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Article  |   October 2014
Binocular contributions to linear vertical vection
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Journal of Vision October 2014, Vol.14, 5. doi:10.1167/14.12.5
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      Robert S. Allison, April Ash, Stephen Palmisano; Binocular contributions to linear vertical vection. Journal of Vision 2014;14(12):5. doi: 10.1167/14.12.5.

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Abstract
Abstract
Abstract:

Abstract  Compelling illusions of self-motion, known as vection, can be produced in a stationary observer by visual stimulation alone. The role of binocular vision and stereopsis in these illusions was explored in a series of three experiments. Previous research had provided evidence of stereoscopic enhancements for linear vection in depth (e.g., Palmisano, 1996, 2002). Here we examined for the first time the effects of binocular vision and stereopsis on linear vertical vection. Vertical vection was induced by the upward or downward translation of large stereoscopic surfaces. These surfaces were horizontally oriented depth corrugations produced by disparity modulation of patterns of persistent or short lifetime dot elements. We found that binocular viewing of such surfaces significantly increased the magnitudes and decreased the onset delays of vertical vection. Experiments utilizing short lifetime dot stereograms demonstrated that these particular binocular enhancements of vection were due to the motion of stereoscopically defined features.

Introduction
Self-motion through the world generates patterns of visual stimulation called optic flow (Gibson, 1950). Most self-motion research to date has considered the optic flow provided to a single eye; however, self-motion (like object motion) produces different patterns of optic flow at the left and right eyes. This raises the following question: Is there an additional, or even independent, contribution of binocular viewing or binocular motion stimulation to the perception of self-motion? In this paper we consider this question for lamellar flow, corresponding to the simulated vertical motion of either the self or the whole visual environment (i.e., self- or scene-motion parallel to the coronal plane of the head). In addition to uncovering the underlying sensory processing of self-motion, the answer to this general question is practically important for self-motion simulation applications such as vehicle simulators, rides, and virtual reality, where the benefit of stereoscopic display must be weighed against the cost and technical challenges of presenting full-field stereoscopic displays. 
There are several ways that binocular vision could contribute to the perception of linear self-motion, over and above the view provided by a single eye: (a) increased field of view; (b) binocular summation; (c) stereoscopically defined features and motion; (d) improved information about environmental layout, depth, and parallax; and (e) improved perception of rigidity and structure. Here, for the first time, we describe each of these possible binocular contributions in detail and then discuss the available evidence supporting their involvement in the perception of self-motion. 
Field of view
One of the most basic benefits of binocular vision is the increased field of view provided, an advantage maximized in lateral-eyed animals but important even for frontal-eyed animals, such as humans, that typically have a significantly larger total field of view than can be seen from either eye. Both circular and linear vection reportedly increase with stimulus area (e.g., Telford & Frost, 1993), so the increased binocular field of view should promote vection. We do not consider this aspect further as stimuli in the present study were restricted to only the binocular visual field and were visible to both eyes. 
Binocular summation
Binocular summation refers to the combination of typically redundant signals from the left and right eyes to form a stronger signal, improve task performance, or improve the signal-to-noise ratio (for a recent review see Howard & Rogers, 2012). Increases in effective contrast from binocular summation improve the detectability and discriminability of low-contrast stimuli but not high-contrast stimuli (Legge, 1984) and performance on spatial vision tasks at low contrast (Banton & Levi, 1991; Home, 1978). Thus, binocular summation could enhance the visibility of low-contrast stimuli and allow them to contribute to vection. In line with this reasoning, binocular summation has been shown to improve global motion coherence detection at low contrast (Hess, Hutchinson, Ledgeway, & Mansouri, 2007). 
Binocular summation of similar inputs is not the only way that binocular inputs can combine. The most important form of combination of dissimilar inputs is stereopsis, which is considered below; however, different information to the two eyes can also be combined to form a composite dichoptic image that is the sum of the monocular images. Such binocular combination of dissimilar images is most likely at low contrast; binocular rivalry is more likely at higher contrast (Liu, 1992). Hess et al. (2007) also found that dichoptic presentation (signal dots to one eye and noise dots to the other) did not improve performance over monocular presentation (signal and noise dots both presented to one eye; a uniform gray field of mean luminance presented to the other). When combined with their findings on contrast dependence, these authors concluded that (a) the motion signals for the two eyes are combined at an early, contrast-dependent stage of processing and (b) global motion processing is purely binocular. 
Stereoscopically defined features and motion
Stereopsis is a potent cue to depth and consequently moving stereoscopic features are a cue to three-dimensional motion. Since the two eyes are laterally separated in the head, the images on the two retinas differ. In particular, the position of the image of an object can differ on the two retinas; this is referred to as a positional disparity. In the 19th century, Wheatstone (1838) demonstrated clearly that a compelling sense of depth perception, known as binocular stereopsis, could be obtained from these binocular disparities. When an observer moves in depth relative to an object its positional disparity changes, providing the changing disparity cue to motion-in-depth; furthermore, when an observer or object moves in depth the images of the object typically move at different velocities in the two eyes, leading to the cue of interocular velocity difference (Regan, 1993). Similarly, disparity change and interocular velocity differences can provide information about the direction of motion in depth (Regan, 1993). Psychophysical studies have shown that motion in depth can be elicited by either changing disparity or interocular velocity differences (Allison & Howard, 2011; Allison, Howard, & Howard, 1998; Shioiri, Saisho, & Yaguchi, 2000). During self-motion these interocular velocity difference and changing disparity cues are available across the optic flow field. These binocular cues could elicit or contribute to perceived motion in depth and hence to linear vection in depth. Palmisano (2002) found that adding consistent stereoscopic depth to simulated forward self-motion displays increased apparent self-motion speed and distance traveled. Additional experiments suggested that the enhanced vection was due to binocular cues to motion in depth rather than improved perception of layout of the three-dimensional scene. 
Binocular disparity can also define stereoscopically defined contours that are not visible in the monocular images. Such features are known as cyclopean features because they are defined and visible only after the binocular inputs are combined (Julesz, 1971). Cyclopean images can support the perception of form and motion and even geometrical illusions. If the position of the cyclopean contours is changed over time then the cyclopean form appears to move, and this stereoscopically defined motion could produce vection. To our knowledge the possibility that moving cyclopean contours can induce vection has never been tested. However, moving cyclopean contours in a dynamic random-dot stereogram can produce optokinetic nystagmus in observers with normal stereoscopic vision (Fox, Lehmkuhle, & Leguire, 1978). Furthermore, Loomis and colleagues have reported that observers can make accurate judgments about the direction of self-motion (i.e., heading judgments; Macuga, Loomis, Beall, & Kelly, 2006) and guide interceptive movements (Loomis, Beall, Macuga, Kelly, & Smith, 2006), even if the only information about the simulated self-motion is provided by the motion of cyclopean features. 
Information about environmental layout, depth, and parallax
The motion perspective in optic flow is complex and potentially ambiguous. One problem is the scale ambiguity of the motion perspective in the flow field—did the flow result from a large motion in a large environment or a small motion in a small environment? Binocular information about distance from vergence and vertical disparity could, in principle, provide the scaling factor, at least in relatively near space (Rogers & Bradshaw, 1995). Butler, Campos, Bülthoff, and Smith (2011) found that, for stationary observers, heading discrimination was not improved when stereoscopic cues were added to optic flow displays simulating self-motion (compared with when both eyes viewed an equivalent nonstereoscopic display). However, combined visual–vestibular just-noticeable differences for physically moving observers were closer to optimal cue integration under stereoscopic presentation; suboptimal combined just-noticeable differences were obtained under binocular, nonstereoscopic presentation. As the task was simply discrimination of the heading direction relative to straight ahead, the assumed scale of the optic flow display should have affected only the apparent magnitude, not the direction, of the heading offset. The authors speculated that disparity cues help determine the ambiguous scale of the optic flow display and thus promote integration with the vestibular cues—this assumes that effective visual–vestibular integration depends on compatible vestibular and visual estimates of heading direction. 
Another potential ambiguity arises from difficulties in parsing the flow field into various components. Local flow can arise from self-motion or object/scene motion. Even if object/scene motion can be discounted, the effects of linear and rotational self-motion also need to be distinguished. Theoretically (Longuet-Higgins & Prazdny, 1980) monocularly available optic flow could be so decomposed, assuming both rigidity and depth variation in the scene. However, this processing would be simplified substantially if the layout and depth relations in the environment could be estimated. Consistent with this notion, van den Berg and Brenner (1994) reported that heading judgments were more tolerant to randomly directed local motion noise when short-duration (1.5 s) looming optic flow was presented stereoscopically as opposed to synoptically (i.e., identical images were presented to the two eyes). Interestingly, tolerance to this motion noise was similar when the moving dots had a fixed disparity (appropriate to their simulated three-dimensional layout on the first frame) compared with when their changing disparities represented the appropriate motion in depth. This latter finding suggested that the improved resilience was due to information about spatial layout rather than stereoscopic cues to motion in depth. As noted in the previous paragraph, Butler et al. (2011) did not find any stereoscopic advantage for heading perceptions based on purely visual self-motion simulation. 
The only systematic studies of the effect of stereoscopic layout cues on vection were conducted by Palmisano (1996, 2002). In the earlier paper, he found that stereoscopic displays elicited stronger (shorter latency and longer duration) vection in depth than did monocular or nonstereoscopic binocular displays. He considered that the stereoscopic enhancement could have been due to improved information about the layout of the simulated objects, improved impressions of depth, or improved motion-in-depth cues. Since the monocular displays contained strong cues to relative depth, he argued that it was unlikely that stereoscopic cues could further help disambiguate layout. In the later paper, he found that stereoscopic information did not appear to be improving vection in depth by increasing the perceived maximum extent of displays or by making displays appear more three-dimensional. This led him to conclude that the stereoscopic enhancement of vection was due to stereoscopic motion-in-depth cues (rather than an improved perception of layout). In the present experiments we simulated vertical motion, rather than motion in depth, in order to focus on aspects of the binocular contribution to vection other than binocular motion in depth. 
Improved perception of rigidity and structure
Grigo and Lappe (1998) showed that transparently superimposing a horizontally translating optic flow field on a looming flow pattern shifts the perceived focus of expansion (FOE). Lappe, Bremmer, and van den Berg (1999) suggested that this shift results from compensatory mechanisms that interpret the horizontal translation as a head–eye rotation and correct the observer's heading estimate accordingly. According to their proposal, visual motions of the most distant parts of the scene provide the best estimates of head-and-eye rotation (as the looming and parallax arising from whole-body self-motion is more evident in the image motions of nearer points). Importantly, they also found that the shift in the apparent FOE was modulated by the relative disparity between the translating and looming patterns. The weakest shift in the FOE was found when the translating pattern was stereoscopically simulated to be in front of the looming pattern—possibly because this particular arrangement of motion vectors implies a nonrigid optic flow field, which would be expected to degrade the perception of self-motion. 
Depth information has been identified as being important for the effective visual parsing of object motion from self-motion (Warren & Rushton, 2009). Rigid movement of all objects in the world is rare and typically results from self-motion rather than the movement of the world. There is evidence that visual environments that are perceived as rigid are more likely to induce vection or postural responses than are those not seen as rigid (Holten, Donker, Verstraten, & van der Smagt, 2013; Nakamura, 2010; but see Palmisano, Allison, & Howard, 2006; Palmisano, Kim, & Freeman, 2012). However, the role that binocular disparity plays in perceived rigidity has not been explored. Consistent disparity and optic flow-based information about layout should promote the perception of self-motion through a stable, rigid environment. By contrast, stereomotion or stereoscopic depth inconsistent with the optic flow should further reinforce the perception of object movement or deformation. 
Related but distinct from rigidity, the foreground–background relationship of objects moving in the image is important. Binocular disparity is potentially important to separate foreground from background and to provide depth order. Logically, a moving background should signal self-motion, whereas foreground objects could move due to either object motion or self-motion. The more distant surface is usually perceived as background, and vection is usually perceived in the direction opposite to the background motion (Ohmi, Howard, & Landolt, 1987). Similarly, Ito and Shibata (2005) superimposed either (1) radially contracting and expanding optic flow or (2) two separate expanding optic flows that were horizontally shifted (i.e., the two FOE were offset). They found that when separated in depth (based on disparity), vection direction was always based on the more distant flow. Nakamura (2008) used binocular disparity to promote different foreground–background relations between central and peripheral stimuli. He found that central and peripheral stimuli covering equal retinal area produced equivalent vection when the foreground–background relationship was controlled. He concluded that previous evidence for peripheral dominance in vection was due to confounding of apparent depth and eccentricity. 
The current study: Stereoscopic contributions to linear vection
While there are many potential benefits that binocular vision could provide to self-motion perception, the role of binocular vision in vection has received very little empirical examination. What little research has been conducted has focused on vection in depth, and the binocular advantage found for this has been suggested to arise from the extra stereoscopic information about motion in depth. Whether binocular vision also improves other types of self-motion is currently unknown. Furthermore, there are many other ways that binocular vision could improve self-motion perception. Here we investigate (a) whether binocular vision can improve a very different type of vection (not involving self-motion in depth but rather self-motion parallel to the frontal plane) and (b) whether binocular benefits (other than added information about motion in depth) might also significantly enhance vection. 
Due to the close link between optic flow and the environmental layout during self-motion, we expected that linear vection would vary depending on the cues to three-dimensional layout present in the scene. In this study we concentrated on the contribution of binocular vision and stereopsis to the perception of vertical linear vection induced by lamellar flow. Simulating translational self-motion parallel to a frontal cyclopean surface permits assessment of the role of binocular viewing, stereoscopic surface perception, and stereoscopic features in the production of vection independent of binocular cues to self-motion in depth (the so-called stereomotion cues). 
The current experiments examined the ability of cyclopean motion stimuli (vertically translating, disparity-defined depth corrugations) to induce vection. We examined not only whether cyclopean motion stimulation could enhance the vection induced by monocular motion signals but also whether such stimulation induces vection on its own. We also examined the vection induced by binocular viewing both with and without stereoscopically-defined depth corrugations and manipulated the strength of the monocularly available motion signals. To investigate these questions systematically we (a) compared the vection induced by dynamic random-dot stereogram (DRDS) with random-dot stereogram (RDS) stimuli to isolate the effects of cyclopean motion (the former providing only cyclopean motion information; the latter providing both cyclopean and monocular motion information); (b) varied the three-dimensional stimulus shape (i.e., the disparity waveform) to control the presence and extent of stereoscopically-defined moving features; (c) evaluated the influence of stereoscopic vision by comparing vection elicited in binocular viewing with monocular viewing of the same stimuli; (d) evaluated the effect of moving cyclopean form by comparing the vection induced by moving disparate surfaces (i.e., with depth corrugations) with that induced by zero-disparity (i.e., flat) surfaces; and (e) controlled the strength of monocular motion signals in our vection-inducing displays by varying the lifetime of moving features. We also varied the simulated speed of self-motion and compared free viewing with fixation to test the generality of our results across both stimulus factors (known to be important in the production of vection; for review see Howard, 1982). 
General methods
The experiments were performed under a protocol adhering to the Declaration of Helsinki and approved by the Human Participants Review Committee of York University. 
Stimuli were presented on a large stereoscopic television monitor (LG 55L W5700, LG Electronics, Seoul, Korea). This display has a film-patterned retarder overlay that acts as a micropolarizer array to circularly polarize the light. The pitch of the micropolarizer array matches the display pitch and is overlaid on the liquid-crystal display pixel grid so that the circular polarization of light from even rows of pixels is opposite the circular polarization of light from odd rows. Stereoscopic presentation was achieved by presenting the right-eye image on odd rows and the left-eye image on even rows. The observer wore glasses with an orthogonal pair of polarizing filters that matched the micropolarizer array. These glasses act as an analyzer and ensured that the left eye saw only the even rows and the right eye saw only the odd rows. The level of interocular crosstalk (white on black) was 0.4%. The images were presented at the native resolution of the display (1920 × 1080 pixels) and refreshed at 60 Hz. 
The subject was seated in a chair and viewed the screen at a distance of 215 cm, with the chair adjusted to center the point midway between the eyes with the screen. Each pixel subtended 1.0 arcmin. At this distance the screen subtended 31.4° wide by 18.0° high (121 × 68 cm), but a rectangular aperture was placed 141 cm from the screen and defined the stimulus size at 27.3° by 17.6°. Two vertical bars subtending 0.77° in width and extending across the aperture were located 10.8° to the left and right of middle of the aperture. This provided the strong impression of looking through a window at the display beyond (similar to looking out the window of a moving vehicle). This manipulation generated very compelling vection illusions despite the relatively small central display. Note that compelling, centrally induced vection has previously been reported for both lamellar and radial optic flow when these stimuli are viewed through such apertures (e.g., Andersen & Braunstein, 1985; Andersen & Dyre, 1989; Howard & Howard, 1994; Ohmi & Howard, 1988; Telford & Frost, 1993). The room was light proofed, and an enclosure covered in black cloth and cardboard ensured that only the display was visible within the dark frame of the aperture window. 
The stimuli were computer generated on a desktop workstation (Intel i7-860 2.80 GHz 4 GB, Intel Corp., Santa Clara, CA; Windows 7 64 bit, Microsoft Corp., Redmond, WA; Nvidia GE-Force GTX460, Nvidia Corp., Santa Clara, CA). Stereoscopic image sequences were produced and presented with Python scripts using OpenGL (via pyglet 1.1.4; www.pyglet.org). Participant responses were recorded with a Logitech dual-action gamepad (Logitech International SA, Morges, Switzerland). 
Stereoscopic image sequences each depicted a horizontally oriented, depth-modulated waveform (visible only during binocular viewing). The disparity profile of each waveform varied as a function of vertical screen position according to frequency (f) of 6 cycles per screen and peak disparity (Dpeak) of 5.44 arcmin (10.88 arcmin peak to peak). The disparity profile was consistent with a sinusoidal wave, a sawtooth wave, a triangle wave, or a square wave surface in depth, in each case centered on the screen disparity (Figure 1). When the stimulus moved, the waveform translated up or down on the screen (depending on the sign of the velocity). 
Figure 1
 
(a) Disparity waveforms used in the experiment (vertically offset for visibility). Disparity was modulated as a function of vertical (y-axis) position on the screen. Disparity modulations had the same peak amplitudes and period but differed in the smooth and discontinuous disparity changes. (b) The subject viewed the moving corrugated surface through an aperture in a dark room.
Figure 1
 
(a) Disparity waveforms used in the experiment (vertically offset for visibility). Disparity was modulated as a function of vertical (y-axis) position on the screen. Disparity modulations had the same peak amplitudes and period but differed in the smooth and discontinuous disparity changes. (b) The subject viewed the moving corrugated surface through an aperture in a dark room.
Each frame of the motion stimulus comprised 4,000 antialiased dot pairs (dot diameter 2.0 arcmin; dot luminance 73.9 cd·m−2 on a 0.007 cd·m−2 background), randomly positioned in the stimulus image but with a matching or correlated position in images of both eyes. The disparity required for a given dot pair was introduced by shifting the dots in equal and opposite directions in the two eyes by half of the required disparity. Three types of RDS motion stimuli (which varied in terms of dot lifetime and the types of motion that were available) were examined: 
  • (1)  
    RDS motion stimuli. These displays consisted of left- and right-eye dot pairs, which were created on the first frame and persisted until the end of the stimuli. Each dot pair had an initial two-dimensional image position and disparity for the first frame. As the waveform translated on subsequent frames, the disparity and horizontal position of the dot pair remained the same but its vertical position was updated so that all dots moved upward or downward together with the disparity wave (as though the dots were painted on the moving three-dimensional surface).
  • (2)  
    DRDS motion stimuli. In these displays the positions of all left- and right-eye dot pairs were refreshed every 16.67 ms. Essentially, 4,000 new dot pair positions were chosen on each frame, and the disparity of these dot pairs was assigned according to the current position of the disparity waveform.
  • (3)  
    Limited-lifetime RDS stimuli. These displays were similar to DRDS except the left- and right-eye dot pairs persisted over several frames, after which they were extinguished and their positions were refreshed (as in the DRDS). Essentially, 4,000/L new dot pair positions were chosen on each frame for the expiring dots, where L is the dot lifetime in frames, and the disparity of these dot pairs was assigned according to the current position of the disparity waveform.
All of these motion stimuli were presented for 30 s (1,800 frames). Representations of RDS and DRDS stimuli are shown in Movie 1 and Movie 2. For trials where fixation was controlled, a fixation cross was presented in the center of the display at zero disparity with respect to the screen. The cross consisted of one horizontal and one vertical line, each 21.8 arcmin long with a stroke (width) of 5.4 arcmin, visible in both eyes. 
Movie 1
 
Representation of an RDS moving surface. This movie represents the class of stimulus used but is not a representation of the actual stimulus. For better tolerance to video compression and as a web demo, the stimulus has been modified to a smaller window size, different aspect ratio, fewer dots, larger dots, and anaglyph presentation. Note that vection is not likely to be elicited when viewed on a monitor with other stationary features in view. (Movie 1 can be viewed in the Supplemental data.)
Movie 1
 
Representation of an RDS moving surface. This movie represents the class of stimulus used but is not a representation of the actual stimulus. For better tolerance to video compression and as a web demo, the stimulus has been modified to a smaller window size, different aspect ratio, fewer dots, larger dots, and anaglyph presentation. Note that vection is not likely to be elicited when viewed on a monitor with other stationary features in view. (Movie 1 can be viewed in the Supplemental data.)
Movie 2
 
Representation of a DRDS moving surface. This movie represents the class of stimulus used but is not a representation of the actual stimulus. For better tolerance to video compression and as a web demo, the stimulus has been modified to a smaller window size, different aspect ratio, fewer dots, larger dots, and anaglyph presentation. Note that vection is not likely to be elicited when viewed on a monitor with other stationary features in view. (Movie 2 can be viewed in the Supplemental data.)
Movie 2
 
Representation of a DRDS moving surface. This movie represents the class of stimulus used but is not a representation of the actual stimulus. For better tolerance to video compression and as a web demo, the stimulus has been modified to a smaller window size, different aspect ratio, fewer dots, larger dots, and anaglyph presentation. Note that vection is not likely to be elicited when viewed on a monitor with other stationary features in view. (Movie 2 can be viewed in the Supplemental data.)
The observer's task was to monitor their sensation of self-motion and rate its strength—that is, how compelling the experience was—relative to a standard using magnitude estimation (Stevens, 1975). The standard stimulus was a reliable vection-inducing stimulus of moderate strength. The standard was chosen to be similar to the stimuli presented in the experiment (differed by experiment; see below) and was presented to the observer at the beginning of each block of trials. Subjects were told to (a) assign this standard stimulus a strength of ‘50’ (the modulus) and (b) make estimates of vection strength proportionally relative to this modulus. For instance, if the subject's experience of vection was twice as strong as the standard they were to report 100, whereas if vection was only half the strength of the standard they were to report 25. 
In addition to making poststimulus magnitude responses, subjects were instructed to continuously monitor whether they experienced vection during each trial. If they experienced vection at any time they were told to press a gamepad button and hold it while the sensation was maintained, releasing the button whenever the sense of vection was lost. From these data we measured the total duration of the vection sensation during the trial and the latency of vection. The latency was defined as the time between the start of the trial and the first press, or the trial length (30 s) if the button was not pressed. 
Experiment 1: Can vection be induced or enhanced by cyclopean motion signals?
The primary purpose of Experiment 1 was to determine whether vection could be induced by purely cyclopean display motion. To this end we studied the perception of vection elicited by two types of binocularly viewed stereoscopic motion stimuli: one defined only by cyclopean features and the other defined by both cyclopean features and monocularly visible texture motion. Moving RDS and DRDS stimuli provide different types of information about motion in the stimulus. With RDS stimuli, the disparity-defined stimuli move but so do the monocularly visible texture elements forming the pattern. Thus, RDS stimuli provided both cyclopean and monocular motion signals indicating vertical self-motion. In a DRDS, the only coherently moving features correspond to cyclopean features defined by change in depth (there were binocular, but no monocular, motion signals indicating vertical self-motion; dot lifetime was one frame only). Because the depth modulation in a DRDS carries all the motion information, the form of the modulation might be important. Square wave modulations provide cyclopean motion information only at the transitions, whereas continuously varying modulations, such as a sinusoidal waveform, provide this information along the entire stimulus waveform. In this experiment we addressed the ability of cyclopean stimuli to induce vection. 
Methods
See General methods for a description of the apparatus, stimuli, and procedures. 
A total of 12 naïve observers (five males and seven females ranging in age from 22 to 49 years; mean age 28 ± 7.8 years) participated in Experiment 1
Viewing was always binocular in this experiment. Trials were grouped into blocks of eight, and the standard stimulus was presented before each block. Subjects participated in two sessions, each consisting of 64 trials (plus standards); the trials were counterbalanced across sessions and randomized within blocks for each subject. The standard stimulus was a sawtooth RDS disparity wave moving at 0.082 m/s with fixation on a central fixation cross. As described in the General methods, observers were instructed to assign a magnitude of 50 to this stimulus. Presentation of the standard stimulus was followed by the experimental trials. The independent variables were (a) the type of disparity-defined waveform (square, sinusoid, triangle, sawtooth), (b) stimulus speed (0.082 or 0.163 m/s), (c) disparity direction (i.e., a phase of 0° or 180° for the modulating waveform corresponding to whether a peak or valley was first seen in the center of the screen), (d) fixation (fixation or free viewing), and (e) stereogram type (RDS or DRDS). 
Results
Vection strength rating data
Mean vection magnitude estimates in Experiment 1 are shown in Figure 2. It can be seen that RDS stimuli (filled symbols) elicited much more robust vection responses than did DRDS stimuli (open symbols), which elicited little or no vection. There was very little difference between the vection produced by the different stimulus patterns. Vection increased with stimulus speed in the RDS conditions but not in the DRDS conditions. In the latter case, vection responses were weak or absent in all conditions, which may explain the lack of any modulation of the effect by speed. 
Figure 2
 
Vection magnitude ratings in Experiment 1 as a function of disparity modulation waveform, dot lifetime (stereogram type: RDS or DRDS), and stimulus velocity. Each data point represents the mean of 12 subjects for the given condition; error bars indicate ±1 standard error of the mean.
Figure 2
 
Vection magnitude ratings in Experiment 1 as a function of disparity modulation waveform, dot lifetime (stereogram type: RDS or DRDS), and stimulus velocity. Each data point represents the mean of 12 subjects for the given condition; error bars indicate ±1 standard error of the mean.
A repeated-measures analysis of variance (ANOVA) was used to analyze the results. The dependent measure was the vection magnitude (strength ratings) and the independent variables were the factorial combination of waveform, speed, and lifetime plus disparity direction and fixation type. Tests of univariate hypotheses were corrected with Greenhouse-Geisser adjustments where appropriate. 
Stereogram type had the largest influence on vection magnitudes, which were considerably larger on average for RDS stimuli than for DRDS stimuli, F(1, 9) = 125.26, p < 0.001, η2p = 0.933; mean difference M = 57.201, 95% confidence interval (CI) [45.64, 68.76]. Across subjects and the other factors, vection was reported on more than 99% of the RDS (unlimited dot lifetime) trials, while subjects did not experience vection on 47% of the DRDS (one-frame dot lifetime) trials. This difference was confirmed by logistic regression (Wald χ2 = 52.27, p < 0.001). When vection was induced, it tended to be much weaker for the DRDS stimuli compared with the RDS stimuli. Thus, robust vection was reliably obtained under RDS, but not under DRDS, conditions. 
There was also a significant effect of stimulus speed, F(1, 9) = 35.93, p < 0.001, η2p = 0.800, but this main effect was marginal to a stimulus speed by stereogram type interaction, F(1, 9) = 19.29, p = 0.002, η2p = 0.689. Vection was larger for the 0.163 m/s stimuli compared with the slower 0.082 m/s stimuli under RDS stimuli, mean difference M = 15.72, 95% CI [9.23, 22.21]. Little vection was reported under either speed condition for the DRDS stimuli. 
There were no other significant interactions and no significant effects of disparity direction, F(1, 9) = 0.602, p = 0.809, η2p = 0.007; fixation, F(1, 9) = 1.597, p = 0.238, η2p = 0.151; or waveform type, F(2.07, 18.603) = 0.953, p = 0.406, η2p = 0.096 on the vection magnitudes. 
Vection time course data
We also measured vection onset times (defined as the latency from the start of the motion stimulus until the button press indicating that the subject was experiencing vection) and vection durations (defined as the accumulated time that the subject pressed the button during the trial; see Figure 3). 
Figure 3
 
Vection duration in Experiment 1 (N = 12) as a function of stereogram type (RDS or DRDS), fixation condition, and stimulus velocity. Each data point corresponds to the median across observations; error bars indicate 95% confidence intervals for the medians.
Figure 3
 
Vection duration in Experiment 1 (N = 12) as a function of stereogram type (RDS or DRDS), fixation condition, and stimulus velocity. Each data point corresponds to the median across observations; error bars indicate 95% confidence intervals for the medians.
Consistent with the vection strength ratings, RDS stimuli (filled symbols) elicited vection that persisted for most of the 30-s trial (median durations of greater than 25 s), while DRDS stimuli (open symbols) elicited vection with median durations of less than a few seconds. There was very little difference between the vection produced by the different stimulus patterns (disparity modulation type). Vection duration appeared to increase slightly with stimulus speed and with fixation compared with free viewing. 
The onset latency data were subject to pronounced ceiling effects (onset could not be larger than trial length), especially for the DRDS conditions where median onset latency was at least as long as the trial. Therefore, we analyzed the data using repeated-measures censored regression (using package censReg in R; http://cran.r-project.org/package=censReg) of onset latency on fixation, speed, and lifetime. There was a significant effect of stereogram type, t(9) = 29.14, p < 0.001, d = 19.43: Mean vection onsets were significantly longer for DRDS stimuli (17.96 ± 2.95 s, mean ± standard error of the mean [SEM]) than for RDS stimuli (4.33 ± 0.88 s). Onset was slightly shorter with fixation compared with free viewing, mean difference = 1.1 s, t(9) = 2.73, p = 0.023, d = 1.82, and only slightly longer, t(9) = 2.19, p = 0.057, d = 1.46, for the 0.082 m/s condition (11.61 ± 1.63 s) compared with the 0.163 m/s condition (10.68 ± 1.74 s). There were no other significant main effects or interaction effects on vection onset. 
The longer the onset latency, the shorter the possible vection duration for a fixed-length trial. Thus, as might be expected, there was a strong negative correlation between vection onset and vection duration, r = −0.84, 95% CI [−0.856, −0.826]. The lack of perfect correlation is due to vection dropouts, where vection ceases after it has been initiated. Censored regression analysis demonstrated significant effects of stereogram type, t(9) = 43.84, p < 0.001, d = 29.2; fixation, t(9) = 3.66, p < 0.01, d = 2.44; and stimulus speed, t(9) = 3.22, p = 0.01, d = 2.15. Consistent and complementary to the vection onset data, vection duration was increased by higher stimulus speeds and sustained dots (i.e., RDS as opposed to DRDS) and was slightly longer with subjects fixating compared with free viewing (Figure 3). 
Discussion
The above findings suggest that vection processing is relatively insensitive to purely cyclopean motion stimuli. The DRDS stimuli did not reliably produce vection responses, mean vection magnitudes were small, and vection took longer to develop for DRDS stimuli than for RDS stimuli. This result was found despite the fact that the DRDS stimuli produced strong impressions of both a surface modulated in depth and grating motion. The lack of any disparity waveform-type effect was not surprising given that we had expected this influence to be more apparent for DRDS (as opposed to RDS) stimuli, and, as it turned out, this type of stimuli did not elicit much vection. 
To maximize the likelihood of obtaining vection we chose a DRDS stimulus that produced strong depth and motion impressions. The period of the disparity modulation was near the peak of the cyclopean depth modulation sensitivity function (Schumer & Julesz, 1984; Tyler, 1975). Similarly, we used a depth modulation large enough to provide a strong impression of depth but modest enough to remain comfortably within Panum's fusional limit (Ogle, 1950). While we varied disparity waveform amplitude, direction, and frequency over a range of values in pilot experiments, we did not observe evidence of large sensitivity to these factors; this is consistent with Kohly and Regan's (1999) finding that observers can ignore variations in spatial frequency, temporal frequency, and displacement when judging the speed of moving cyclopean gratings. However, we did not explore this large stimulus space extensively and thus it is possible that another cyclopean stimulus could be more effective for the production of linear vection. 
To further promote vection we used a stationary foreground reference to provide both relative motion and a frame of reference for vection. (This physical enclosure and aperture also served the function of blocking the view of the observer's physically stationary surroundings.) Like luminance-defined motion, disparity-defined relative motion is easier to detect and discriminate than is absolute motion, although there has been little systematic study of this issue. 
In the case of the DRDS stimuli, all of the moving features were cyclopean. As noted above they were defined only where the disparity changed. The failure to find compelling vection with DRDS stimuli in this experiment does not necessarily mean that cyclopean features cannot contribute to vection when combined with monocularly visible motion signals (as was the case with the RDS stimuli). In the next experiment we investigated whether the addition of moving cyclopean features and binocular input provide additional stimulus for linear vection when combined with monocular motion signals. 
Experiment 2: Binocular versus monocular viewing of RDS displays
All of the vection-inducing conditions tested in the first experiment were binocularly viewed random-dot stereogram motion displays (both DRDS and RDS). Only RDS motion displays were found to induce compelling vertical vection. Here, in Experiment 2, we compared binocular and monocular viewing of RDS motion to see whether the binocular viewing of such displays actually enhances vertical vection. These RDS motion displays simultaneously present moving cyclopean forms and moving texture under binocular viewing conditions but only moving textured images under monocular viewing conditions. If stereoscopically defined features contribute to visually induced experiences of self-motion, then we expect that vection will be elicited more strongly from binocularly viewed RDS motion stimuli than from monocularly viewed RDS motion. 
Methods
See General methods for a description of the apparatus, stimuli, and procedures. 
A total of 15 naïve observers (five males and 10 females ranging in age from 19 to 46 years; mean age 27 ± 7.0 years) participated in Experiment 2
Trials were grouped into blocks of eight trials, with the standard stimulus presented before each block. The standard stimulus was a sawtooth RDS disparity wave moving at 0.082 m/s with fixation on a central fixation cross. As described in the General methods, observers were instructed to assign a magnitude of 50 to this stimulus. The independent variables were (1) the type of disparity waveform (square, sinusoid, triangle, or sawtooth, which was perceptible only when the stimulus was viewed binocularly), (2) stimulus speed (0.082 or 0.163 m/s), (3) fixation (central fixation or free viewing), and (4) viewing type (binocular or monocular), with two repeats of every combination for each observer. The inducing stimuli were always RDS images moving upward. Monocular viewing (when required) was achieved by placing an eye patch over the subject's left eye. There were two experimental sessions, each session consisting of two blocks under binocular viewing and two blocks under monocular viewing, producing a total of 64 trials per subject. The order of monocular and binocular blocks was randomized and counterbalanced across sessions for each subject. 
Results
Vection strength rating data
Mean vection magnitude as a function of viewing condition (binocular or monocular), disparity modulation type, and stimulus speed is shown in Figure 4. The manipulation of most interest in this experiment was viewing condition. Figure 4 shows that binocular viewing of disparate moving stimuli produced stronger mean vection ratings than monocular viewing for all conditions. Consistent with the results of Experiment 1, vection magnitude estimates increased with increased stimulus speed, but there was little indication of an effect of stimulus pattern (disparity modulation type). The latter finding is expected in the monocular conditions because the disparity modulation would not be visible without stereopsis. For the binocular conditions it suggests that the particular pattern of disparity-defined features was not critical for the vection enhancement with binocular viewing. 
Figure 4
 
Vection magnitude ratings in Experiment 2 as a function of disparity modulation waveform, viewing condition (monocular or binocular), and stimulus velocity. Each bar represents the mean of 15 subjects for the given condition; error bars indicate ±1 standard error of the mean.
Figure 4
 
Vection magnitude ratings in Experiment 2 as a function of disparity modulation waveform, viewing condition (monocular or binocular), and stimulus velocity. Each bar represents the mean of 15 subjects for the given condition; error bars indicate ±1 standard error of the mean.
A repeated-measures ANOVA (with Greenhouse-Geisser correction where appropriate) indicated a significant main effect of stimulus speed, with higher speeds producing stronger vection ratings, F(1, 14) = 30.35, p < 0.001, η2p = 0.684. There was also a main effect of viewing condition, F(1, 14) = 4.75, p = 0.047, η2p = 0.253, and an interaction between disparity waveform type and viewing condition, F(2.22, 31.07) = 4.512, p = 0.016, η2p = 0.244. The main effects of disparity waveform and fixation were not significant—F(2.76, 38.69) = 0.37, p = 0.762, η2p = 0.025 and F(1, 14) = 0.45, p = 0.513, η2p = 0.031, respectively—nor were there any other significant interactions. One subject reported much smaller vection magnitude under monocular conditions than other subjects; the analyses repeated with this subject removed yielded the same pattern of results as with the full data set. 
The interaction of disparity waveform and viewing type was analyzed by looking at the simple main effects of viewing for each waveform. This interaction was expected since the waveform was defined by cyclopean features—hence invisible monocularly—so if there was an effect of waveform it should be apparent only under binocular viewing. Binocular viewing increased vection magnitudes, but this increase was significant only for the sine and square waveforms. Binocular viewing on average generated 8.2 (±3.49 SEM) and 9.3 (±3.49) increases in vection magnitude ratings, respectively—F(1, 14) = 5.93, p = 0.033, η2p = 0.285 and F(1, 14) = 7.11, p = 0.018, η2p = 0.337, respectively—with smaller effects for the sawtooth and triangle waveforms—mean rating increases of 7.1 (±3.79) and 4.6 (±3.00), respectively; F(1, 14) = 3.50, p = 0.083, η2p = 0.200 and F(1, 14) = 2.34, p = 0.148, η2p = 0.143, respectively. Thus, while binocular viewing generally increased vection magnitudes, the effect depended on the type of disparity waveform. 
Vection time course data
An equivalent repeated-measures ANOVA on vection onset indicated only a significant effect of stimulus speed, F(1, 14) = 21.01, p < 0.001, η2p = 0.600. Vection latency was shorter for the 0.163 m/s condition (5.99 ± 1.42 s) than for the 0.082 m/s condition (8.37 ± 1.85 s) when averaged across the other variables and observers. Unlike for the magnitude measure, the effect of viewing condition did not reach significance: Mean vection latency was lower for binocular compared with monocular viewing by 0.83 ± 0.45 s, F(1, 14) = 3.43, p = 0.085, η2p = 0.197, and all other main effects and interactions were not significant. 
Discussion
The finding that binocular viewing of RDS stimuli produces stronger vertical vection than monocular viewing is consistent with the hypothesis that movement of stereoscopically defined form contributes generally to the perception of linear self-motion. However, this improvement was modest and depended on the type of disparity waveform. It is possible that the modest effects were due to vection induced by monocular stimulation already being relatively strong and saturated, leaving little room for stereoscopic form to have an effect (i.e., ceiling effects). 
It is also possible that the vection increases found for binocular viewing were not due to the presence of stereoscopic features but rather to the fact that two eyes were being stimulated as opposed to only one. However, differences in binocular and monocular field of view cannot explain our current results, as the stimulus was contained well within the visual field of both eyes. On the other hand, binocular inputs are known to sum in some cases to produce a stronger signal-to-noise ratio. Hess et al. (2007) argued that global motion processing occurs after the site of binocular combination and that binocular improvements in their global coherence detection tasks could be attributed to binocular contrast enhancement. While binocular summation may play a role in the binocular advantage found in this experiment, it cannot be the whole story because binocular summation cannot explain the effect of disparity waveform type—a stimulus feature that is available only at a cyclopean level of processing. The next experiment addressed these issues of monocular self-motion signal strength and binocular summation. 
Experiment 3: Short-lifetime cyclopean stimuli
The third experiment compared vection elicited by stimuli with and without cyclopean features. This allowed us to dissociate the effects of stereoscopically defined features from binocularity. We used RDS stimuli with limited dot lifetime to weaken the monocular dot motion signals driving vection so that the stereoscopic contribution could be assessed more sensitively. By using short-lifetime dots, the monocular motion signals were degraded and less likely to dominate and saturate the vection response, allowing us to probe for the effects of moving cyclopean form on vection. 
Methods
A total of 13 naïve observers (six males and seven females ranging in age from 19 to 49 years; mean age 28 ± 8.1 years) participated in Experiment 3
Trials were randomized and grouped into blocks of eight trials, with the standard stimulus presented before each block. A total of 16 of these blocks were run over two sessions for each subject. The standard stimulus was a short-lifetime (dot lifetime of 10 frames) RDS depicting a sinusoidal disparity wave moving upward at 0.082 m/s with fixation on a central fixation cross. The independent variables were (a) the type of disparity waveform (square wave or sinusoid; note that when disparity amplitude was zero—see below—a flat frontal surface was defined), (b) stimulus speed (0.082 or 0.163 m/s), (c) fixation (fixation or free viewing), (d) disparity direction, (e) disparity amplitude (5.44- or 0-arcmin peak), and (f) dot lifetime (5 or 10 frames). 
Results
Likelihood of vection induction
The main independent variables of interest in this experiment were (a) disparity amplitude, which determined whether moving disparity-defined three-dimensional surface features were present, and (b) dot lifetime, which was intended to modulate the strength of monocular motion signals. Subjects were less likely to experience vection on five-frame lifetime trials (74%) than on 10-frame lifetime trials (92%). A logistic regression of the dichotomous variable of vection presence on the independent variables indicated that likelihood of vection was influenced by dot lifetime (Wald χ2 = 94.84, p < 0.001), speed (Wald χ2 = 18.54, p < 0.001), disparity (Wald χ2 = 29.88, p < 0.001), and fixation (Wald χ2 = 74.09, p < 0.001). While dot lifetime had the greatest influence, vection was also more likely to occur for faster (compared with slower) stimulus speeds, with fixation (compared with free viewing), and with disparity-defined depth corrugations (compared with a disparity-defined flat frontal plane). 
Vection strength rating data
Figure 5 shows mean vection magnitude ratings as a function of dot lifetime for each combination of speed and disparity amplitude. Vection strength ratings were larger for the depth corrugation (disparate) than for the flat (zero disparity) conditions for all combinations of speed and dot lifetime. For the slower speed case, the enhancement from disparity-defined three-dimensional surface features was more pronounced for the shorter, five-frame lifetime than for the 10-frame dot lifetime. This is presumably the condition with the weakest monocular motion signals, and the effect of disparity modulation is clearest here. Figure 6 shows that the enhancement effect of disparity-defined three-dimensional surface features was greater for the sinusoidal disparity modulation than for the square wave disparity modulation. 
Figure 5
 
Vection magnitude ratings in Experiment 3 as a function of dot lifetime and disparity amplitude (flat versus corrugated). The circular symbols show data for a stimulus speed of 0.082 m/s, and the square symbols show data for a stimulus speed of 0.163 m/s. Filled symbols show data for 5.44-arcmin disparity (corrugated), and open symbols show data for 0-arcmin disparity (flat). Mean data for 13 observers; error bars indicate ±1 standard error of the mean.
Figure 5
 
Vection magnitude ratings in Experiment 3 as a function of dot lifetime and disparity amplitude (flat versus corrugated). The circular symbols show data for a stimulus speed of 0.082 m/s, and the square symbols show data for a stimulus speed of 0.163 m/s. Filled symbols show data for 5.44-arcmin disparity (corrugated), and open symbols show data for 0-arcmin disparity (flat). Mean data for 13 observers; error bars indicate ±1 standard error of the mean.
Figure 6
 
. Waveform–disparity interaction in vection magnitude ratings in Experiment 3. Mean data for 13 observers collapsed across velocity and fixation conditions; error bars indicate ±1 standard error of the mean.
Figure 6
 
. Waveform–disparity interaction in vection magnitude ratings in Experiment 3. Mean data for 13 observers collapsed across velocity and fixation conditions; error bars indicate ±1 standard error of the mean.
A repeated-measures factorial ANOVA on the vection magnitude data revealed several interactions. Vection strength ratings tended to increase with disparity amplitude, dot lifetime, and stimulus speed (Figure 5), and there was a three-way interaction between these variables, F(1, 12) = 5.23, p = 0.040, η2p = 0.305. Further analysis demonstrated that the simple main effects of stimulus speed, disparity, and lifetime held at all levels of each of the other two variables: Marginal main effects were significant for lifetime, F(1, 12) = 25.12, p < 0.001, η2p = 0.677; disparity, F(1, 12) = 18.51, p = 0.001, η2p = 0.607; and speed, F(1, 12) = 21.36, p = 0.001, η2p = 0.640. Marginal to this three-way interaction was a two-way interaction between speed and lifetime, F(1, 12) = 11.43, p = 0.005, η2p = 0.488, with this interaction depending on disparity. Specifically, the increase in vection ratings with longer dot lifetimes was smaller for the 5.44-arcmin disparity, slow-speed condition (mean increase 10.3 ± 3.73 SEM) compared with the 0-arcmin conditions at the slower speed (19.4 ± 4.28) or with the 0-arcmin and 5.44-arcmin conditions at the higher speed (mean increases 22.5 ± 4.10 and 20.9 ± 4.36, respectively). 
There was also an interaction between disparity waveform and disparity amplitude, F(1, 12) = 6.32, p = 0.027, η2p = 0.345 (see Figure 6). This interaction was expected and reflects the fact that when disparity amplitude was zero the sinusoidal and square wave stimuli were identical (both flat RDS). Thus, as expected, there was no difference between the vection strength ratings for the two waveforms when disparity was zero (mean difference = 0.66 ± 0.685, p = 0.351, η2p = 0.073), but when there was disparity, the sinusoid produced significantly more vection than did the square wave case (3.95 ± 1.67, p = 0.035, η2p = 0.312). There was a significant effect of disparity for both waveforms, with more vection for disparate stimuli compared with flat stimuli: main effect of disparity, F(1, 12) = 18.51, p = 0.001, η2p = 0.607. Significant simple main effects of disparity were also found for both sinusoid and square wave stimuli. 
There was also a significant effect of fixation type, F(1, 12) = 6.92, p = 0.022, η2p = 0.366, with vection magnitude increased for fixation compared with free viewing. 
Vection time course data
Vection onset times tended to decrease with increasing dot lifetime, stationary fixation, disparity amplitude, and stimulus speed (Figure 7). Consistent with the magnitude estimation results, latency measures indicated that vection was enhanced when disparity-defined features were present compared with when they were not (corrugated versus flat conditions). For the flat, free-view case, vection was typically not obtained when dot lifetime was five frames (median onset latency was the length of the trial). Latency in the flat condition was more comparable with the disparity corrugation condition in the 10-frame, free-view case and for both lifetimes with fixation. Nevertheless, in all cases median vection latency was shorter in the disparate conditions compared with the zero-disparity conditions. Fixation had a large effect on vection latencies, which were shorter under fixation than free-view conditions. This fixation enhancement was smallest for the strongest vection condition (10 frame, 0.163 m/s), probably reflecting a floor effect because vection latencies were typically short and near those found for the strong vection in the RDS conditions in Experiment 1
Figure 7
 
Onset latency in Experiment 3 as a function of dot lifetime, stimulus speed, disparity, and fixation. Solid lines indicate conditions with no disparity modulation (flat), and dashed lines indicate disparity-modulated patterns (corrugated). Median data are shown for each condition; error bars indicate 95% confidence intervals.
Figure 7
 
Onset latency in Experiment 3 as a function of dot lifetime, stimulus speed, disparity, and fixation. Solid lines indicate conditions with no disparity modulation (flat), and dashed lines indicate disparity-modulated patterns (corrugated). Median data are shown for each condition; error bars indicate 95% confidence intervals.
Censored regression indicated that there were significant main effects of lifetime, t(12) = 7.87, p < 0.001, d = 4.55; disparity, t(12) = 6.11, p < 0.001, d = 3.53; speed, t(12) = 2.389, p = 0.034, d = 1.38; and fixation, t(12) = 7.08, p < 0.001, d = 4.09. There was also a two-way interaction between lifetime and disparity, t(12) = 4.54, p < 0.001, d = 2.62, with the effect of disparity significant for both lifetimes but smaller at the longer lifetime compared with the shorter lifetime (mean difference between disparity levels of 1.23 ± 0.529 and 4.86 ± 1.30 s, respectively). A two-way interaction between fixation and lifetime was also significant, t(12) = 3.14, p = 0.008, d = 1.81, and reflected a larger decrease in vection latency with fixation for the shorter-lifetime dots compared with the longer-lifetime dots. 
Discussion
Our use of short-lifetime dots appeared to have the desired effect of weakening the monocular vection stimulus. In Experiment 2, vection was reported on 98.8% of the trials versus only 83.3% of trials in the current experiment. Similarly, vection onset was delayed relative to Experiment 2, suggesting a weaker vection stimulus in the current experiment (12.65 ± 2.20 s vs. 7.18 ± 1.63 s averaged across all trials). Note that vection magnitude is a relative measure defined by the standard and thus cannot be used to compare vection strength across the two experiments. The weakened monocular stimulus used in this experiment appears to have made the experiment more sensitive to effects of stimulus parameters, and we found significant effects of fixation type as well as interactions that were not observed in the previous experiments. 
General discussion
Binocular contributions to vection
These experiments identified a clear binocular contribution to the production of vertical linear vection from lamellar optic flow. While purely cyclopean motion did not generate compelling vection on its own (Experiment 1), binocular viewing of stereoscopic (three-dimensional) optic flow produced more compelling vection than either the monocular viewing of these same optic flow displays or the binocular viewing of nonstereoscopic (flat) displays (Experiments 2 and 3). Importantly, the addition of cyclopean three-dimensional surface features to binocularly viewed optic flow displays was found to significantly enhance vection. This stereoscopic enhancement was more apparent when the monocular motion signals were weakened (by reducing RDS dot lifetimes; Experiment 3). 
As we outlined in the Introduction, there are several possible ways that binocular motion stimulation could have contributed to vection processing. While increased field of view and binocular summation are probably important factors in many natural situations, they cannot explain the binocular enhancements found here because the stimuli were always constrained to the binocular visual field and because enhancements were found for stereoscopic compared with equivalent binocular but nonstereoscopic displays. Thus, the present experiments suggest a clear contribution of depth from binocular stereopsis to the experience of vection. 
Importantly, the current findings demonstrate that binocular vection enhancements are not restricted to conditions where changing-disparities and interocular-velocity differences provide extra information about motion in depth (e.g., those examined previously by Palmisano, 1996, 2002). Since our displays all simulated self-motion parallel to a frontal cyclopean surface, these findings reveal a new binocular contribution to vection enhancement. 
Mechanisms underlying these binocular enhancements
Improvements in perceived rigidity of the scene (Nakamura, 2010) due to stereopsis are also not likely to explain the binocular advantage found in the present study. While stereoscopic depth and motion parallax could constrain and disambiguate each other in a rigid scene (Di Luca, Domini, & Caudek, 2007; Richards, 1985), this is not the case with the stereoscopic displays in the present experiments. In our displays with stereoscopic depth, the lack of motion parallax between near and far parts of the display should have conflicted with stereoscopic depth and, if anything, degraded the perceived rigidity of the scene. For instance, in Experiment 3 all the dots in a given display drifted vertically at the same speed. Thus, the monocularly available motion cues were consistent with a frontal plane drifting vertically and inconsistent with a rigid interpretation of the cyclopean corrugated surface. If rigidity were the driving force then we would expect that vection would have been stronger for the flat, zero-disparity stimulus than for the corrugated surface, but in fact the opposite was true. 
Similarly, the binocular vection enhancement was not likely due to improved perception of layout or to segregation of figure from ground. While binocular viewing would have provided disparity cues to segregate the near physical aperture from the more distant motion display, this cue was available in all conditions with binocular viewing regardless of the disparity in the random-dot stimulus. Since the aperture was always stereoscopically segregated from the moving stimulus on the television monitor in Experiment 3 (by real, as opposed to simulated, binocular disparities), this cannot explain the cyclopean vection advantages we found.1 Similarly, binocular cues to environmental layout were not likely to play a determining role either since, as noted above in the discussion of rigidity, the disparity-specified layout and the motion-defined layout were not consistent. Furthermore, the theoretical stereoscopic depth between peaks and valleys was 23 cm, which, although appreciable, was much smaller than the viewing distance or the separation between the aperture and screen. As a result, the stereoscopic depth modulations would have provided relatively little additional information about environmental layout. 
Thus, the most parsimonious explanation of our results is that the stereoscopic displays provided cyclopean features that moved and were interpreted by the visual system as the consequence of self-motion. These features enhanced the motion of the dots themselves and produced a more compelling vection stimulus. 
Self-motion from higher-order motion stimuli
The binocular stimuli in Experiments 1 and 2 and the disparate stimuli in Experiment 3 all provided moving stereoscopic three-dimensional surface features. In persistent or short-lifetime RDS stimuli these moving surface features provide additional motion signals that could reinforce and strengthen the monocularly visible optic flow of the dots. It appears that the visual system treated these cyclopean features as part of the static environment and attributed their motion to self-motion. To our knowledge this is the first demonstration that stereoscopic cyclopean stimuli can drive linear vection, although there is other evidence of cyclopean contributions. 
For instance, Wolfe and Held (1980) designed an experiment to investigate binocular contributions to circular vection using dichoptic apparent motion. They illuminated a rotating optokinetic drum with separate strobe lights for the left and right eyes. When the flashes were synchronized and in phase, vection was minimal for flash rates below 7 Hz, after which vection magnitude increased with strobe frequency. When the flashes were out of phase in the two eyes, vection magnitudes were larger than for in-phase flashes at the same rate, consistent with the observers combining the two eyes' input to form a signal with a higher effective flash rate. The temporal offset between flashes would also produce disparity signals because of the shift of the stimulus during the interflash interval. However, the facts that the resulting disparity would be ambiguous—as both the preceding and following frames are potential matches—and that Wolfe and Held found similar results for stereoblind individuals suggest that this binocular vection enhancement was not mediated by stereopsis. 
The studies by Palmisano (1996, 2002) discussed in the Introduction suggested that stereoscopic motion in depth could provide a stimulus to vection in depth. We found that vection from lamellar flow can also be enhanced by stereoscopic features moving in the frontal plane. This suggests that stereoscopic enhancement could be a more general response to moving cyclopean features and not specific to stereoscopic motion in depth. Lowther and Ware (1996) also found that both circular vection and linear vection onset latencies were lower for stereoscopically presented stimuli compared with nonstereoscopic binocular displays, but they did not explore the nature of the stereoscopic benefit. 
Motion of cyclopean features provides an alternative vection stimulus to the movement of luminance-defined features (first-order motion). This is consistent with other evidence that vection can be elicited by motion stimuli that are not luminance defined. So-called second-order (and third-order) motion refers to motion percepts elicited by stimuli such as contrast envelope, texture, and flicker that can define moving features without corresponding moving luminance-defined features. Gurnsey, Fleet, and Potechin (1998) presented displays simulating forward motion through a tunnel and varied the relative contribution of first- and second-order motion in the stimulus. Both motion aftereffect and vection durations were strongest when the stimulus contained coherent first-order motion energy. Similarly, Seno and Palmisano (2012) found that forward vection was enhanced by addition of vertical oscillation of the simulated viewpoint when the oscillatory movement was defined by first-order motion but not second-order motion. These findings are similar to the results of our Experiment 1, where vection responses were small or absent in the absence of first-order motion of the dots (i.e., in DRDS displays compared with RDS displays). Consistent with a lack of an influence of DRDS stimuli on self-motion, presenting a visual display as a DRDS reportedly eliminates the stabilizing effect of vision on sway (Kelly, Riecxe, Loomis, & Beall, 2008). 
In Gurnsey et al.'s (1998) second experiment they modulated the relative contribution of first-order motion by varying the scale of the noise carrier. While motion aftereffect duration decreased as the relative amount of first-order motion energy declined, they found that duration of vection was unaffected. They concluded that vection was driven by optic flow that combines both first- and second-order motion energy. Analogously, in Experiment 3 we degraded the effectiveness of the first-order motion signal by limiting dot lifetime and demonstrated a contribution of cyclopean motion signals when combined with weak but consistent first-order dot motion. 
In many natural situations the self-motion signals from cyclopean features, second-order features, and luminance-defined features are consistent and redundant. In the present experiments the cyclopean and luminance-defined motions were either consistent or effectively absent. It will also be of interest in future work to examine how these cues combine when either weakly or strongly inconsistent. In a pilot experiment we designed a stimulus consisting of a moving cyclopean sinusoidal grating but with persistent rather than short-lifetime (scintillating) dots. Each dot in these displays maintained its cyclopean position; that is, its disparity changed as the disparity wave travelled over it. This display is similar to the DRDS case where monocular dot motion is on average zero; however, in these persistent displays the dot motion was unambiguously zero. As such the conflict with the monocular motion cue is stronger than the DRDS case (Allison & Howard, 2000). Consistent with our DRDS results, there was no vection reported by four out of the five observers in this pilot experiment; the other reported no vection on most trials but weak and nonspecific self-motion (instability) on a few trials. 
Effects of cyclopean pattern and phase
This study examined for the first time the vection and vection enhancement provided by cyclopean motion. When examining the motion of purely cyclopean features, the disparity modulation of the surface is (in principle) an important consideration. Accordingly, a number of different disparity modulations (sawtooth, sinusoidal, square wave, and triangle wave) were examined to see whether the type of display modulation mattered. 
The type of disparity modulation is a feature that by definition exists in the cyclopean domain. Not surprisingly, then, we found no effect of the disparity waveform pattern or phase (disparity sign) on vection in Experiment 1, consistent with the DRDS producing no vection. In contrast, the disparity modulation waveform had modest interaction effects with view type (binocular versus monocular) in Experiment 2 and waveform disparity amplitude (5 vs. 0 arcmin) in Experiment 3. These interactions were expected as the disparity waveform had no meaning for monocular or zero-disparity stimuli. 
The disparity waveform was of interest in these experiments for two reasons. First, the cyclopean motion is defined only where the disparity changes since the motion stimulus does not exist except at cyclopean features. This is potentially important because vection depends on the number and density of moving features (Brandt, Wist, & Dichgans, 1975). The sinusoid has continually varying disparity; therefore, cyclopean motion is defined throughout the stimulus while it is defined only at the discontinuities for the square wave. Consistent with this, we found that significantly more vection magnitude was produced by the sinusoidal stimulus compared with the square wave stimulus in Experiment 3. However, the difference was modest, and in Experiment 2 the binocular improvement was similar for the sine and square wave patterns. These findings suggest that the continuity of moving cyclopean features was only a minor factor in the production of vection enhancements, particularly in the presence of strong monocular motion as in Experiment 2
Second, spatial and temporal frequency changes are confounded in drifting sinusoidal gratings (Kohly & Regan, 1999) and, to a lesser extent, in other periodic patterns. Variation in harmonic content and phase in different patterns can help to alleviate this confound. Although the binocular improvement in Experiment 2 was significant only for the sinusoid and square wave cases, the improvements were only slightly smaller with the sawtooth wave: These three patterns have different spatiotemporal spectra but produced similar binocular improvements. Thus, covariation of spatial and temporal frequency does not appear to be a significant factor in the current experiment. Similarly, the disparity sign affects the phase of the waveform and hence the features appearing near fixation at the start of the trial. Furthermore, the sawtooth wave presents only one direction of surface slant that is determined by the sign of the disparity, and there are known anisotropies and biases in the perception of stereoscopic slant about a horizontal axis (e.g., Allison, Howard, Rogers, & Bridge, 1998). However, we did not find effects of the disparity sign and thus there was no evidence that these phase-dependent differences affected vection. 
The smallest binocular improvement in Experiment 2 was observed for the triangle wave. Except at the peaks, this stimulus has only gradients of disparity (alternately slanted sections). Observers are relatively insensitive to stereoscopic slant, particularly when presented in these so-called hinge arrangements (Gillam, Blackburn, & Brooks, 2007; Gillam, Chambers, & Russo, 1988). This insensitivity has been confirmed for both motion and stereopsis (Allison, Rogers, & Bradshaw, 2003) and could explain why the binocular improvement was somewhat smaller for the triangle wave modulation compared with the other waveforms. 
Effects of fixation
The role that stationary fixation plays in the induction of (typically nonstereoscopic) vection has long been a matter of some debate. Some previous work has suggested that circular vection tends to be weaker when observers follow the visual-inducing pattern compared with static fixation conditions (de Graaf, Wertheim, & Bles, 1991; Fushiki, Takata, & Watanabe, 2000). This increase in circular vection with fixation has not always been found; for example, de Graaf et al. (1991) found the effect only when following and fixation conditions were presented sequentially in such a way that they could be compared immediately. Consistent with an earlier study by Dichgans and Brandt (1978), they found no effect of fixation when the conditions were presented separately (i.e., in isolation). Similarly, while vection in a physically tumbling room was found to increase or decrease with fixation for individual subjects, there was no consistent overall effect (Allison, Howard, & Zacher, 1999). Central fixation on a stationary target reportedly improves vection for centrally presented, but not peripherally presented, horizontal linear vection stimuli compared with free viewing (Tarita-Nistor, González, Spigelman, & Steinbach, 2006), although alternating gaze between central and peripheral locations increased looming vection compared with stable central fixation (Palmisano & Kim, 2009). 
In the present studies we did not find a significant effect of fixation on ratings of stereoscopic (and nonstereoscopic) vection strength in the first two experiments. However, vection onset latencies were slightly reduced with fixation compared with free viewing in Experiment 1. Furthermore, in Experiment 3, with brief-lifetime dots we found that vection magnitudes were increased and onset latencies were reduced with fixation compared with free viewing. Monocular motion cues were diminished by the use of short-lifetime dots in this experiment, and it may be that this allowed a more subtle effect of fixation to be measured. Contrary to this proposal, Tarita-Nistor et al. (2006) found that the enhancement of vection with fixation was more pronounced for their larger, more compelling inducing stimuli. 
We found that when fixation had an influence, vection latency was reduced and magnitude increased by the presence of the stationary fixation point. However, the fixation manipulation introduced both a feature to the display (the fixation cross) and instructions to fixate. This is also true of most previous studies looking at the effects of fixation. Previous research has assumed that the act of fixation is the important manipulation and have tried to explain the increase in vection sensation through mechanisms such as the Aubert-Fleischl phenomenon, where the perceived speed of a moving target is higher during steady fixation compared with when it is tracked (de Graaf et al., 1991). 
However, there could also be more direct effects of the fixation point on vection. First, addition of a fixation point introduced an additional reference for relative motion, which has been reported to increase vection (Howard & Howard, 1994). Furthermore, in our study there was also a very strong percept of induced motion apparent in the fixation point. Researchers have distinguished between vection-entrained induced motion, where objects that appear fixed with respect to the head appear to move with it during vection, and egocentric induced motion, where a moving stimulus induces opposite motion of another stimulus without the percept of self-motion (e.g., Heckmann & Howard, 1991). In principle, the fixation point in our experiments could have been subject to both these effects. Thus, while there was a large effect of fixation on vection in Experiment 3, it is possible that this effect could have been mediated by induced motion rather than by fixation per se (although fixation plays a key role in many theories of induced motion). We are currently exploring the role of fixation stability versus induced motion in the production of vection. 
Relation of the current findings to neurophysiology
Much of the visual cortex is sensitive to motion or disparity, and thus the neurophysiological underpinnings of the effects of cyclopean motion on vection are difficult to localize precisely. Cyclopean form depends on binocular combination and disparity sensitivity, but substantial numbers of cells responsive to these features and to luminance-defined motion are found as early as V1 (Hubel & Wiesel, 1962; Poggio & Fischer, 1977). However, disparity-sensitive cells in V1 do not signal relative disparity or cyclopean form, and the earliest evidence for representations of cyclopean edges is in V2 (Bredfeldt & Cumming, 2006; Zhou, Friedman, & von der Heydt, 2000). Representations of cyclopean shape appear to arise later in the ventral pathway, and cells sensitive to disparity-defined form have been reported in the inferior temporal cortex (Tanaka, Uka, Yoshiyama, Kato, & Fujita, 2001). 
One possibility is that such cells produce local cyclopean features and related motion signals and that these motion signals then feed into global self-motion processing (see Patterson, 1999 for a comprehensive review of this proposal). Disparity sensitivity is a common feature throughout the motion-sensitive visual pathway. Thus, these signals would be processed much as luminance-defined motion features arising in V1 are processed and integrated in subsequent stages of the motion-sensitive pathways such as the medial temporal (MT) and medial superior temporal (MST) areas. Consistent with this, DeAngelis, Cumming, and Newsome (1998) reported that stimulating clusters of MT neurons in rhesus monkeys produced predictable bias in coarse depth judgments. Area MT is intimately linked with primate motion processing and is selective for disparity, which could help segregate motion signals at different distances (Bradley, Qian, & Andersen, 1995). One problem with the proposal that cyclopean motion features are treated identically to luminance-defined motion is that disparity signals in MT do not appear to code for disparity-defined boundaries or cyclopean motion and may be better suited to guiding distance-dependent motor action. More generally, it has been proposed that disparity processing in ventral cortical areas may support representations of three-dimensional shape while dorsal cortical areas support motor action and segregation of motion signals (for review see Parker, 2007). To the extent that this is accurate, contributions of moving cyclopean form must rely either on communication between the dorsal and ventral streams or on some unknown representation of stereoscopic shape in the dorsal stream. 
The contribution of moving cyclopean stimuli to vection may be more specific to the processing of self-motion and the perception of vection rather than simply providing an alternative input. For instance, cortical area MST, which has been associated with egomotion processing, is sensitive to both patterns of optic flow and binocular disparity (Roy, Komatsu, & Wurtz, 1992). Some cells are jointly tuned to disparity and motion and some are sensitive to depth from relative disparity and motion parallax (Eifuku & Wurtz, 1999; Upadhyay, Page, & Duffy, 2000). Cardin and Smith (2011, p. 1246) proposed that a signature of a brain region encoding egomotion is that it “responds well to optic flow and the response is systematically enhanced when depth cues are consistent with observer motion.” The only region they found with these properties was V6, and they suggested that this area was important for integrating stereopsis and motion to dissociate egomotion from object motion. They found that when stereoscopic layout was consistent with the optic flow stimulus there was an enhancement of the response to optic flow. This facilitation of optic flow by consistent stereopsis appears similar to our finding that consistent cyclopean motion enhanced vection from monocular optic flow even when it was ineffective on its own. However, the stimuli used by Cardin and Smith (2011) were not cyclopean and provided layout cues as well as cyclopean form. Thus, any specific links between specialized processing of cyclopean form and egomotion-specific cortical regions remain speculative. 
Conclusions
Previous work has demonstrated an enhancement of vection with binocular stereopsis (Palmisano, 1996, 2002). We outlined possible factors underlying this binocular enhancement and isolated one important component: that of the motion of stereoscopically defined features. In sum, the current experiments provide compelling evidence for the influence of cyclopean features but only when paired with consistent monocular self-motion signals. Vection from purely cyclopean stimuli (DRDS) was not obtained despite robust perceptions of the motion of their cyclopean features. However, the DRDS stimuli depicting translating gratings have lower apparent contrast than do RDS stimuli, which might in turn have resulted in lower apparent velocities in the DRDS case (Brooks, 2001; Thompson, 1982). Such DRDS stimuli also have motion discrimination thresholds that are slightly (Kohly & Regan, 1999; Portfors & Regan, 1997) or considerably (Harris & Watamaniuk, 1996) higher than for equivalent luminance gratings. Also, the scale of features in the cyclopean gratings was coarser than that of the monocular features, which could have possibly produced spatial frequency-dependent apparent speed reductions in the cyclopean gratings (Diener, Wist, Dichgans, & Brandt, 1976). Thus, while we have compelling evidence that cyclopean features can promote self-motion perception when combined with monocular motion signals, more work is necessary before we can convincingly conclude that cyclopean motion cannot produce vection on its own. 
Supplementary Materials
Acknowledgments
A brief report on this work was published as an abstract and presented at the Asia-Pacific Conference on Vision 2013. This research was supported by grants from the Ontario Media Development Corporation and NSERC (Canada) as well as by an Endeavour Fellowship to A. A. from the government of Australia. 
Commercial relationships: none. 
Corresponding author: Robert S. Allison. 
Email: allison@cse.yorku.ca. 
Address: Department of Electrical Engineering and Computer Science, York University, Toronto, Canada. 
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Footnotes
1  Stereoscopic segregation of the aperture from the random-dot display might have been a factor in the binocular enhancement of vection (compared with monocular viewing conditions) in Experiment 2. However, in Experiments 1 and 3, all conditions were binocular.
Figure 1
 
(a) Disparity waveforms used in the experiment (vertically offset for visibility). Disparity was modulated as a function of vertical (y-axis) position on the screen. Disparity modulations had the same peak amplitudes and period but differed in the smooth and discontinuous disparity changes. (b) The subject viewed the moving corrugated surface through an aperture in a dark room.
Figure 1
 
(a) Disparity waveforms used in the experiment (vertically offset for visibility). Disparity was modulated as a function of vertical (y-axis) position on the screen. Disparity modulations had the same peak amplitudes and period but differed in the smooth and discontinuous disparity changes. (b) The subject viewed the moving corrugated surface through an aperture in a dark room.
Movie 1
 
Representation of an RDS moving surface. This movie represents the class of stimulus used but is not a representation of the actual stimulus. For better tolerance to video compression and as a web demo, the stimulus has been modified to a smaller window size, different aspect ratio, fewer dots, larger dots, and anaglyph presentation. Note that vection is not likely to be elicited when viewed on a monitor with other stationary features in view. (Movie 1 can be viewed in the Supplemental data.)
Movie 1
 
Representation of an RDS moving surface. This movie represents the class of stimulus used but is not a representation of the actual stimulus. For better tolerance to video compression and as a web demo, the stimulus has been modified to a smaller window size, different aspect ratio, fewer dots, larger dots, and anaglyph presentation. Note that vection is not likely to be elicited when viewed on a monitor with other stationary features in view. (Movie 1 can be viewed in the Supplemental data.)
Movie 2
 
Representation of a DRDS moving surface. This movie represents the class of stimulus used but is not a representation of the actual stimulus. For better tolerance to video compression and as a web demo, the stimulus has been modified to a smaller window size, different aspect ratio, fewer dots, larger dots, and anaglyph presentation. Note that vection is not likely to be elicited when viewed on a monitor with other stationary features in view. (Movie 2 can be viewed in the Supplemental data.)
Movie 2
 
Representation of a DRDS moving surface. This movie represents the class of stimulus used but is not a representation of the actual stimulus. For better tolerance to video compression and as a web demo, the stimulus has been modified to a smaller window size, different aspect ratio, fewer dots, larger dots, and anaglyph presentation. Note that vection is not likely to be elicited when viewed on a monitor with other stationary features in view. (Movie 2 can be viewed in the Supplemental data.)
Figure 2
 
Vection magnitude ratings in Experiment 1 as a function of disparity modulation waveform, dot lifetime (stereogram type: RDS or DRDS), and stimulus velocity. Each data point represents the mean of 12 subjects for the given condition; error bars indicate ±1 standard error of the mean.
Figure 2
 
Vection magnitude ratings in Experiment 1 as a function of disparity modulation waveform, dot lifetime (stereogram type: RDS or DRDS), and stimulus velocity. Each data point represents the mean of 12 subjects for the given condition; error bars indicate ±1 standard error of the mean.
Figure 3
 
Vection duration in Experiment 1 (N = 12) as a function of stereogram type (RDS or DRDS), fixation condition, and stimulus velocity. Each data point corresponds to the median across observations; error bars indicate 95% confidence intervals for the medians.
Figure 3
 
Vection duration in Experiment 1 (N = 12) as a function of stereogram type (RDS or DRDS), fixation condition, and stimulus velocity. Each data point corresponds to the median across observations; error bars indicate 95% confidence intervals for the medians.
Figure 4
 
Vection magnitude ratings in Experiment 2 as a function of disparity modulation waveform, viewing condition (monocular or binocular), and stimulus velocity. Each bar represents the mean of 15 subjects for the given condition; error bars indicate ±1 standard error of the mean.
Figure 4
 
Vection magnitude ratings in Experiment 2 as a function of disparity modulation waveform, viewing condition (monocular or binocular), and stimulus velocity. Each bar represents the mean of 15 subjects for the given condition; error bars indicate ±1 standard error of the mean.
Figure 5
 
Vection magnitude ratings in Experiment 3 as a function of dot lifetime and disparity amplitude (flat versus corrugated). The circular symbols show data for a stimulus speed of 0.082 m/s, and the square symbols show data for a stimulus speed of 0.163 m/s. Filled symbols show data for 5.44-arcmin disparity (corrugated), and open symbols show data for 0-arcmin disparity (flat). Mean data for 13 observers; error bars indicate ±1 standard error of the mean.
Figure 5
 
Vection magnitude ratings in Experiment 3 as a function of dot lifetime and disparity amplitude (flat versus corrugated). The circular symbols show data for a stimulus speed of 0.082 m/s, and the square symbols show data for a stimulus speed of 0.163 m/s. Filled symbols show data for 5.44-arcmin disparity (corrugated), and open symbols show data for 0-arcmin disparity (flat). Mean data for 13 observers; error bars indicate ±1 standard error of the mean.
Figure 6
 
. Waveform–disparity interaction in vection magnitude ratings in Experiment 3. Mean data for 13 observers collapsed across velocity and fixation conditions; error bars indicate ±1 standard error of the mean.
Figure 6
 
. Waveform–disparity interaction in vection magnitude ratings in Experiment 3. Mean data for 13 observers collapsed across velocity and fixation conditions; error bars indicate ±1 standard error of the mean.
Figure 7
 
Onset latency in Experiment 3 as a function of dot lifetime, stimulus speed, disparity, and fixation. Solid lines indicate conditions with no disparity modulation (flat), and dashed lines indicate disparity-modulated patterns (corrugated). Median data are shown for each condition; error bars indicate 95% confidence intervals.
Figure 7
 
Onset latency in Experiment 3 as a function of dot lifetime, stimulus speed, disparity, and fixation. Solid lines indicate conditions with no disparity modulation (flat), and dashed lines indicate disparity-modulated patterns (corrugated). Median data are shown for each condition; error bars indicate 95% confidence intervals.
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