s. However, the position shift at −2.5 deg/s was significantly smaller than that at −3 deg/s in Experiments 1 and 2, indicating that some modulation occurred depending on carrier speed. One possible reason for this is our biological underestimation of retinal image motion for the envelope moving on the retina, resulting in our underestimation of the envelope-relative velocity of the carrier. The envelope motion is a kind of second-order motion defined by displacement of contrast modulation, and the retinal image speed of such second-order motion is arguably underestimated in the brain (Cavanagh & Anstis, 2002; Johnston & Clifford, 1995). In Experiments 1 and 2, the envelope-relative velocity was operationally calculated by subtracting the nominal envelope velocity on the retina, namely 2.5 deg/s, from the carrier's retina-relative velocity. If an underestimation of envelope speed occurred with 0 deg/s of the carrier's retina-relative velocity, the carrier's envelope-relative velocity, nominally −2.5 deg/s, would biologically decrease and might escape from the range of saturation. In contrast, in Experiment 3, the envelope velocity on the retina was 0 deg/s; therefore, the estimated envelope velocity should also be zero even if the same underestimation occurred. Thus, the carrier's envelope-relative velocity should be biologically estimated as we intended. 

Relationship to the curveball illusion

The curveball illusion, which is phenomenally similar to the motion-induced position shift, occurs when the trajectory of a vertically moving disk that contains a horizontally moving sinusoidal pattern appears to move obliquely, in a direction biased toward the direction of the sinusoid (Shapiro, Knight, & Lu, 2011; Shapiro, Lu, Huang, Knight, & Ennis, 2010). According to Shapiro et al. (2010), first-order and second-order motions are integrated in the peripheral visual field, resulting in a distortion of the perceived direction of motion. We propose two differences between this illusion and ours. First, the curveball illusion involves a misperception of motion direction, whereas our illusion involves a misperception of position. Because Shapiro et al. (2011) measured only the perceived direction of the motion trajectory without measuring the perceived horizontal position relative to some other landmark, it remains unknown whether a position shift also occurred. However, if a shift did occur, it would have involved a shift in only the overall horizontal position after the motion-induced position shift became saturated at 500–1000 ms (Chung et al., 2007; McGraw, Whitaker, Skillen, & Chung, 2002); this would never generate an inclination of the subsequent motion direction. Second, the directions of the carrier motion differed. It was orthogonal in the curveball illusion but parallel in our case. If our illusion were a special case of the curveball illusion, the perceived speed of the vertical Gabor patch would differ from that of the reference patch because the parallel carrier and envelope velocities would interact in the curveball situation. However, no such speed difference was observed. We suggest that the two phenomena are fundamentally different. 

Relationship to eye-velocity estimation

In Experiments 2 and 3, we measured the subjects' pursuit gains, which were found to be less than unity, indicating that the retinal motions of the carrier and envelope in each trial were not exactly as intended. The median pursuit gain, ranging from about 0.88 to 0.96, yields a difference of −0.3 to −0.1 deg/s between the intended and the actual image velocities on the retina (where the negative values indicate that the actual velocity was slower than the intended one). However, we believe that the velocity difference related to the under-pursuit would have a negligible effect on the magnitude of the position shift. First, it should be noted that the lower abscissas in Figures 4, 8, and 12 consistently indicate envelope-relative velocity, which, by definition, is not affected by pursuit gain. Second, although our calculation of retina-relative velocity is affected, the possible changes were not large enough to require the re-interpretation of data. When the pursuit gain in Experiment 2 was 0.9 (Figure 5), the nominal retinal envelope velocity of 2.5 deg/s was 2.25 deg/s and the carrier's nominal retina-relative velocities of −0.5, 0, 2.5, 5, and 5.5 deg/s were −0.75, −0.25, 2.25, 4.75, and 5.25 deg/s, respectively. When the pursuit gain was 0.9 in Experiment 3 (Figure 9), the nominal retinal envelope velocity of 0 deg/s was −0.25 deg/s and the nominal retina-relative velocities of −3, −2.5, 0, 2.5, and 3 deg/s were −3.25, −2.75, −0.25, 2.25, and 2.75 deg/s, respectively. In contrast, the motion-induced position shift is known to have velocity dependence in a much broader range such that the illusion begins to occur at the carrier velocity of 0.4–0.6 deg/s, increases up to 1–2 deg/s, then levels off (with 1 cycle/deg Gabor, eccentricity 4 deg, shown in figure 5 of Chung et al., 2007). We conclude that the under-pursuit in Experiments 2 and 3 and the resulting under-calibration of retina-relative velocity up to −0.3 deg/s did not influence our interpretations. 

Biological estimates of one's own eye velocity are not perfect (e.g., Freeman & Banks, 1998; see Goldstein, 2007; Furman & Gur, 2012 for a review). Some visual illusions are related to smooth-pursuit eye movement. For example, the Filehne illusion is a phenomenon in which an environmentally static object appears to move in the direction opposite to smooth pursuit (e.g., Filehne, 1922; Freeman & Banks, 1998; Terao & Murakami, 2011). This phenomenon arguably results from an underestimation of eye velocity attributable to an effort to compensate for the retinal slip originating from eye movement. Did underestimation of smooth-pursuit eye movement influence our results? We argue that the biological estimation of eye velocity and the transformation from retinal to environmental coordinates had negligible effects on the motion-induced position shift during smooth-pursuit eye movement. If the Filehne illusion occurred in the perceived carrier motion and this subjectively altered carrier motion induced the position shift, it would be greater when the carrier motion was opposite to the smooth-pursuit eye movement than when they were in the same direction. Moreover, the position shift would also occur in the direction opposite to the smooth-pursuit movement when the carrier is static on the display. However, the results of Experiment 2 revealed that the illusion was actually greater when the carrier was moving in the same direction as the pursuit eye movements, and that the illusion, if any (i.e., statistical significance was not reached), occurred in the pursuit direction when the carrier was static on the display. The results of Experiments 1 and 2 indicate that it was not the estimated eye velocity but the actual retinal slip of the envelope that affected the perceived position; when the envelope moved on the retina either with or without eye movement, the carrier moving in the direction opposite to the envelope was more effective than was the carrier moving in the same direction as the envelope. When the envelope was static on the retina, with or without eye movement, no bias was detected in the illusion strength. In terms of the negligible effect of underestimating eye velocity, we speculate that our current experimental setup, which included a wide variety of frames of reference, may have allowed the visual system to estimate eye velocity more accurately. 

Conclusion

We conclude that the envelope-relative carrier velocity is the major determinant of the motion-induced position shift and that if the envelope is also moving, the carrier that is moving in an opposite direction is more influential. The latter implies that low-level motion signals, which are represented before the transformation from the retinal to the environmental coordinates, participate in the position calculation for moving objects. 

Acknowledgments

IM was supported by the Nissan Science Foundation and the JSPS Funding Program for Next Generation World-Leading Researchers (LZ004). RH and MT were supported by the Japan Society for the Promotion of Science. 

Commercial relationships: none. 

Corresponding author: Rumi Hisakata. 

Email: [e-mail]. 

Address: Sensory Representation Research Group, Human and Information Science Laboratory, NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation, Atsugi, Kanagawa, Japan.