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Article  |   October 2016
Motion-induced position shift in stereoscopic and dichoptic viewing
Author Affiliations
  • Rumi Hisakata
    School of Human Sciences, Senshu University, Kanagawa, Japan
    Department of Life Sciences, the University of Tokyo, Tokyo Japan
    Japan Society for the Promotion of Science
    rumi.hisakata@icloud.com
  • Daisuke Hayashi
    Department of Psychology, the University of Tokyo, Tokyo, Japan
    daisuke@fechner.c.u-tokyo.ac.jp
  • Ikuya Murakami
    Department of Life Sciences, the University of Tokyo, Tokyo Japan
    Department of Psychology, the University of Tokyo, Tokyo, Japan
    ikuya@l.u-tokyo.ac.jp
Journal of Vision October 2016, Vol.16, 3. doi:10.1167/16.13.3
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      Rumi Hisakata, Daisuke Hayashi, Ikuya Murakami; Motion-induced position shift in stereoscopic and dichoptic viewing. Journal of Vision 2016;16(13):3. doi: 10.1167/16.13.3.

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Abstract

The static envelope of a Gabor patch with a moving sinusoidal carrier appears shifted in the direction of the carrier motion (De Valois & De Valois, 1991). This phenomenon is called motion-induced position shift. Although several motion-processing stages, ranging from low- to high-level processes, may contribute to position estimation, it is unknown whether a binocular matching stage or an even earlier stage exerts an influence. To elucidate this matter, we investigated the disparity tuning of this illusion by manipulating the binocular disparities of the carrier and the envelope. If the mechanisms underlying the illusion have disparity selectivity, the illusory shift should disappear when the carrier and envelope have sufficiently different disparities. We conducted an experiment in which a sinusoidal grating inside a Gaussian envelope had a crossed or uncrossed disparity and the background was filled with static random noise; each subject correctly judged whether the grating was in front of or behind the fixation plane. Position shift occurred even when the moving carrier had a vastly different disparity from that of the envelope, suggesting that one of the mechanisms responsible for the phenomenon exists at a monocular visual stage. To confirm this, in the next experiment we examined whether depth perception can be produced by an illusory disparity due to illusory position shifts in opposite directions between eyes. Two Gabor-like patches moving in opposite directions were presented at the same retinal position dichoptically. We found that when each monocular patch had a soft edge in its contrast envelope, the depth perception of such a patch was biased toward the depth consistent with the illusory crossed or uncrossed disparity, whereas depth perception of a stimulus with a hard edge was less biased. We suggest that the underlying mechanisms of motion-induced position shift are present at an early stage of monocular visual processing, and that the altered positions are represented in the left-eye and right-eye monocular pathways in a way that allows them to function as tokens of binocular matching.

Introduction
Determining the precise positions of objects is one of the most important functions of our visual system. On one hand, our visual system at times exhibits hyperacuity for relative position (e.g., Gwiazda, Bauer, & Held, 1989; Levi, Klein, & Aitsebaomo, 1985; Wehrhahn & Westheimer, 1990). On the other hand, position perception is sometimes dramatically altered by the presence of another stimulus in the vicinity. One of the most vivid examples of such alteration occurs when the contour of a stationary stimulus that contains a moving element within it is subjectively shifted in the direction of that motion. Hereafter we will refer to this phenomenon as motion-induced position shift (Anstis, 1989; De Valois & De Valois, 1991; Ramachandran & Anstis, 1990). Ramachandran and Anstis (1990) reported that a random-dot kinematogram embedded within another random-dot pattern appeared shifted in the direction of motion. Furthermore, De Valois and De Valois (1991) demonstrated that the static contrast envelope of a Gabor patch with a moving sinusoidal carrier appeared shifted in the direction of motion. Many different aspects of this latter phenomenon have received extensive study. For example, Bressler and Whitney (2006) found that when a static contrast window contained a moving grating defined by contrast, the second-order motion also produced some illusory shifting of the window in the direction of motion. Hisakata and Murakami (2009), Mather and Pavan (2009), and Rider, McOwan, and Johnston (2009) reported that if two or more distinct motion stimuli were perceptually integrated to yield pattern motion, the position of the display as a whole appeared shifted in the direction of the pattern motion. Hence, a number of studies have examined the kinds of motion that can induce an illusory position shift, exploring the relationship between position perception and motion processing. However, the relationship between illusory shift and visual attributes other than motion has rarely been addressed. In this study, we focus on binocular processing of the visual system and its relationship to the phenomenon of motion-induced position shift. 
Investigations of the processing hierarchy of our visual system reveal two distinct stages, namely the monocular and binocular processing stages. Furthermore, visual psychophysics experiments often reveal distinct contributions of these stages with respect to particular visual phenomena. For example, there are two kinds of motion aftereffects. The static motion aftereffect occurs when a static test pattern is presented after a subject has adapted to unidirectional motion; in such a case, the static pattern appears to be moving slowly in the opposite direction (e.g., Anstis, Verstraten, & Mather, 1998; Wohlgemuth, 1911). The dynamic motion aftereffect, on the other hand, occurs when a counterphase flicker is presented after adaptation; the flickering pattern is likely to be perceived as moving in the opposite direction (e.g., Hiris & Blake, 1992; Verstraten, Fredericksen, & Van Wezel, 1996; Verstraten, van der Smagt, & van de Grind, 1998). One of the major differences between these aftereffects can be seen in the rate of interocular transfer. The static motion aftereffect shows only partial transfer when the adaptation stimulus is presented to one eye and the static test stimulus is presented to the other eye (e.g., Tao, Lankheet, Grind, & Wezel, 2003; Wade, Swanston, & de Weert, 1993), indicating involvement of both monocular and binocular mechanisms. On the other hand, the dynamic motion aftereffect transfers nearly perfectly (Nishida & Ashida, 2000), indicating that the mechanism responsible operates primarily after binocular integration. Moreover, higher-level motion processing shows evidence of binocular disparity tuning. Shorter, Bowd, Donnelly, and Patterson (1999) and Patterson, Bowd, Phinney, Fox, and Lehmkuhle (1996) demonstrated that the motion aftereffect following adaptation to a moving stimulus defined by binocular disparity was selective for binocular disparity, with the maximum effect occurring when the test stimulus had the same degree of disparity as the adaptation stimulus. A seemingly corresponding neurophysiological fact is that a majority of neurons in areas MT and MST, in which nearly all neurons are directionally selective and are considered to contribute significantly to motion perception, also exhibit disparity tuning (e.g., Bradley, Qian, & Andersen, 1995; Cottereau, McKee, Ales, & Norcia, 2011; DeAngelis & Newsome, 1999; Roy, Komatsu, & Wurtz, 1992). 
Several studies have examined how motion in depth or in binocular interactions relates to the phenomenon of motion-induced position shift. Edwards and Badcock (2003) revealed that an optic-flow motion stimulus, composed of random dots and perceived to move in depth, induced a shift in the apparent depth of the entire stimulus in the direction of the motion in depth. Tsui, Khuu, and Hayes (2007) also found that the perceived depth of a moving three-dimensional object appeared to shift in the direction of the motion in depth. Murakami and Kashiwabara (2009) investigated whether a moving grating defined only by interocular correlation induces position shift. They found that such a grating, which can only be detected by a binocular mechanism, also displaced the position of the contrast-defined contour delimiting the spatial extent of the moving stimulus in the direction of the cyclopean motion. These studies clearly indicate that, at least in some cases, higher-level and binocular mechanisms are responsible for the motion-induced position shift. However, this conclusion does not exclude the possibility that a monocular mechanism also contributes to motion-induced position shift and might be observed in other cases. 
If the mechanism underlying the position shift is located solely at a binocular stage, this illusion may show evidence of binocular disparity tuning; that is, the effect may deteriorate when the inducing motion stimulus and the stationary contour demarcating the entire stimulus have different disparities. On the other hand, if a monocular mechanism contributes to the illusion, then the position shift should persist even with different disparities. In Experiment 1, we manipulated the disparities of the carrier and envelope of a Gabor patch to examine the disparity tuning associated with the motion-induced position shift. In Experiment 2, we examined whether the position shift could be induced independently for each eye, and if so, whether illusory positions induced oppositely between the two eyes could serve as an illusory binocular disparity on the basis of which a stereo matching process arrives at a solution of a particular depth. 
Experiment 1
Methods
Subjects
One of the authors (RH) and four naïve subjects with normal or corrected-to-normal vision and normal stereo depth perception served as participants. We ensured that no subject was stereo-blind through an initial visual acuity test. Viewing was from a distance of 67.3 cm. 
Apparatus
Stimuli were generated by a computer (Apple MacPro) and were displayed on a CRT monitor (Mitsubishi Electric RDF233H, 1024 × 768 pixels, 2 min/pix, refresh rate 120 Hz, background luminance 49 cd/m2), using Matlab (MathWorks) and the Psychophysics Toolbox extensions (Brainard, 1997; Kleiner, Brainard, & Pelli, 2007; Pelli, 1997). A color look-up table was used to linearize the gamma relationship. Stereo shutter goggles (StereoGraphics corporation CrystalEyes 3) were used for dichoptic viewing. 
Stimuli
Static random noise was displayed throughout the fixation plane. Two oppositely moving Gabor patches were used to assess the magnitude of the illusion. One was presented in the upper half of the visual field and the other was presented in the lower half. The standard deviation of the Gaussian envelope of each Gabor was 1.67°, and the maximal Michelson contrast of the inside carrier was 0.99. The spatial frequency of the carrier was 0.4 cycles/° and its temporal frequency was 2.4 Hz. 
There were three conditions: the near disparity, zero disparity, and far disparity conditions (Figure 1). In the near disparity condition, the Gabor patches appeared to be floating over the fixation plane (Figure 2a). To make the Gabor patches appear to be in front of the background, the same crossed disparity was applied to both the envelope and the carrier. The carrier of the Gabor had an interocular phase difference of π/2, or 37.5 arcmin, in the crossed disparity. The envelope also had the same binocular disparity, i.e., 37.5 arcmin. In the far disparity condition, the Gabor patch did not appear to be one figural object (Figure 2b). In this case, it was perceived as though a moving grating pattern lay behind a stationary window on the fixation plane. Hence, only the carrier had a far disparity, defined by an interocular phase difference of π/2, or 37.5 arcmin, in the uncrossed disparity, whereas the envelope had zero binocular disparity. This manipulation was inevitable because fusion was quite unstable if the envelope also had a far disparity. In the zero disparity condition, both the carrier and envelope had zero binocular disparity. 
Figure 1
 
Illustrations of the perceived depth relationships under each condition. In the near condition, both the envelope and carrier had the same crossed disparity. In the far condition, only the carrier had a far disparity.
Figure 1
 
Illustrations of the perceived depth relationships under each condition. In the near condition, both the envelope and carrier had the same crossed disparity. In the far condition, only the carrier had a far disparity.
Figure 2
 
Examples of stimuli in the near and far disparity conditions. Note that the illustrations are for cross-fusers, so that the left-hand and right-hand images represent the right-eye and left-eye images, respectively. (a) The near disparity condition: Both carrier and envelope had the same crossed disparity. Subjects perceived the grating to be floating in front of the noise texture. (b) The far disparity condition: Only the carrier had an uncrossed disparity. Subjects perceived the grating to be behind a hole in the noise texture.
Figure 2
 
Examples of stimuli in the near and far disparity conditions. Note that the illustrations are for cross-fusers, so that the left-hand and right-hand images represent the right-eye and left-eye images, respectively. (a) The near disparity condition: Both carrier and envelope had the same crossed disparity. Subjects perceived the grating to be floating in front of the noise texture. (b) The far disparity condition: Only the carrier had an uncrossed disparity. Subjects perceived the grating to be behind a hole in the noise texture.
Note that although the carriers presented to the left and right eyes had a phase difference in the near and far disparity conditions, these carriers always moved in the same direction at the same speed between eyes. This ensured stable fusion on the basis of the stable phase disparity. 
Procedure
Subjects were asked to press a button when Nonius lines presented at the center of the display appeared aligned vertically and horizontally. Once these were turned off as a result of the button press, the upper and lower Gabors were presented for 1 s at 7° eccentricities from the center of the display. After the cessation of the Gabor stimuli, subjects were asked to perform two consecutive tasks. The first task was to judge whether the carrier gratings of the Gabors were behind or in front of the fixation plane. The second task was to judge whether the upper Gabor was to the left or to the right of the lower Gabor. The method of constant stimuli (in which the independent variable was the horizontal offset between the upper and lower Gabors within a range of ±120 min in five steps, with 30 repetitive trials per point) was used to determine the point of subjective alignment, which in turn was taken as the index of the illusion strength of the position shift. Data were flipped and merged between leftward and rightward carrier directions so that the probability of seeing the Gabors horizontally shifted in the direction of the carrier motion was plotted as a function of the physical stimulus offset between the Gabors, with the negative offsets indicating offsets in the direction of carrier motion. Thus, a positive value of the point of subjective alignment meant that the Gabor's position had apparently shifted in the direction of carrier motion. 
Results
First, we ensured that the various disparity conditions resulted in the expected changes in the depth perception of the carriers. In Figure 3, the curved line indicates the percentage of reporting that the carriers were behind the fixation plane. The rate was nearly 0% in the near disparity condition and nearly 100% in the far disparity condition. In clear contrast, the magnitudes of the motion-induced position shift, shown by the gray bars in Figure 3, were robust throughout the three conditions: for near, t(4) = 7.96, p < 0.01; for zero, t(4) = 6.02, p < 0.01; for far, t(4) = 6.43, p < 0.01; these values yielded no significant difference due to the disparity condition, F(2, 8) = 0.21, p = 0.81. 
Figure 3
 
Results of Experiment 1. The gray bars indicate the magnitude of the position shift whereas the curve indicates the probability of reporting that the carrier gratings were behind the background. The error bars on the gray bars represent the standard errors calculated on the basis of 5,000 repetitions of Bootstrap fitting to each psychometric function.
Figure 3
 
Results of Experiment 1. The gray bars indicate the magnitude of the position shift whereas the curve indicates the probability of reporting that the carrier gratings were behind the background. The error bars on the gray bars represent the standard errors calculated on the basis of 5,000 repetitions of Bootstrap fitting to each psychometric function.
These results unequivocally indicate the absence of disparity tuning in the motion-induced position shift. It is highly unlikely that a larger disparity than tested here would result in a disparity dependence because we applied the maximally attainable sinusoidal phase disparity of π/2, which yielded nearly perfect reports of stereo depth for all subjects, and because this phase disparity translates to the visual angle of 37.5 arcmin, which would be close to the fusion limit (Howard & Rogers, 1995; Schor, Wesson, & Robertson, 1986; Schor, Wood, & Ogawa, 1984; Yeshurun & Schwartz, 1999). 
The near disparity condition had a large absolute disparity from the fixation plane. The fact that this condition yielded a robust position shift as great as that observed for the stimulus on the fixation plane means that this illusion does not require that a test stimulus be perceived as being on the same depth plane as the background, the stimulus configuration adopted by almost all previous studies of this illusion. But a far more surprising finding is the robust occurrence of this illusion under the far disparity condition; this condition involved a large relative disparity between the carrier and envelope, resulting in a peculiar situation in which subjects perceived the carrier as lying behind the fixation plane as though a stationary window had been made on the fixation plane. In other words, the carrier and envelope not only had physically different disparities, but they were also subjectively located on different depth planes. This far disparity condition yielded a position shift as great as the one found in the zero disparity condition, thereby indicating that, for the position shift to occur, motion does not need to have the same disparity as the stationary envelope, and furthermore, that motion does not need to appear to be on the same subjective depth plane as the envelope. 
These results clearly indicate that the binocular disparities of the carrier and envelope did not influence the illusory position shift. In light of previous studies showing that many kinds of motion can induce the illusory position shift, thus indicating that responsible sites for the position shift exist at multiple stages of visual processing, two possible interpretations can be made based on these findings; that is, the position shift as revealed in this experiment may already be represented at a monocular processing stage prior to binocular integration, or may be represented at a binocular stage but in a disparity-insensitive way. If the former scheme is the case, position shifts that are induced monocularly in opposite directions may construct an illusory disparity to work as a depth cue. Experiment 2 examined this possibility. 
Experiment 2
In a classical study of the motion-induced position shift, Anstis (1989) tested binocular interactions between monocularly produced position shifts. When two oppositely moving vertical gratings with stationary windows were presented dichoptically, the static window delimiting the grating, when fused, appeared to be displaced in depth. However, this manipulation suffers from spurious disparities due to false matches, from binocular rivalry seen in a dichoptic display, and also from an interocular velocity difference (IOVD) in each binocularly corresponding region between the two gratings. IOVD could directly affect depth perception, as indicated in the literature on motion in depth from interocular signals (e.g., Fernandez & Farell, 2005; Shioiri, Saisho, & Yaguchi, 2000). To minimize such binocular interactions, we spatially intermingled visible parts of the Gabor patch between the two eyes. 
Methods
Subjects and apparatus
Two of the authors (RH and DH) and four naïve subjects with normal or corrected-to-normal vision and normal stereo depth perception served as participants. Viewing was from a distance of 67.3 cm. The apparatus was identical to that used in Experiment 1
Stimuli
Subjects fixated the crossing of Nonius lines presented at the center of the display. Static noise (34.13° wide and 3° high) was presented along the horizontal meridian to both eyes to help fuse binocular images. Two types of stimuli, one with a soft edge and the other with a hard edge, were tested in separate sessions. The stimulus with a soft edge was equivalent to a Gabor patch with a horizontally moving carrier and a static envelope except for the following deviation. The stimuli delivered to the two eyes moved in opposite directions, and the binocular images were spatially intermingled between eyes to avoid spurious depth cues from false matches of the carriers at the same retinal position (Figure 4). Thus, the left-eye and right-eye images occupied odd and even rows, respectively. The standard deviation of the Gaussian contrast envelope determining edge softness was 1.33°. The stimulus with a hard edge was essentially the same as the stimulus described above, except that the contrast envelope was not Gaussian but an isotropic boxcar function (Figure 4). The radius of the contrast envelope was 2.66°. Under both conditions, the maximum contrast was 50%, the carrier's spatial frequency was 0.4 cycles/°, its temporal frequency was 0, 0.4, or 0.8 Hz (velocities were 0°/s, 1°/s, or 2°/s), and each row of spatial interlamination was 30 arcmin high. 
Figure 4
 
Illustrations of the stimuli under each condition. Under the soft-edge condition, two Gabors were presented in the two eyes in spatially alternate fashion. Under the hard-edge condition, the Gabor's soft envelope was replaced by a boxcar function with a clear-cut contour.
Figure 4
 
Illustrations of the stimuli under each condition. Under the soft-edge condition, two Gabors were presented in the two eyes in spatially alternate fashion. Under the hard-edge condition, the Gabor's soft envelope was replaced by a boxcar function with a clear-cut contour.
There were two types of dichoptic motion presentation (Figure 5). In the “crossed-motion” stimulus, the left-eye image moved rightward and the right-eye image moved leftward. In this case, according to our hypothesis, the left-eye image should induce a rightward position shift and the right-eye image should induce a leftward shift, resulting in an illusory crossed disparity if position shifts occur monocularly and independently. In contrast, in the “uncrossed-motion” stimulus, the left-eye image moved leftward and the right-eye image moved rightward. This condition should induce an illusory uncrossed disparity if position shifts occur monocularly and independently. Note that the physical disparity of the carrier was undefined because the dichoptic images were spatially intermingled with no stereo match, whereas the disparity of the contrast envelope was always zero. 
Figure 5
 
Predicted stereovision in each condition in accordance with illusory disparities.
Figure 5
 
Predicted stereovision in each condition in accordance with illusory disparities.
There were two edge conditions—the soft-edge and hard-edge conditions—as indicated above. Previous studies have demonstrated that a moving stimulus with a soft-edge stationary contrast envelope yields a large motion-induced position shift, whereas a moving stimulus with a hard-edge envelope yields only a small or no position shift (Anstis, 1989; Whitney et al., 2003). We hypothesized that if these relationships also hold for monocularly induced position shifts, the soft-edge stimulus should yield a larger illusory disparity than the hard-edge stimulus (Figure 5). 
Results
We measured monocular position shifts for the left and right eyes separately, predicted an illusory disparity that may be constructed from them, confirmed reliable depth perception for static stimuli having a physical disparity matched to this illusory disparity, and finally tested whether depth perception occurs in stimuli moving in opposite directions and presumably producing opposite position shifts between eyes, which would thereby create an illusory disparity. 
Measurement of motion-induced position shift for each eye
First, we measured the position shift induced by a monocular stimulus employing the method of constant stimuli. Only one of the gratings shown in Figure 4 was presented for 1 s to one eye, and two vertically aligned bars (0.17° × 0.3° each) were provided, as the position reference, above and below the grating. The distance between the bars was 8.6°, and the centers of the reference bars were vertically offset by 4.3° from the center of the grating. The grating's location was chosen randomly from the left or right upper quadrant of the visual field, 6° above and 5° horizontally away from the fovea. The carrier grating moved at 0°/s, 1°/s or 2°/s leftward or rightward. There were two edge conditions, soft and hard. After the grating disappeared, the subject reported whether it had been offset leftward or rightward compared to the reference bars. We manipulated the horizontal position of the reference within a range of ±60 min around the center of the grating in five steps, with 30 repetitive trials per point. 
Figure 6 indicates the average position shift in each speed condition relative to that at the 0°/s speed. The degrees of position shift were flipped and merged between the leftward and rightward motion directions so that a positive value indicates the position shift in the direction of motion. In line with previous studies (Arnold, Thompson, & Johnston, 2007; Whitney et al., 2003), the stimulus with a hard edge yielded smaller position shifts than that with a soft edge. In a 2 × 2 (edge × speed) repeated-measures analysis of variance (ANOVA), the main effect of edge was significant, F(1, 5) = 54.66, p < 0.001. There was also a significant difference between 1°/s and 2°/s speeds in the soft edge, as revealed by a significant interaction, F(1, 5) = 19.38, p < 0.01, and a significant simple main effect of speed in the soft-edge condition, F(1, 5) = 51.83, p < 0.001. Each individual subject's pattern of results was similar to the averaged data shown in Figure 6
Figure 6
 
Motion-induced position shift averaged across eyes and subjects. The error bars indicate the standard errors.
Figure 6
 
Motion-induced position shift averaged across eyes and subjects. The error bars indicate the standard errors.
A one-sample t test for each condition indicated whether a significant position shift occurred. Although the 1°/s speed in the hard edge revealed only a marginally significant difference from zero, t(5) = 2.37, p = 0.064, all other conditions yielded significant conventional position shifts: 2°/s hard-edge, t(5) = 3.01, p < 0.05; 1°/s soft-edge, t(5) = 8.67, p < 0.001; 2° d/s soft-edge, t(5) = 8.31, p < 0.001. 
Depth judgment at a physical envelope disparity equated to predicted illusory disparity
Next, we checked each subject's depth perception for a binocular static stimulus whereby the envelope for each eye was physically offset to mimic the position shift that had been measured above. The left-eye and right-eye images, as shown in Figure 4, were presented simultaneously for 1 s. Each grating stimulus had a static carrier that was antiphase between eyes, yielding no binocular fusion in the carrier. The horizontal offset of each envelope was equated to the previously measured amplitude of motion-induced position shift for each edge, speed, eye, and subject. Hence, a stimulus having a crossed envelope disparity was made by shifting the envelope of the left-eye stimulus rightward to the degree of the position shift by rightward motion measured for the left eye, and by shifting the envelope of the right-eye stimulus leftward to the degree of the position shift by leftward motion measured for the right eye. A stimulus having an uncrossed envelope disparity was made by shifting the envelopes in opposite directions according to the position shifts measured for the opposite conditions. 
Figure 7 plots the averaged envelope disparity that was calculated from the monocularly measured position shifts. The bottom and top abscissae indicate the carrier velocities for the left and right eyes, respectively, where negative and positive velocities indicate leftward and rightward motions, respectively. The ordinate indicates what illusory disparity would be created from monocular position shifts if the left and right eyes received the carrier velocities designated on the bottom and top abscissae, respectively. For example, the rightmost point indicates what would happen if the left-eye image moved rightward (+2°/s) and the right-eye image moved leftward (−2°/s); the left-eye image would be monocularly shifted rightward whereas the right-eye image would be leftward, thus creating a crossed illusory disparity. The disparity under the static baseline condition simply indicates a constant error that, on average, static stimuli presented only to the left and right eyes have been judged as slightly shifted rightward and leftward, respectively. To mimic this constant error, the stimulus in this dichoptic presentation had a small crossed disparity. Relative to this static baseline condition, the disparity for each combination of velocity and edge conditions was roughly twice as large as the monocularly measured position shift shown in Figure 6. This is because the horizontal envelope offsets matched to the monocularly measured position shifts were simultaneously applied in opposite directions between eyes to create a crossed or uncrossed envelope disparity. 
Figure 7
 
Averaged envelope disparity calculated from the monocularly measured position shift. The bottom and top abscissae indicate the velocities of the left-eye and right-eye images respectively. Negative and positive values on the abscissae indicate leftward and rightward motions respectively. Negative values on the ordinate indicate uncrossed illusory disparities whereas positive values indicate crossed illusory disparites. The error bars indicate the standard errors of the mean.
Figure 7
 
Averaged envelope disparity calculated from the monocularly measured position shift. The bottom and top abscissae indicate the velocities of the left-eye and right-eye images respectively. Negative and positive values on the abscissae indicate leftward and rightward motions respectively. Negative values on the ordinate indicate uncrossed illusory disparities whereas positive values indicate crossed illusory disparites. The error bars indicate the standard errors of the mean.
In the experiment measuring depth judgment at a physical envelope disparity equated to predicted illusory disparity, two such stimuli were simultaneously presented in the left and right upper quadrants of the visual field, 6° above and 5° to the left and right of the fovea. There were two edge conditions (soft and hard) and five velocity conditions (−2, −1, 0 (static), +1°/s, and +2°/s). In each velocity condition, physical displacements corresponded to the measured amplitudes of the position shift that had previously been obtained for each edge, speed, eye, and subject. A positive velocity on the bottom abscissa of Figure 8 means that a stimulus having a crossed disparity was presented to the right, and also that another stimulus having the opposite disparity was presented to the left. After the stimuli disappeared, the subject reported which stimulus, the left-hand or right-hand, had appeared to be nearer in depth. There were 100 repetitive trials for each condition. 
Figure 8
 
Averaged probability of seeing the right-hand grating as “near.” Positive velocities on the bottom abscissa mean that stimuli having uncrossed and crossed disparities were presented to the left and right, respectively, and vice versa for negative velocities. The error bars indicate the standard errors of the mean. Note that the stimuli were always stationary; indications along the abscissae mean that these conditions used monocular position shifts that had previously been measured in the respective velocity conditions.
Figure 8
 
Averaged probability of seeing the right-hand grating as “near.” Positive velocities on the bottom abscissa mean that stimuli having uncrossed and crossed disparities were presented to the left and right, respectively, and vice versa for negative velocities. The error bars indicate the standard errors of the mean. Note that the stimuli were always stationary; indications along the abscissae mean that these conditions used monocular position shifts that had previously been measured in the respective velocity conditions.
The ordinate of Figure 8 shows the averaged probability of seeing the right-hand grating as nearer in depth. When the left-hand and right-hand stimuli had physically uncrossed and crossed disparities, respectively (i.e., at positive velocities on the bottom abscissa), it was more likely that the right-hand stimulus appeared nearer, and vice versa. When the stimuli had soft edges, depth judgment in each condition significantly changed from that in the static condition: −2°/s, t(5) = 2.92, p < 0.05; −1°/s, t(5) = 2.99, p < 0.05; +1°/s, t(5) = −3.18, p < 0.05; +2°/s, t(5) = −4.45, p < 0.01. In contrast, when the stimuli had hard edges, changes in depth judgment were only marginally significant or statistically unsupported: −2/s, t(5) = 1.63, p = 0.17; −1°/s, t(5) = 1.65, p = 0.16; +1°/s, t(5) = −2.12, p = 0.059; +2°/s, t(5) = 2.44, p = 0.087. This may have resulted from relatively small physical envelope disparities in the hard-edge condition (Figure 7). Because the stimuli in the negative velocity and positive velocity conditions were simply mirror-symmetrical, we flipped and merged the probabilities to collapse these conditions in each speed, and performed a 2 × 2 (edge × speed) repeated-measures ANOVA. The interaction was significant, F(1, 5) = 7.97, p < 0.05, and the simple main effect of edge in the 2°/s condition, F(1, 5) = 4.54, p = 0.086, and the simple main effect of speed in the soft-edge condition, F(1, 5) = 4.20, p = 0.096, were marginally significant. These results indicate that the envelope disparity, which had an amplitude that was calculated from the monocularly measured position shifts, was a valid depth cue when physically applied to a static stimulus, and that the probability of seeing depth as predicted from envelope disparity was higher in the soft-edge condition than in the hard-edge condition at a larger envelope disparity. 
Depth judgment for an illusory disparity predicted from monocular position shifts
Finally, we examined each subject's depth perception for a binocular moving stimulus in which the envelope had zero physical disparity but was predicted to have an illusory disparity due to monocularly induced position shifts. The left-eye and right-eye images, as shown in Figure 4, were presented simultaneously for 1 s. The carrier moved oppositely between eyes. Two such stimuli were presented in the left and right upper quadrants of the visual field, 6° above and 5° to the left and right of the fovea. Positive velocities on the bottom abscissa of Figure 9 mean that the left-hand and right-hand stimuli were the “uncrossed-motion” and “crossed-motion” stimuli, respectively; at negative velocities, the locations of these stimuli were horizontally flipped. For each velocity condition, there were two edge conditions (soft and hard). After the stimuli disappeared, the subject reported which stimulus, the left-hand or right-hand, appeared to be nearer in depth. There were 100 repetitive trials for each condition. 
Figure 9
 
Averaged probability of seeing the right-hand grating as “near.” Positive velocities on the bottom abscissa mean that the left-hand and right-hand stimuli were the “uncrossed-motion” and “crossed-motion” stimuli, respectively; at negative velocities, the locations of these stimuli were horizontally flipped. The error bars indicate the standard errors of the mean. Note that the carriers were moving at the velocities indicated along the abscissae, whereas the static envelopes had zero physical disparity but were predicted to have an illusory disparity, as shown in the ordinate of Figure 8 for each condition.
Figure 9
 
Averaged probability of seeing the right-hand grating as “near.” Positive velocities on the bottom abscissa mean that the left-hand and right-hand stimuli were the “uncrossed-motion” and “crossed-motion” stimuli, respectively; at negative velocities, the locations of these stimuli were horizontally flipped. The error bars indicate the standard errors of the mean. Note that the carriers were moving at the velocities indicated along the abscissae, whereas the static envelopes had zero physical disparity but were predicted to have an illusory disparity, as shown in the ordinate of Figure 8 for each condition.
The ordinate of Figure 9 shows the averaged probability of seeing the right-hand grating as being nearer in depth. Depth judgment yielded a profile that was similar to that in Figure 8; namely, it was more likely that the “crossed-motion” stimulus appeared nearer than the “uncrossed-motion” stimulus. Depth judgments in all conditions significantly changed from that in the static condition, regardless of whether the stimuli had a soft edge [−2°/s, t(5) = 6.61, p < 0.005; −1°/s, t(5) = 8.00, p < 0.001; +1°/s, t(5) = −8.48, p < 0.001; +2°/s, t(5) = −7.17, p < 0.001] or a hard edge [−2°/s, t(5) = 5.22, p < 0.005; −1°/s, t(5) = 4.97, p < 0.005; +1°/s, t(5) = −3.82, p < 0.05; +2°/s, t(5) = −3.58, p < 0.05]. Because the stimuli in the negative velocity and positive velocity conditions were simply mirror-symmetrical, we flipped and merged the probabilities to collapse these conditions in each speed. A 2 × 2 (edge × speed) repeated-measures ANOVA revealed a significant main effect of edge, F(1, 5) = 7.32, p < 0.05, whereas speed had no significant effect, F(1, 5) = 0.11, p = 0.76. 
Discussion
In this study, we examined the relationship between binocular processing and motion-induced position shift. In Experiment 1, we explored the effects of binocular disparity on the illusion. The position shift occurred even when the stimulus had a very large binocular disparity in the moving carrier and/or envelope, indicating the existence of an underlying mechanism that functions robustly despite the introduction of a discrepancy in disparity. One extreme interpretation of this finding would be that all position shifts have been processed prior to binocular integration, but this is at odds with a line of supporting evidence for the involvement of higher-level motion processing stages (e.g., Murakami & Kashiwabara, 2009; Bressler & Whitney, 2006; Hisakata & Murakami, 2009). Thus, a more realistic interpretation is that there exist multiple mechanisms for position shift, one of which resides in a monocular processing stage, whose contribution fully explains the present results without additional contributions from binocular stages. If one of the mechanisms exists monocularly, the representation of such an altered position within each eye's monocular processing pathway should serve as an artificial depth cue when the monocular position of the stimulus is shifted in opposite directions for each of the two eyes. In Experiment 2, two gratings that moved in horizontal directions opposite to each other were presented dichoptically, with the result that such a moving grating appeared to shift in the depth direction predicted on the basis of the above hypothesis. Moreover, the stimuli with soft edges yielded greater depth perception than those with hard edges. 
Possible mechanisms underlying motion-induced position shifts
Experiment 1 revealed that a stationary window whose binocular disparity is nearer than that of a moving stimulus can also be subjectively displaced in the direction of motion. Under this far disparity condition, the moving grating appeared as a moving surface that was only partially visible through a stationary window on the fixation plane. In this case, even though the border of the window was perceptually owned by the fixation plane filled with static noise and not by the motion inside, the moving grating still had an influence on the estimation of the edge position on the front plane. In other words, perceived unity of the stimulus as one object was not a prerequisite for the position shift of a contour induced by the motion within it. This remote effect may be viewed as a three-dimensional extension of positional mislocalization of a remote object in the direction of another moving object (Whitney & Cavanagh, 2000); in this phenomenon, often called the flash-drag effect, a briefly flashed stationary stimulus appears to be shifted in the direction of motion even though the moving stimulus is spatially separated from the flash. Likewise, the present study demonstrates that a stationary envelope, which is defined by second-order soft edges with large positional uncertainty, appears to be shifted in the direction of motion even though the moving stimulus is localized on a different depth plane. 
As for the kind of stimulus velocity that is the most pertinent cue for inducing the motion-induced position shift, Hisakata, Terao, and Murakami (2013) found that the carrier's velocity relative to the envelope was the primary determinant. They measured the motion-induced position shift in a Gabor patch with a moving carrier and a moving envelope during smooth pursuit eye movement and created situations in which the retina-relative, display-relative, and envelope-relative velocities of the carrier all differed from each other. Based on the finding that the envelope-relative velocity of the carrier determined the magnitude of the position shift, it was concluded that the mechanism underlying the position shift involves high-level motion processing that is sensitive to differential motion. Other studies have also demonstrated the contribution of higher-level motion processing stages by demonstrating that a wide variety of motion stimuli (global motion, second-order motion, motion in depth, etc.) can induce a position shift in the direction of the perceived direction of motion (Bressler & Whitney, 2006; Hisakata & Murakami, 2009; Mather & Pavan, 2009; Murakami & Kashiwabara, 2009; Mussap & Prins, 2002; Rider, McOwan & Johnston, 2009). These studies indicate that higher-level motion processing is important for the position shift; however, they do not eliminate the possibility that computation related to the position shift also occurs at early stages of visual processing. 
We propose that computation resulting in an illusory position shift occurs at multiple visual stages involved in the processing of motion information. In some physiological studies, the receptive fields of direction-selective neurons in several visual areas (e.g., the primary visual cortex in the cat and V4 in the monkey) can be shifted by a motion signal (Fu et al., 2002; Fu, Shen, Gao, & Dan, 2004; Sundberg, Fallah, & Reynolds, 2006). In functional magnetic resonance imaging of the human cortex, the size of the population receptive field was found to increase with the speed of a moving stimulus used for receptive-field mapping in visual areas including V1, V3A, and MT+ (Harvey & Dumoulin, 2016). As such, the receptive-field positions of neurons in a visual cortex that preserves retinotopy, from which the system estimates each object's position, can be flexible in many stages of the visual hierarchy (Bressler & Whitney, 2006; Hisakata & Murakami, 2009). Our findings suggest that the receptive-field positions of neurons at a monocular stage can also be as flexible in the presence of motion signals, and furthermore that binocular vision can use such temporarily altered position information as if it was binocular disparity. 
Relative contributions of illusory disparity and interocular velocity difference
To examine the possibility that position shifts can already be represented in a monocular stage, we tested whether illusory disparity calculated from monocular position shifts in the left and right eyes could induce depth perception. The results of Experiment 2 clearly indicate that depth was perceived in accordance with the expected illusory disparity. However, the contribution from IOVD should also be considered (Shioiri et al, 2000). The prediction from IOVD dictates that when the left-eye and right-eye images move rightward and leftward, respectively (our “crossed-motion” stimulus), the stimulus appears to come closer in depth, whereas when the left-eye and right-eye images move leftward and rightward, respectively (our “uncrossed-motion” stimulus), the stimulus appears to recede. Thus, IOVD does predict that our “crossed-motion” and “uncrossed-motion” stimuli appear to be nearer and farther, respectively, as was indeed found in Experiment 2. Slightly higher probabilities of perceiving depth in the illusory disparity case (Figure 9) than in the physical disparity case (Figure 8) makes it probable that IOVD contributes to some aspects of our data. However, IOVD does not predict two key aspects of our results, namely, that the envelope with a soft edge was more strongly influenced by motion than the envelope with a hard edge and that the speed of motion, whether 1°/s or 2°/s, did not affect depth judgment. Therefore, we believe that, in addition to IOVD, illusory disparity must be introduced to fully explain our data. 
Conclusion
In conclusion, Experiment 1 demonstrated that motion-induced position shift had no binocular disparity tuning between a moving carrier and a stationary envelope of a Gabor patch. Experiment 2 demonstrated that depth was perceived when motion-induced position shifts were produced in opposite directions between eyes, as if illusory position shifts created an illusory binocular disparity. Based on these results, we suggest that one of the underlying mechanisms of position shift is at work at an early monocular visual processing stage, and that altered positions are represented in the left-eye and right-eye monocular pathways, contributing to depth perception. Also, it is likely that position shifts can be generated at multiple sites of the visual processing hierarchy, so that it is interesting to examine how such different representations are integrated into our perception of position. 
Acknowledgments
IM was supported by JSPS Funding Program NEXT Grant Number LZ004 and by JSPS KAKENHI Grant Numbers 15H01984 and 25119003. RH was supported by the Japan Society for the Promotion of Science. 
Commercial relationships: none. 
Corresponding author: Rumi Hisakata. 
Email: rumi.hisakata@icloud.com. 
Address: School of Human Sciences, Senshu University, Kanagawa, Japan. 
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Figure 1
 
Illustrations of the perceived depth relationships under each condition. In the near condition, both the envelope and carrier had the same crossed disparity. In the far condition, only the carrier had a far disparity.
Figure 1
 
Illustrations of the perceived depth relationships under each condition. In the near condition, both the envelope and carrier had the same crossed disparity. In the far condition, only the carrier had a far disparity.
Figure 2
 
Examples of stimuli in the near and far disparity conditions. Note that the illustrations are for cross-fusers, so that the left-hand and right-hand images represent the right-eye and left-eye images, respectively. (a) The near disparity condition: Both carrier and envelope had the same crossed disparity. Subjects perceived the grating to be floating in front of the noise texture. (b) The far disparity condition: Only the carrier had an uncrossed disparity. Subjects perceived the grating to be behind a hole in the noise texture.
Figure 2
 
Examples of stimuli in the near and far disparity conditions. Note that the illustrations are for cross-fusers, so that the left-hand and right-hand images represent the right-eye and left-eye images, respectively. (a) The near disparity condition: Both carrier and envelope had the same crossed disparity. Subjects perceived the grating to be floating in front of the noise texture. (b) The far disparity condition: Only the carrier had an uncrossed disparity. Subjects perceived the grating to be behind a hole in the noise texture.
Figure 3
 
Results of Experiment 1. The gray bars indicate the magnitude of the position shift whereas the curve indicates the probability of reporting that the carrier gratings were behind the background. The error bars on the gray bars represent the standard errors calculated on the basis of 5,000 repetitions of Bootstrap fitting to each psychometric function.
Figure 3
 
Results of Experiment 1. The gray bars indicate the magnitude of the position shift whereas the curve indicates the probability of reporting that the carrier gratings were behind the background. The error bars on the gray bars represent the standard errors calculated on the basis of 5,000 repetitions of Bootstrap fitting to each psychometric function.
Figure 4
 
Illustrations of the stimuli under each condition. Under the soft-edge condition, two Gabors were presented in the two eyes in spatially alternate fashion. Under the hard-edge condition, the Gabor's soft envelope was replaced by a boxcar function with a clear-cut contour.
Figure 4
 
Illustrations of the stimuli under each condition. Under the soft-edge condition, two Gabors were presented in the two eyes in spatially alternate fashion. Under the hard-edge condition, the Gabor's soft envelope was replaced by a boxcar function with a clear-cut contour.
Figure 5
 
Predicted stereovision in each condition in accordance with illusory disparities.
Figure 5
 
Predicted stereovision in each condition in accordance with illusory disparities.
Figure 6
 
Motion-induced position shift averaged across eyes and subjects. The error bars indicate the standard errors.
Figure 6
 
Motion-induced position shift averaged across eyes and subjects. The error bars indicate the standard errors.
Figure 7
 
Averaged envelope disparity calculated from the monocularly measured position shift. The bottom and top abscissae indicate the velocities of the left-eye and right-eye images respectively. Negative and positive values on the abscissae indicate leftward and rightward motions respectively. Negative values on the ordinate indicate uncrossed illusory disparities whereas positive values indicate crossed illusory disparites. The error bars indicate the standard errors of the mean.
Figure 7
 
Averaged envelope disparity calculated from the monocularly measured position shift. The bottom and top abscissae indicate the velocities of the left-eye and right-eye images respectively. Negative and positive values on the abscissae indicate leftward and rightward motions respectively. Negative values on the ordinate indicate uncrossed illusory disparities whereas positive values indicate crossed illusory disparites. The error bars indicate the standard errors of the mean.
Figure 8
 
Averaged probability of seeing the right-hand grating as “near.” Positive velocities on the bottom abscissa mean that stimuli having uncrossed and crossed disparities were presented to the left and right, respectively, and vice versa for negative velocities. The error bars indicate the standard errors of the mean. Note that the stimuli were always stationary; indications along the abscissae mean that these conditions used monocular position shifts that had previously been measured in the respective velocity conditions.
Figure 8
 
Averaged probability of seeing the right-hand grating as “near.” Positive velocities on the bottom abscissa mean that stimuli having uncrossed and crossed disparities were presented to the left and right, respectively, and vice versa for negative velocities. The error bars indicate the standard errors of the mean. Note that the stimuli were always stationary; indications along the abscissae mean that these conditions used monocular position shifts that had previously been measured in the respective velocity conditions.
Figure 9
 
Averaged probability of seeing the right-hand grating as “near.” Positive velocities on the bottom abscissa mean that the left-hand and right-hand stimuli were the “uncrossed-motion” and “crossed-motion” stimuli, respectively; at negative velocities, the locations of these stimuli were horizontally flipped. The error bars indicate the standard errors of the mean. Note that the carriers were moving at the velocities indicated along the abscissae, whereas the static envelopes had zero physical disparity but were predicted to have an illusory disparity, as shown in the ordinate of Figure 8 for each condition.
Figure 9
 
Averaged probability of seeing the right-hand grating as “near.” Positive velocities on the bottom abscissa mean that the left-hand and right-hand stimuli were the “uncrossed-motion” and “crossed-motion” stimuli, respectively; at negative velocities, the locations of these stimuli were horizontally flipped. The error bars indicate the standard errors of the mean. Note that the carriers were moving at the velocities indicated along the abscissae, whereas the static envelopes had zero physical disparity but were predicted to have an illusory disparity, as shown in the ordinate of Figure 8 for each condition.
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