Short Report

Effects of Vertical Direction and Aperture Size on the Perception of Visual Acceleration

Perception 2016, 0(0) 1–14 ! The Author(s) 2016 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0301006616629034 pec.sagepub.com

Alexandra S. Mueller Psychology Department, University of Western Ontario, London, Ontario, Canada

Esther G. Gonza´lez Vision Science Research Program, Toronto Western Hospital, Toronto, Canada Department of Ophthalmology and Vision Sciences, University of Toronto, Toronto, Canada Centre for Vision Research, York University, Toronto, Canada

Chris McNorgan Psychology Department, University at Buffalo, The State University of New York, Buffalo, NY, USA

Martin J. Steinbach Vision Science Research Program, Toronto Western Hospital, Toronto, Canada Department of Ophthalmology and Vision Sciences, University of Toronto, Toronto, Canada Centre for Vision Research, York University, Toronto, Canada

Brian Timney Psychology Department, University of Western Ontario, London, Ontario, Canada

Abstract It is not well understood whether the distance over which moving stimuli are visible affects our sensitivity to the presence of acceleration or our ability to track such stimuli. It is also uncertain whether our experience with gravity creates anisotropies in how we detect vertical acceleration and deceleration. To address these questions, we varied the vertical extent of the aperture through which we presented vertically accelerating and decelerating random dot arrays. We hypothesized that observers would better detect and pursue accelerating and decelerating stimuli that extend over larger than smaller distances. In Experiment 1, we tested the effects of vertical direction and aperture size on acceleration and deceleration detection accuracy. Results indicated that detection is Corresponding author: Alexandra S. Mueller, School of Rehabilitation Science, McMaster University, Hamilton, Ontario, Canada L8S 1C7. Email: [email protected]

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better for downward motion and for large apertures, but there is no difference between vertical acceleration and deceleration detection. A control experiment revealed that our manipulation of vertical aperture size affects the ability to track vertical motion. Smooth pursuit is better (i.e., with higher peak velocities) for large apertures than for small apertures. Our findings suggest that the ability to detect vertical acceleration and deceleration varies as a function of the direction and vertical extent over which an observer can track the moving stimulus. Keywords Vertical acceleration, vertical deceleration, motion perception, aperture size, visual field, smooth pursuit

In nature, as a consequence of the energy required to overcome earth’s gravitational pull, objects travel upward less frequently than downward (e.g., fruit growing on a tree is more likely to fall than rise into the air). Furthermore, downward movement may be more behaviorally relevant because we tend to intercept or avoid descending objects more often than those moving upward. Our asymmetrical experience with vertical motion raises the question of whether it has consequences for the human visual system in terms of anisotropies in acceleration and deceleration perception. There is support for this as motion duration discrimination has been reported to be more precise for downward than upward acceleration under conditions in which downward acceleration is consistent with the effects of gravity (Moscatelli & Lacquaniti, 2011). Expectations about how objects typically accelerate downward and decelerate upward due to the effects of gravity manifest themselves early in life (Kim & Spelke, 1992), and the downward bias in acceleration duration discrimination reported by Moscatelli and Lacquaniti may be the result of an adaptation based on experience. However, due to the effects of gravity, when an object is thrown upward it decelerates upward until it reaches a vertical speed of zero, after which it accelerates downward at a constant rate. It is therefore an open question whether we have a bias in the opposite direction for deceleration perception. A further consideration for how humans perceive vertical acceleration is whether the physical constraints of the visual field size influence sensitivity. Every day we see the effects of gravity on object motion through apertures of various sizes, such as windows or spaces between objects. In view of the fact that the size of an aperture determines the distance over which an object can travel and also for how long it remains visible, the vertical height of an aperture may affect how well we can detect the presence of vertical acceleration and deceleration. Given that the ability to detect the presence of acceleration improves as the stimulus presentation duration increases (Brouwer, Brenner, & Smeets, 2002; Gottsdanker, Frick, & Lockard, 1961; Timney, Solti, & Fernando, 2010), the longer a stimulus is able to travel uninterrupted (and the longer we are able to view this motion uninterrupted) the better we may be at discerning its motion profile (i.e., that the stimulus is accelerating as opposed to moving at constant velocity). Similarly, an aperture’s vertical size may also influence an observer’s ability to visually pursue vertical acceleration, which in turn may be related to how well the observer can detect acceleration. Specifically, there are reports that tracking a moving stimulus, as opposed to viewing under fixation, improves sensitivity to motion (Braun et al., 2008; Braun, Schu¨tz, & Gegenfurtner, 2010; Haarmeier & Thier, 2006; Spering, Schu¨tz, Braun, & Gegenfurtner, 2011). Hence, we should be better at perceiving and pursuing vertical acceleration and deceleration over large vertical distances than small ones.

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There is evidence that aperture size influences smooth pursuit (Heinen & Watamaniuk, 1998) and abrupt velocity change detection (Hohnsbein & Mateeff, 2002) on the horizontal axis. However, Heinen and Watamaniuk varied the vertical height of the aperture while presenting horizontal motion, and Hohnsbein and Mateeff presented their stimuli peripherally under stationary fixation. One of the goals of this study was to manipulate aperture size on the vertical axis in order to explore how sensitivity to the presence of vertical acceleration (and our ability to track it) is affected by physically constraining the distance over which the stimulus can travel. If the ability to detect continuously changing velocity is better over larger than smaller distances, manipulations of aperture size may alter the strength of the asymmetry (if one exists) between acceleration and deceleration detection as a function of vertical direction. This paper tested two alternative hypotheses with respect to the effects of vertical direction and sign of acceleration on acceleration detection. First, it is possible that the visual system is sensitive to the effects of gravity and thereby also to the sign of acceleration as a function of vertical direction. If this were the case, we should detect downward acceleration and upward deceleration better than upward acceleration and downward deceleration. On the other hand, such a degree of sensitivity needed to distinguish between vertical acceleration and deceleration may be an inefficient use of resources. The second hypothesis holds that the downward bias in detection may persist regardless of the sign of acceleration. Both hypotheses are in line with the idea of an experience-based adaptation. Moreover, each hypothesis would predict acceleration and deceleration detection to improve as the distance over which the stimulus is able to travel increases, which in turn should be related to being better able to pursue the moving stimuli. In Experiment 1, we used a psychophysical task to determine whether there are asymmetries in the ability to detect the presence of acceleration and deceleration as a function of vertical direction, and whether the strength of those asymmetries depends on the extent over which a stimulus is able to travel. Experiment 2 was a control experiment to test whether the size of the aperture affects the ability to track vertically accelerating and decelerating stimuli. Schwartz and Lisberger (1994) reported that brief speed perturbations are more effective in eliciting a matching response in eye velocity during pursuit along the axis of stimulus motion than along the orthogonal axis, whereas they are minimally effective when viewed under fixation. Likewise, given that we anticipated aperture size to have a similar influence on psychophysical and smooth pursuit performance, we expected higher peak velocities and fewer deviations in eye position from stimulus position in larger apertures than in smaller apertures.

Experiment 1 Method Participants. Ten volunteers (including author Alexandra S. Mueller), seven of whom were female, with an average age of 24.4 years (SD ¼ 2.07) participated in this experiment. Two additional participants were unable to do the task reliably and were not included. Every participant had normal or corrected-to-normal visual and stereo acuity and had no known ocular motility issues or history of eye muscle surgery. Both experiments in this study were conducted in accordance with institutional regulations and the Declaration of Helsinki. Participants provided informed written consent and were reimbursed up to $40 for travel expenses. Experiment 1 was conducted at the University of Western Ontario, London, Ontario, and Experiment 2 was conducted at the Toronto Western Hospital, Toronto, Ontario.

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Stimuli and apparatus. Stimuli were created and presented using VPixx, a graphics and psychophysics software package (version 2.87, VPixx Technologies Inc., Saint-Bruno, Quebec, Canada), on a 51.5 cm LaCie electron22blue II monitor (Mitsubishi Electric Corporation, Japan), with a display resolution of 1024  768 pixels and 120-Hz refresh rate. A random array of white dots (96.7 cd/m2) moving continuously and 100% coherently upward or downward was presented on a black background (0.06 cd/m2). Dot size (0.15  0.15 ) and average density (1.5 dots/degree2) were held constant, and dot position was updated every frame. When dots disappeared from view after reaching the border of the aperture, they were replaced at random horizontal locations along the opposite border to ensure that average dot density was constant in every frame. There were two aperture size conditions with the vertical distance subtending 1 (small) and 27 (large). The horizontal distance was held constant at 1 . All apertures were stationary and centered in the middle of the screen. The acceleration and deceleration conditions had the same average velocity (10 deg/s). We held the middle velocity (i.e., the mid-point in the range between the initial and final velocities) constant at 10 deg/s using the following formula:

velocity ¼ 10 þ a t  ttotal =2 ð1Þ where a is the acceleration rate, t is time, and ttotal is the total presentation duration of 750 ms. Stimuli that accelerated or decelerated (i.e., the comparison stimuli) did so continuously for the whole presentation. Moreover, all of the dots in the array accelerated or decelerated at the same rate or moved at the same velocity. In addition, for the acceleration and deceleration rates tested in this experiment, the standard (constant velocity) and comparison stimuli traveled the same distance within a given trial for each condition. Therefore, an advantage of holding average velocity constant was that observers could not use distance traveled as a cue to make their judgments as to which stimulus accelerated or decelerated within each aperture condition. Procedure. Participants sat in the dark and, using a chinrest, viewed the display binocularly at 60 cm. A two-interval forced choice task using the method of constant stimuli was used to measure acceleration and deceleration detection accuracy. There were seven rates of acceleration and deceleration in steps of  1.5 deg/s2 from a range between 1.5 and 10.5 deg/s2 in the comparison stimuli for each condition. The standard stimuli moved at a constant velocity of 10 deg/s. Each trial had a standard and comparison stimulus presented in random order, and vertical direction was the same for the two stimuli within every trial. Trials were initiated by the participant pressing the spacebar and began with a red 0.5 crosshair fixation target on a black background for 500 ms. Immediately afterwards, the standard or comparison stimulus was presented for 750 ms, followed by a 500 ms black screen, and then the standard or comparison stimulus for 750 ms. Participants were instructed to fixate the crosshair target at the beginning of every trial until it disappeared and was replaced with the random dot array, which they were encouraged to track, although their eye movements were not recorded. Participants were told to indicate whether it was the first or second stimulus that accelerated or decelerated by pressing a key on a keyboard. Each key press produced an audible beep. Acceleration and deceleration trials were presented in separate blocks, the order of which was counterbalanced across participants. Order of aperture size conditions within each block (vertical direction was randomized within each aperture size condition) and order of stimulus values within each condition were randomized. Participants completed at least 240 practice

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trials prior to the experimental task. They were provided feedback only during the practice trials, but no feedback was provided during the experimental trials. There were a minimum of 20 and a maximum of 60 experimental trials per stimulus value for each condition per participant included for analysis, depending on the number of runs (each containing 10 trials per stimulus value per condition) needed to obtain non-significant goodness of fit measures for the probit regression described below.

Results We analyzed the psychophysical data using SPSS (IBM Corporation, Armonk, NY). The data were plotted in terms of proportion correct as a function of acceleration or deceleration rate, and through probit regression we interpolated the 75% correct detection threshold rates for each condition. All psychometric functions had a non-significant Pearson 2 coefficient as a measure of goodness of fit. Table 1 shows the 75% correct acceleration and deceleration detection threshold rates as absolute values. For ease of comparison with other studies, we transformed the absolute value threshold rates into functionally equivalent Weber fractions; however, we could not use the standard equation (A/A) because the standard stimulus moved at constant velocity of 10 deg/s (i.e., with zero acceleration). Therefore, we transformed the absolute value threshold rates by taking the maximum and minimum velocities (vmax and vmin, respectively) corresponding to the threshold rate and dividing the difference by the velocity of the standard stimulus, which was also the average velocity of every stimulus or (vmax þ vmin)/2. We multiplied the resulting value by 100%. In other words, the transformed thresholds represent the threshold velocity percentage difference between the comparison stimulus’ maximum and minimum velocities relative to the standard stimulus’ velocity that is needed to correctly detect acceleration and deceleration in the comparison stimulus. This method of transforming acceleration detection thresholds has been reported before (e.g., Brouwer et al., 2002; Calderone & Kaiser, 1989; Gottsdanker et al., 1961). These transformed thresholds were submitted to a 2(vertical direction)  2(sign of acceleration)  2(aperture size) repeated measures analysis of variance. (As the transformation was linear, we found the same pattern of results for the absolute value and transformed datasets.) The data were spherical and therefore no correction was used. Consistent with our hypothesis for a general predisposition to be more sensitive to downward acceleration and deceleration, detection tends to be more accurate for downward motion (M ¼ 45.59%, SD ¼ 13.34) than upward motion (M ¼ 48.72%, SD ¼ 13.39), F(1, 9) ¼ 7.21, p ¼ .03, Z2p ¼ 0.45, but there is little difference between the acceleration and deceleration conditions, F(1, 9) ¼ 1.82, p ¼ .21. Furthermore, the distance over which a stimulus can travel appears to affect vertical acceleration and deceleration Table 1. Mean Absolute Value 75% Correct Acceleration and Deceleration Detection Threshold Rates (deg/s2). Acceleration rate

Deceleration rate

Vertical direction

Aperture size

Mean (SD)

Mean (SD)

Upward

Small Large Small Large

6.72 5.31 6.40 5.46

7.43 6.52 6.39 6.07

Downward

(1.90) (2.03) (1.86) (1.83)

(2.08) (2.37) (2.19) (2.19)

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perception, because detection is better for large apertures (M ¼ 43.81%, SD ¼ 14.42) than for small apertures (M ¼ 50.51%, SD ¼ 12.86), F(1, 9) ¼ 9.74, p ¼ .01, Z2p ¼ 0.52 (Figure 1). There are no interactions between the experimental variables.

Experiment 2 Experiment 1 demonstrated that physically constraining the vertical distance over which a stimulus can travel varies the ability to detect the presence of vertical acceleration and deceleration. Experiment 2 was designed to test whether the vertical height of the aperture alters how observers pursue vertically accelerating and decelerating random dot arrays.

Method Participants. Five volunteers (including author Alexandra S. Mueller), four of whom were female, with an average age of 25.6 years (SD ¼ 1.52) from the first experiment participated in Experiment 2. Stimuli and apparatus. This experiment presented the same random dot array stimuli and conditions as those used in Experiment 1 using the VPixx program on a 45 cm Samsung monitor (Sync Master 900 NF; Samsung, Seoul, South Korea) with a 120-Hz refresh rate and a resolution of 1024  768 pixels. The luminance of the white dots was 88.3 cd/m2 and the black background was 3.1 cd/m2. The MacBook Pro laptop used to run VPixx was connected to a desktop remote EyeLink 1000 eyetracker (SR Research Ltd., Mississauga, Ontario, Canada) through a DATAPixx interface (VPixx Technologies Inc., Saint-Bruno, Quebec, Canada) that stored time and stimulus condition information in the eye position data files at a rate of 250 Hz. For every participant, and prior to the experimental task, the eye tracker was calibrated using its standard calibration and validation procedures. Unlike Experiment 1, the large field height in this experiment was 23 (pilot testing revealed a negligible difference in psychophysical performance between the 23 and 27 aperture sizes). Procedure. Participants sat in an illuminated room, 60 cm from the screen, with their head resting on a chin and headrest as they viewed the display binocularly. One accelerating or decelerating stimulus was presented in each trial and, although response accuracy was not

Figure 1. Mean transformed acceleration and deceleration detection thresholds (%) as a function of vertical direction and aperture size. Error bars are  1 SE.

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measured, participants were instructed to judge whether the stimulus accelerated or decelerated. Trials were initiated automatically and began with the same red fixation target used in Experiment 1 for 1000 ms. The random dot stimulus then appeared for 750 ms, after which another trial began immediately. The order of each aperture size condition was randomized (vertical direction was randomized within each aperture size condition), and acceleration and deceleration trials within each condition were randomly interlaced. There were three stimulus values within each condition (vertical direction by aperture size) and they were unique to each participant. The first value for each condition was the acceleration or deceleration rate corresponding to the participant’s 75% correct detection threshold obtained in Experiment 1. The second and third stimulus values for each condition were 50% and 100% greater than the threshold rate, respectively. This was done to provide a range of stimuli to assess smooth pursuit, although we found little difference in pursuit between the three stimulus values within each condition. There were 10 replications per stimulus value. Analyses. Before analyzing the smooth pursuit data, we removed saccades, fixations, and blinks from the data belonging to the right eye. For this, we used the standard EyeLink saccade detection algorithm with a combined velocity > 22 deg/s and an acceleration > 4000 deg/s2 criterion. For blinks, the data obtained 100 ms before and after the pupil’s initial occlusion were removed for all analyses (Aguilar & Castet, 2011). Peak eye velocity was calculated using a custom MATLAB (MATLAB, MathWorks, Natick, MA) script that used a 5-point differentiator. The program approximated the first derivative of eye position with respect to time (i.e., eye velocity) through the 5-point stencil method (Equation (2), for which x is eye position and h is the spacing between eye positions):  0 f ðxÞ ¼ ðfðx þ 2hÞ þ 8fðx þ hÞ  8fðx  hÞ þ fðx  2hÞÞ 12h ð2Þ First, we calculated the peak velocity for every uninterrupted epoch of smooth pursuit for a given trial. Then we created a weighted average of all of the peak velocities taking into account the number of data points that contributed to each peak velocity value that occurred for a given stimulus value within an experimental condition for each participant. (Recall that there were three stimulus values, i.e., acceleration or deceleration rates, per condition.) Finally, we averaged those weighted average values in order to obtain a measure of mean weighted average peak velocity for each condition per participant. We submitted the mean weighted average peak velocity data to a 2(vertical direction)  2(sign of acceleration)  2(aperture size) repeated measures analysis of variance. No correction was used because the data were spherical. Only eye movements made in the direction of the stimulus motion are reported for the peak eye velocity analysis and for the examination of the eye position traces. In order to compare the eye and stimulus position traces, we calculated the stimulus’ velocity as a function of time using Equation (1). Then, using Equation (3), we calculated the changes in stimulus position over time: positioniþ1 ¼ positioni þ velocityi ðtiþ1  ti Þ

ð3Þ

Given that we used a random dot array, it was not possible to identify which dots participants tracked during the course of the presentation, so we set the initial position of the stimulus to that of the eye at the beginning of every epoch of uninterrupted smooth pursuit, but when the initial eye position was outside the aperture area, we set the stimulus’

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initial position to the vertical position of the closest aperture boundary. Whenever the computed stimulus position reached the edge of the aperture, it was reset to the vertical position of the opposite side of the aperture for the subsequent time point. The examination of the eye position traces allowed us to understand the peak velocity data. Examples are shown in Figures 3 and 4. Finally, we also explored the number and amplitude of regressive (i.e., in the direction opposite to the stimulus) and catch-up saccades (i.e., in the same direction as the stimulus) made by the right eye as a function of experimental condition. We excluded those that occurred during the initial 200 ms of the stimulus presentation; that is, during beginning of smooth pursuit from fixation (Rashbass, 1961; Westheimer, 1954).

Results Peak eye velocity. Although there are no main effects of vertical direction, F(1, 4) ¼ 2.11, p ¼ .22, or sign of acceleration, F(1, 4) ¼ 1.41, p ¼ .30, as hypothesized, peak eye velocity is higher for the large apertures (M ¼ 15.09 deg/s, SD ¼ 2.28) than for the small ones (M ¼ 6.78 deg/s, SD ¼ 1.11), F(1, 4) ¼ 51.23, p ¼ .002, Z2p ¼ 0.93 (Figure 2). Moreover, there is an interaction between direction and aperture size, F(1, 4) ¼ 8.50, p ¼ .04, Z2p ¼ 0.68. The overall difference between the large and small aperture conditions is somewhat greater in the upward condition (M difference ¼ 8.93 deg/s, SD ¼ 2.78) than in the downward condition (M difference ¼ 7.68 deg/s, SD ¼ 2.48), t(4) ¼ 2.92, p ¼ .04, Cohen’s d ¼ 1.30. There is also an interaction between sign of acceleration and aperture size, F(1, 4) ¼ 10.85, p ¼ .03, Z2p ¼ 0.73, as the difference between the large and small aperture conditions tends to be slightly greater for the deceleration condition (M difference ¼ 8.61 deg/s, SD ¼ 2.76) than for the acceleration condition (M difference ¼ 8.00 deg/s, SD ¼ 2.43), t(4) ¼ 3.29, p ¼ .03, Cohen’s d ¼ 1.47. Eye and stimulus position traces. Observers do not track well in the small aperture conditions (Figure 3). In many trials, the eye tends to hover over the stimulus area with little movement in the direction of the stimulus, often without saccade interruption. For the trials in which the eye follows the stimulus, observers do not appear to track an individual dot but rather the global motion and eye trajectory rarely changes when the dot disappears from view.

Figure 2. Mean weighted average peak eye velocity (deg/s) as a function of vertical direction, sign of acceleration, and aperture size. Error bars are  1 SE.

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Figure 3. Example eye traces of one participant for trials belonging to the acceleration and deceleration upward and downward small aperture conditions. (Stimulus traces belong to threshold acceleration and deceleration rates.)

Eye positions also frequently occur outside the area of the small aperture (on average, in 85% of trials), which indicates that observers do not consistently track the stimuli foveally and may be related to the difficulty in tracking elements in a small array. In contrast, observers track better in the large aperture conditions (Figure 4). Eye positions never occur outside the area of the large aperture, although one participant’s eye trajectory remained constant after the dot reached the border of the large aperture in 7 out of 120 trials, but usually toward the end of the trial. Saccades. There are more regressive than catch-up saccades (M regressive saccades per trial ¼ 0.77, SD ¼ 0.35; M catch-up saccades per trial ¼ 0.14, SD ¼ 0.07), but with so few saccades in general it is unclear whether there are any meaningful differences as a function of aperture size or vertical direction. Nevertheless, saccade amplitude is greater in the large (M regressive saccades ¼ 2.24 , SD ¼ 1.07; M catch-up saccades ¼ 1.43 , SD ¼ 0.85) than small aperture conditions (M regressive saccades ¼ 0.76 , SD ¼ 0.27; M catch-up saccades ¼ 0.71 , SD ¼ 0.53). Finally, there are no differences in the number and amplitude of either type of saccade between the acceleration and deceleration conditions.

Discussion Our results indicate that the downward bias in the ability to detect visual acceleration persists regardless of the size of the aperture or the sign of acceleration. This anisotropy is compatible with the idea that the visual system adaptively responds to the salience of upward and downward events in general, but it does not further distinguish between vertically accelerating and decelerating events. The absence of an asymmetry in our sensitivity to the

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Figure 4. Example eye traces of the same participant in Figure 3 for trials belonging to the acceleration and deceleration upward and downward large aperture conditions. (Stimulus traces belong to threshold acceleration and deceleration rates.)

presence of vertical acceleration and deceleration is not entirely surprising considering that we are relatively insensitive to variable velocity (Snowden & Braddick, 1991; Werkhoven, Snippe, & Toet, 1992). Our weak sensitivity has been attributed to the fact that we do not appear to have cortical neurons that are sensitive to the rate of visual acceleration directly and, instead, velocity-sensitive neurons are responsible for detecting changes in velocity over time to signal the presence of visual acceleration (Lisberger & Movshon, 1999; Price, Ono, Mustari, & Ibbotson, 2005; Schlack, Krekelberg, & Albright, 2007). This would account for the fairly high acceleration and deceleration detection thresholds reported in Experiment 1. We also note that smooth pursuit performance was very similar between the acceleration/ deceleration rates tested in Experiment 2 (even when the rates were twice the size of the threshold rates). This finding is consistent with earlier studies on the smooth pursuit of accelerating stimuli, in that the human pursuit and perceptual systems appear similarly insensitive to visual acceleration (e.g., Watamaniuk & Heinen, 2003). Nevertheless, despite our relative insensitivity to the rate of visual acceleration, Indovina et al. (2005) found that the human vestibular network selectively activates when the visual system processes acceleration that is consistent with the effects of gravity. Vestibular organs, such as the semicircular canals, are inherently sensitive to acceleration and deceleration (Waespe & Henn, 1977), and the vestibular network processes multimodal information related to self-motion and orientation with respect to gravity (Angelaki, Shaikh, Green, & Dickman, 2004; Merfeld, Zupan, & Peterka, 1999; Nishiike et al., 2002). Consequently, Indovina et al. argued that the vestibular network’s response to gravity-consistent visual acceleration indicates that it stores an internal model of gravitational motion that can be used by the visual system. It is interesting that we observed a downward bias (although it was

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relatively small) in the absence of any contextual cues of gravity in our random dot displays, although it is possible that having participants sitting upright was enough of an orientation cue. It has also been suggested that this internal representation of gravity is the result of experience and, given that downward motion may be more behaviorally relevant than upward motion, this may help to explain the tendency to better perceive visual acceleration and deceleration in downward motion. The behavioral implications for the downward bias in acceleration detection may be related to those that have been suggested to explain why motion sensitivity tends to be higher in the lower visual field than in the upper visual field (e.g., Edwards & Badcock, 1993). Although the effect of vertical direction on acceleration and deceleration perception is modest given the overall size of our sample’s detection thresholds, it may nevertheless have implications for how observers navigate the environment safely. For instance, there should be an advantage to looking downward to avoid obstacles and to maintain one’s balance when walking (e.g., Marigold & Patla, 2008, found that observers rely on the lower visual field when walking on varied terrain). Moreover, a downward bias in acceleration detection would also be beneficial for catching and avoiding falling objects accurately (Moscatelli & Lacquaniti, 2011; Senot, Zago, Lacquaniti, & McIntyre, 2005). Our data also show that the vertical distance over which a stimulus can travel influences the ability to detect and visually track vertical acceleration and deceleration. Both psychophysical and smooth pursuit performance are better for large vertical apertures than for small ones, and the amplitude of saccades increases as the size of the aperture increases. Given that tracking is generally poor in the small aperture conditions, and at times hardly occurs at all, our results can be interpreted as suggesting that the visual system does not continuously incorporate information about eye movements into the motion perceptual signal. The dissociation of ocular motor activity from the conscious perception of motion has been reported before (e.g., Gonza´lez, Lillakas, Greenwald, Gallie, & Steinbach, 2014; Spering, Pomplun, & Carrasco, 2011; Tavassoli & Ringach, 2010). Nonetheless, despite the absence of a statistically significant interaction between aperture size and vertical direction, the downward bias in acceleration and deceleration detection tends to be greater in the small aperture condition (M difference between upward and downward conditions ¼ 5.14%, SD ¼ 5.67) than in the large aperture condition (M difference between upward and downward conditions ¼ 1.13%, SD ¼ 5.16). We also observed a similar, although much weaker, pattern in the peak eye velocity data. Given that the increase in aperture size enhances detection and pursuit, the improvement of each may contribute to the moderate weakening of the downward bias when viewing vertical acceleration and deceleration over larger distances as compared to smaller ones. It could be argued that holding average velocity constant while blocking acceleration and deceleration into separate detection tasks introduced a possible confound in our study, in that the accelerating stimuli were initially slower whereas the decelerating stimuli were initially faster than the standard stimuli (the opposite was true for final velocities). Nevertheless, the presentation order of the standard and comparison stimuli was random across trials and participants never knew which stimulus they were seeing ahead of time. However, given that motion integration can occur over periods as brief as 100 ms (e.g., Huff & Papenmeier, 2013; McKee & Welch, 1985; Snowden & Braddick, 1991; Werkhoven et al., 1992), it is possible that participants could have used the initial or final velocity difference between the standard and comparison stimuli to make acceleration and deceleration detection judgments. To address this possibility, in a series of unpublished experiments, while holding stimulus parameters constant, we tested accelerating and decelerating stimuli under two conditions: (a) in random order within the same velocity change detection task and

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(b) blocked into separate tasks. When acceleration and deceleration were randomly interleaved, participants could not rely on an initial or final velocity discrimination strategy to do the task. Humans are much better at discriminating between temporally separated velocities than between contiguously presented velocities (e.g., Snowden & Braddick, 1991; Werkhoven et al., 1992). Therefore, if observers had been using a velocity discrimination strategy by comparing the initial or final velocities of the standard and comparison stimuli to make their judgments, their performance in the blocked task should have been better than for the randomly interleaved task. Our results revealed that observers actually have very similar thresholds for both methods of presentation, which suggests that they were using a similar strategy of detecting the accelerating/decelerating stimulus to perform each task, as opposed to relying on the stimulus that was initially faster or slower. In the present study, we separated acceleration and deceleration into independent detection tasks because participants in our unpublished studies reported that the task was much more difficult when acceleration and deceleration were randomly interleaved. This is likely due to the cognitive load of the interleaved task being greater as it requires participants to discriminate between constant and changing velocity while keeping in mind the sign of the acceleration. The blocked task, on the other hand, requires that participants only discriminate between acceleration and constant velocity. The brevity of the stimulus likely makes the difference in cognitive load more important than it would be for tasks with longer stimulus presentations. Furthermore, an important indicator of how participants performed the psychophysical task in Experiment 1 is the size of the transformed thresholds, which are functionally equivalent to Weber fractions. Velocity discrimination thresholds expressed as Weber fractions have typically been reported to be very low across a wide range of stimulus parameters, approximately between 4% and 7% of base velocities spanning between 4 and 64 deg/s (e.g., Clifford, Beardsley, & Vaina, 1999; De Bruyn & Orban, 1988; McKee, 1981; McKee & Nakayama, 1984; Orban, De Wolf, & Maes, 1984; Snowden & Braddick, 1991; Werkhoven et al., 1992). In comparison, acceleration detection thresholds tend to be much higher; for example, Brouwer et al. (2002) reported that a minimum 25% difference between the initial and final velocities is necessary for observers to reliably detect the presence of acceleration. The transformed thresholds reported in Experiment 1 are considerably higher than would be expected if participants had used a velocity discrimination strategy to distinguish the standard and comparison stimuli based on either initial or final velocities. Therefore, we conclude that observers were detecting changes in velocity with respect to time in order to perform the psychophysical task. We note, however, that our findings cannot distinguish whether participants were using the rate of acceleration per se or the difference between the initial and final velocities of individual stimuli to do the task. In general, the evidence suggests that human observers rely on the difference between the initial and final velocities of an accelerating stimulus to identify the presence of acceleration (e.g., Brouwer et al., 2002; Gottsdanker et al., 1961; Timney, Kearney, & Asa, 2012), at least for stimulus presentations as brief as ours. Acknowledgments The authors are extremely grateful to Hans Mueller for his technical help, Runjie Shi for programming the MATLAB script, Dr. Tutis Vilis for his insights, and Peter April for his assistance with stimuli programming. A subset of the psychophysical data was presented at the 2014 meeting of the Society for Neuroscience.

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Declaration of Conflicting Interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was funded by an Ontario Graduate Scholarship to Alexandra S. Mueller; the Vision Science Research Program and Toronto Western Hospital to Esther G. Gonza´lez and Martin J. Steinbach; Natural Sciences and Engineering Research Council of Canada grant and an anonymous donor to Martin J. Steinbach; and a Provost’s Research Grant to Brian Timney.

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