Open Access
Article  |   May 2024
Effect of spatial context on perceived walking direction
Author Affiliations
  • Chang Chen
    School of Psychology, University of New South Wales, Sydney, NSW, Australia
    chang.chen2@unsw.edu.au
  • W. Paul Boyce
    School of Psychology, University of New South Wales, Sydney, NSW, Australia
    wpaulboyceresearch@gmail.com
  • Colin J. Palmer
    School of Psychology, University of New South Wales, Sydney, NSW, Australia
    Department of Psychology, National University of Singapore, Singapore, Singapore
    colin.palmer@unsw.edu.au
  • Colin W. G. Clifford
    School of Psychology, University of New South Wales, Sydney, NSW, Australia
    colin.clifford@unsw.edu.au
Journal of Vision May 2024, Vol.24, 11. doi:https://doi.org/10.1167/jov.24.5.11
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      Chang Chen, W. Paul Boyce, Colin J. Palmer, Colin W. G. Clifford; Effect of spatial context on perceived walking direction. Journal of Vision 2024;24(5):11. https://doi.org/10.1167/jov.24.5.11.

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Abstract

Contextual modulation occurs for many aspects of high-level vision but is relatively unexplored for the perception of walking direction. In a recent study, we observed an effect of the temporal context on perceived walking direction. Here, we examined the spatial contextual modulation by measuring the perceived direction of a target point-light walker in the presence of two flanker walkers, one on each side. Experiment 1 followed a within-subjects design. Participants (n = 30) completed a spatial context task by judging the walking direction of the target in 13 different conditions: a walker alone in the center or with two flanking walkers either intact or scrambled at a flanker deviation of ±15°, ±30°, or ±45°. For comparison, participants completed an adaptation task where they reported the walking direction of a target after adaptation to ±30° walking direction. We found the expected repulsive effects in the adaptation task but attractive effects in the spatial context task. In Experiment 2 (n = 40), we measured the tuning of spatial contextual modulation across a wide range of flanker deviation magnitudes ranging from 15° to 165° in 15° intervals. Our results showed significant attractive effects across a wide range of flanker walking directions with the peak effect at around 30°. The assimilative versus repulsive effects of spatial contextual modulation and temporal adaptation suggest dissociable neural mechanisms, but they may operate on the same population of sensory channels coding for walking direction, as evidenced by similarity in the peak tuning across the walking direction of the inducers.

Introduction
Walking direction is a simple visual cue that helps us to perceive and communicate with others. Our ability to perceive whether someone is walking toward us, for example, can help us to understand their disposition and intentions and to coordinate our behavior with theirs. Research into high-level vision has often focused on the recognition of biological motion, including the perception of walking direction (Jackson & Blake, 2010), as well our ability to extract other social information from another person's walking style, such as their gender (Cutting & Kozlowski, 1977). The visual and neural mechanisms underlying the perception of biological motion are now described in some detail (Blake & Shiffrar, 2007; Giese & Poggio, 2003; Lappe, 2012), although still relatively unexplored is the effect of the visual context on our perception of biological motion. Our visual impression of other people is always embedded within a specific context (e.g., at work, on a busy street, during an emergency) that commonly includes the exposure to simultaneous and/or preceding behaviors of other people in a group (e.g., seeing a person walking among a crowd of other people). In the current paper, we investigate how the visual context modulates the perception of walking direction, with the aim of shedding light on sensory interactions underlying high-level vision. 
It is well known that our perception of a visual stimulus can be altered by the presence of surrounding information (Todorović, 2010). In early works, contextual effects in vision were studied for a range of fundamental physical attributes, such as the size and orientation of visual features. In the tilt illusion, for example, the perceived orientation of a line or grating can be biased by the presence of an oriented surround stimulus (Clifford, 2014; Gibson & Radner, 1937). More recently, contextual effects have been studied for a wide range of high-level visual attributes, such as face (e.g., Walker & Vul, 2014) and body perception (e.g., Wedell, Santoyo, & Pettibone, 2005). In the study by Walker and Vul (2014), they found a “cheerleader effect” in facial attractiveness perception, such that people tend to appear more attractive when they are seen as part of a group rather than as individuals. 
There are typically two ways contextual effects in vision manifest—namely, contrast and assimilation, depending on whether the perception of visual features of the target stimulus is shifted away from or toward the features of the contextual stimulus (Jordan & Uhlarik, 1985). The well-known Ebbinghaus illusion is an example of the size contrast effect, in which a central circle that is encompassed by larger circles appears smaller compared with one surrounded by smaller circles (e.g., Massaro & Anderson, 1971), as shown in Figure 1A. In contrast, when two concentric circles are compared with a single circle that has the same size as the inner circle of the concentric pair, an effect known as size assimilation occurs, such that the inner circle appears larger than the single circle (Howe & Purves, 2004; Pressey, 1977), as shown in Figure 1B. Numerous studies have demonstrated that assimilation effects can influence our perception of high-level visual attributes, such as facial attractiveness (Walker & Vul, 2014; Ying, Burns, Lin, & Xu, 2019), facial age (Awad, Clifford, White, & Mareschal, 2020; Pilz & Lou, 2022), and facial race (Sun & Balas, 2012). Although there is limited evidence of spatial contrast effects in high-level vision, a contrast effect has been found in body perception, in which the silhouette of a person's body was judged to be thinner when surrounded by wider silhouettes compared with when surrounded by thinner silhouettes (Wedell et al., 2005). Also, in gender perception, the gender of a central target face/point-light walker was more likely to be perceived as opposite to the surrounding gender, resulting in a contrast effect (Liu, Cheng, Yuan, & Jiang, 2023). 
Figure 1.
 
(A) Illustration of the classic Ebbinghaus illusion (contrast effect). The central circle surrounded by smaller circles (on the right side) appears larger than the one of the same size surrounded by larger circles (on the left side). (B) Illustration of an assimilation effect. The inner of two concentric circles appears larger than a single circle of the same size as the inner one.
Figure 1.
 
(A) Illustration of the classic Ebbinghaus illusion (contrast effect). The central circle surrounded by smaller circles (on the right side) appears larger than the one of the same size surrounded by larger circles (on the left side). (B) Illustration of an assimilation effect. The inner of two concentric circles appears larger than a single circle of the same size as the inner one.
Contextual modulation of visual perception occurs not only across space but also across time. A well-studied temporal effect in vision is adaptation, in which prolonged exposure to a particular visual stimulus can alter the perception of a subsequently viewed stimulus. Comparing the spatial and temporal aspects of contextual modulation can be insightful regarding the sensory processes that underlie these effects. For example, in the context of orientation perception, the tilt illusion (spatial) and tilt aftereffect (temporal) show a similar reliance on the angular difference between the target and inducer (Gibson & Radner, 1937), implicating similar sensory gain control mechanisms in both phenomena (Clifford, 2014). Other studies have compared spatial and temporal modulation of high-level attributes. For example, Ying et al. (2019) found contrastive effects in the context of face attractiveness judgments, whereby people appeared more attractive when presented simultaneously with unattractive friends, and, similarly, people appeared more attractive when shown after a group of unattractive individuals. In the context of perceived walking direction, repeated exposure to a specific walking direction (e.g., viewing an animated stimulus walking to the left) produces a repulsive perceptual aftereffect, such that the perceived angle at which subsequently presented stimuli are perceived as walking is biased away from the angle to which the observer was adapted (Jackson & Blake, 2010; Chen, Boyce, Palmer, & Clifford, 2023). In contrast, Cheng, Liu, Yuan, and Jiang (2022) recently found an attractive effect of spatial context on perceived walking direction, such that the perceived direction of a walker was biased toward the walking direction of a set of surrounding walkers. Although no single study has yet compared spatial and temporal effects on the perception of walking direction, these previous studies raise a question of why these effects seem to differ in being attractive and repulsive, respectively. 
Whether contextual modulation is attractive or repulsive can also depend on the magnitude of the difference between test and inducing stimuli. For example, the tilt illusion displays a characteristic angular tuning (Clifford, 2014). Within a range of 0° to 50° of the angular difference between the test and surrounding stimuli, a repulsive effect occurs, with the peak repulsive effect occurring at around 15°. A smaller attractive effect has been observed in the tilt illusion for larger angle differences, with the peak attractive effect occurring at around 75° (e.g., Over, Broerse, & Crassini, 1972; Wenderoth & Johnstone, 1987). These findings provide insights into the underlying mechanisms of orientation perception, as the observed angular tuning profile is characteristic of interactions between neurons sensitive to orientation (Clifford, 2014). In particular, the repulsive tilt illusion can be explained by lateral inhibition between neural mechanisms tuned to different orientations (Blakemore, Carpenter, & Georgeson, 1970), whereas the attractive tilt illusion can be accounted for by incorporating disinhibition (O'Toole & Wenderoth, 1977). In our recent study on perceived walking direction (Chen et al., 2023), we found a specific tuning profile of adaptation to walking direction, characterized by local repulsion of perceived walking direction around the direction to which the observer was adapted, with peak aftereffects occurring when there was a magnitude of ±30° between adapting and test directions. This tuning profile can be well accounted for by a population coding model of perceived walking direction and is informative about the number and width of sensory channels required. In the context of spatial modulation of perceived walking direction, Cheng et al. (2022) only tested simultaneous surround walkers oriented ±15° from directly toward the observer. Thus, the angular tuning of the spatial context effect across a wider range of simultaneous walking direction stimuli has not yet been studied. 
Overall, the extent to which spatial contextual modulation affects high-level visual processing remains largely unexplored compared with low-level visual processing. The sensory coding of higher and lower level visual features can often be explained with respect to similar concepts, such as population coding and sensory gain control operating in parallel at different stages of visual processing (e.g., Suzuki, 2005). However, spatial receptive fields are likely to be larger for sensory neurons that respond selectively to high-level visual attributes, such as faces and bodies, compared with those responding to low-level visual attributes such as orientation. Thus, the extent to which sensory interactions that are thought to mediate spatial contextual modulation in lower level vision (e.g., lateral inhibition between neurons coding for orientation in neighboring areas of visual space) are likely to operate at later stages of visual processing is not obvious. Similarities and differences exhibited in spatial contextual modulation between high-level and low-level visual processing may therefore have implications for understanding the sensory mechanisms responsible. Thus, investigating spatial contextual modulation in high-level vision presents an intriguing avenue for research. Walking direction, being a high-level attribute that is perceived across a continuous dimension of angles, provides a suitable means to examine spatial modulation in high-level visual processing at a level of detail similar to that which has been performed for orientation processing. 
In the current study, we examined the effect of spatial context on perceived walking direction using classic point-light animations (Johansson, 1973) that represent the movement of key features of the body over time. Specifically, this study holds importance in advancing our understanding of how contextual effects modulate the perception of walking direction across space (simultaneous presentation) and time (sequential presentation). Moreover, we aimed to quantify the angular tuning of spatial contextual modulation across a wide range of flanker walking directions. In Experiment 1, we compared the direction and magnitude of spatial and temporal contextual effects using a within-subjects design and identical test stimuli. In Experiment 2, we measured the angular tuning of the spatial effect as a function of flanker walking direction. To foreshadow our results, we found that spatial contextual modulation is assimilative across the full range of flanker walking directions, in contrast to the repulsive effects of adaptation to walking direction. However, similarities in the peak tuning of these effects suggest that spatial and temporal contextual modulation can be explained as different sensory operations (namely, summation of signals from target and flanker walkers vs. sensory gain control) operating on the same sensory channels. 
Experiment 1. Comparison of spatial and temporal contextual effects on walking direction
Experiment 1 included two parts. The spatial context task was designed to assess the spatial contextual modulation of walking direction, and the adaptation task was a replication of one of our previous studies (Chen et al., 2023) with adapting directions of ±30°. The adaptation phase was included to investigate the effect we observed in the previous study in a larger sample size and to allow a within-subjects comparison of the relative magnitude of spatial and temporal (adaptation) contextual effects. 
Methods
Participants
The participants were 30 undergraduates (12 males, 18 females), with a mean ± SD age of 19.8 ± 3.7 years, who participated in the experiment for course credit. Two additional participants completed the experiment but were excluded from the analysis for not completing the task as instructed. The target sample size of 30 participants was determined with a power analysis performed using G*Power 3.1. The expected effect size used in the power analysis was based on our previous study (Chen et al., 2023) on adaptation in walking direction (two-tailed; Cohen's d = 0.544; α = 0.05; 1 – β = 0.80; required sample size, 29) to help ensure adequate power to detect a perceptual aftereffect in the adaptation task used in the current experiment. All participants were naïve as to the purpose of the experiments and had normal or corrected-to-normal vision. 
Apparatus and stimuli
Stimulus presentation was controlled in MATLAB (MathWorks, Natick, MA) using Psychtoolbox (Brainard, 1997) on a 32-inch Display++ LCD Monitor (1920 × 1080-pixel resolution and 120-Hz refresh rate; Cambridge Research Systems, Rochester, UK). Prototypical walking action was obtained from the Carnegie Mellon University motion-capture database (http://mocap.cs.cmu.edu) and displayed as point-light stimuli using the Biomotion Toolbox (van Boxtel & Lu, 2013). Point-light animations of human walkers were shown in the middle of the screen as white dots (120 cd/m2) on a black background at a viewing distance of 57 cm in a darkened room, such that 1 cm on screen subtended 1° of visual angle at the observer, and each pixel subtended 2.2 minutes of arc. The number of dots on the body of each point-light walker was 41, and the dots were anti-aliased circles set to 1-pixel diameter. The animation data in each point-light walker were a representation of where the joints were located over time in three-dimensional (3D) space, and so could be rotated in 3D to precisely manipulate the horizontal walking angle relative to the viewer. The speed of the point-light walker was kept constant at one full step cycle per second. 
Experimental design
Spatial context task
In the spatial context task (Figure 2), the test stimuli (8° in height) were presented in the center of the screen flanked by two other walker stimuli. The two flanking stimuli were generated using the same method as the test stimuli and presented left and right of the central test walker at a distance of 4.6° from the center of the screen. The two flankers had the same size (8° in height) as the center walker and were presented as intact walkers or scrambled dots according to the experimental condition. The scrambled stimuli were created by scrambling the spatial location and temporal phase of the dots from an intact walker. Each dot of a scrambled stimulus started at a random frame within each animation, varying within a range of ±50 pixels along the x-axis and ±200 pixels along the y-axis. 
Figure 2.
 
(A) Illustration of different conditions in the spatial context task in Experiment 1. Shown from top to bottom are the test stimulus presented alone in the center of the screen, the center test stimulus flanked by two other intact walker stimuli (walking toward −30°), and the center test stimulus flanked by two other scrambled stimuli. (B) Mean illusion as a function of the flanker direction in the spatial context task. The stimulus orientation perceived as walking directly toward the observer was estimated by finding the PSE between walking directions that the participant judged as leftward versus rightward. The magnitude of the illusion is reported as the difference in the PSEs between the test stimulus presented with and without flankers such that illusions of the opposite sign as the flanker direction correspond to perceptual assimilation. The error bars represent ±1 SEM across participants for each flanker direction. (The plot of the mean PSE as a function of the walking direction can be found online at the OSF repository.) (C) Mean aftereffect as a function of adapting walking direction. Aftereffects of the same sign as the adapting direction correspond to perceptual repulsion. The error bars represent ±1 SEM across participants for each adapting direction.
Figure 2.
 
(A) Illustration of different conditions in the spatial context task in Experiment 1. Shown from top to bottom are the test stimulus presented alone in the center of the screen, the center test stimulus flanked by two other intact walker stimuli (walking toward −30°), and the center test stimulus flanked by two other scrambled stimuli. (B) Mean illusion as a function of the flanker direction in the spatial context task. The stimulus orientation perceived as walking directly toward the observer was estimated by finding the PSE between walking directions that the participant judged as leftward versus rightward. The magnitude of the illusion is reported as the difference in the PSEs between the test stimulus presented with and without flankers such that illusions of the opposite sign as the flanker direction correspond to perceptual assimilation. The error bars represent ±1 SEM across participants for each flanker direction. (The plot of the mean PSE as a function of the walking direction can be found online at the OSF repository.) (C) Mean aftereffect as a function of adapting walking direction. Aftereffects of the same sign as the adapting direction correspond to perceptual repulsion. The error bars represent ±1 SEM across participants for each adapting direction.
We included three different conditions in the spatial context task: a walker alone in the center of the screen, a walker with two intact flanking walkers, and a walker flanked by two sets of scrambled dots; in intact and scrambled conditions, one flanker was always positioned to the left of the target and one to the right of the target. The same point-light walker stimulus was used for both target and flankers; however, the intact flankers were presented at a different phase of the animation to that of the target, such that flankers were always in synchrony with each other but were never synchronous/in-step with the target. Stimulus duration was 500 ms. Participants were required to perform a forced-choice task to indicate with a button press whether the central walker was heading to their left or right in each trial. The central walker differed in walking direction from trial to trial in the range of 15° to +15° with a precision of 0.1°, where negative angles were used to indicate walking directions to the left of the viewer, and positive angles indicated directions to the right of the viewer. Test direction presented in each trial was governed by a single adaptive staircase, “Psi” (Kontsevich & Tyler, 1999), giving rise to a point of subjective equality (PSE) and associated standard error. The PSE indicated the direction of the test stimulus where the participant was equally likely to respond with “left” or “right.” It served as a precise indicator of the true direction of the test that was perceived to be heading directly toward the viewer. Trials were divided into three runs based on the flanker direction of the intact or scrambled flankers (±15°, ±30°, and ±45°). The scrambled flankers were generated from intact walkers of ±15°, ±30°, and ±45° walking direction according to the corresponding setting of flanker direction. Participants completed 150 trials in each run, during which 30 trials from each of five interleaved conditions (intact flankers left/right direction, scrambled flankers plus/minus direction, no flankers) were presented in a random order. 
Adaptation task
The stimuli in the adaptation task were the same point-light walker stimuli used in the spatial context task but were presented alone in the center of the screen in each frame of the animation. In order to make sure that the adaptor and test stimuli had distinct local motion properties, the height of the adaptor stimulus was set to 10° and the height of the test stimulus was 8° (consistent with the spatial context task). 
In the adaptation task, each participant completed a baseline phase followed by an adaptation phase. During the baseline phase, participants were presented with a set of 60 trials, and their task was to indicate the walking direction of a test stimulus by pressing either the left or right key on the keyboard. The test stimulus was displayed for 500 ms, and a gray fixation marker was shown on the screen until a valid response was made. After each response, there was a 500-ms gap before commencement of the next trial. We used two runs of the adaptive staircase within each phase of the task and then averaged the PSE between them. In the adaptation phase, participants were first presented with eight consecutive adaptor stimuli, each displayed for 4 seconds, with a blank screen of 500 ms between each one. When the initial adaptation period was complete, instructions for the following test were presented on the screen and a key press was required to advance. The test period was similar to the baseline phase, but with the addition of a top-up adaptor being shown for 4 seconds before the test stimulus was presented, and a white fixation point was displayed for 750 ms between each adaptor and test stimulus. The adaptation task involved one of two adapting walking directions: 30° and +30°. Half of the participants were tested for 30°and half for +30°. 
Data analysis
For both Experiments 1 and 2, the initial data processing was performed using custom MATLAB scripts. All of the subsequent statistical analyses were conducted with SPSS Statistics 22 (IBM, Chicago, IL) using one-way or two-way repeated-measures analysis of variance (ANOVA), one-sample t-tests, and paired-samples t-tests where appropriate. Also, t-tests with Holm–Bonferroni corrections were used where appropriate. When necessary, post hoc tests following the ANOVAs were conducted with Holm–Bonferroni correction. The threshold for statistical significance was set at 0.05 (p < 0.05). Greenhouse-Geisser corrections were used if the sphericity assumption was violated. Effect sizes are given as partial η2
Results
Overview of data
In the spatial context task, we examined the influence of spatial context on the perception of walking direction. Participants provided walking direction judgments when the target walker was presented alone or surrounded by two flankers. The flankers were either both intact or scrambled walkers, with different walking angles toward ±15°, ±30°, and ±45°. The results in Figure 2B (n = 30) show the mean effect of perceived walking direction as a function of flanker directions (±15°, ±30°, or ±45°). We calculated the difference between the flanked PSEs and the corresponding target-alone PSEs for each flanker direction, which we refer to as “illusion,” such that a positive illusion indicates a flanked PSE more rightward than the target-alone PSE, and a negative illusion indicates a flanked PSE more leftward than the target alone PSE. As can be seen in Figure 2B, in the “intact flankers” condition, a shift in the PSE opposite the flanker direction occurred, indicating an attractive effect of the flanker on the perceived walking direction of the target. Moreover, the magnitude of illusion across flanker directions tended to be symmetrical around the test direction (0°), with peak magnitude observed at ±30° to ±45°. In the “scrambled flankers” condition, the magnitude of the illusion was close to zero across the flanker directions. This observed pattern of data shows assimilation specifically between the intact flankers and target. Given that the scrambled flankers contain the identical local motion trajectories of individual dots compared with the intact flankers, this suggests that the observed assimilation effect for the latter depends more on the global form of the point-light stimulus than on local motion information. 
In the adaptation task, we investigated the aftereffect of perceived walking direction by adopting adapting directions of 30° and +30°, which produced the largest effect in our previous study (Chen et al., 2023). The mean aftereffects across participants (n = 30 total, n = 15 per adapting direction) are shown in Figure 2C. Aftereffects were determined by calculating the difference between the adapted PSEs and the corresponding unadapted (baseline) PSEs. A positive aftereffect indicates that the adapted PSE was shifted more toward the right than the unadapted PSE, whereas a negative aftereffect indicates a shift toward the left. A shift in the PSE toward the side of the adapting stimulus is consistent with a repulsive perceptual aftereffect. Symmetrical repulsive aftereffects were observed for the two adapting directions, as shown in Figure 2C. This result is consistent with our previous findings in adaptation to walking direction (Chen et al., 2023), demonstrated here in a larger sample size compared with this previous study. 
By comparing Figures 2B and 2C, it is clear that the data resulting from the spatial context and adaptation tasks exhibit opposite patterns in the same participants (and when using the identical test stimuli across tasks). Specifically, there is an attraction effect from spatial contextual modulation of walking direction (Figure 2B) and a repulsion effect from temporal contextual modulation (Figure 2C). 
Statistical analysis
In the spatial context task, a two-way repeated-measures ANOVA was performed on the mean PSE. The two factors were “flanker condition” (intact and scrambled flankers), and “flanker direction” (45°, 30°, 15°, +15°, +30°, and +45°). The main effect of “flanker condition” was not significant, F(1, 29) = 0.917, р = 0.346, ηp2 = 0.031. The main effect of ‘flanker direction” was significant, F(5, 145) = 6.05, р = 4 × 10−5, ηp2 = 0.173. Most importantly, the interaction was highly significant, F(5, 145) = 5.28, р = 1.8 × 10−4, ηp2 = 0.154. Post hoc comparisons, Holm–Bonferroni corrected, showed that for three flanker directions the mean PSE was significantly stronger for intact flanker condition than scrambled flanker condition: for 30°, mean difference = 2.83°, SD = 0.682°, p = 2.6 × 10−4; for +30°, mean difference = 1.63°, SD = 0.734°, p = 0.034; for +45°, mean difference = 3.39°, SD = 1.17°, p = 0.007. The results indicate that the effect of flanker condition on the mean PSE varied depending on the flanker direction. We further conducted four paired-samples t-tests to compare the effect between +15° with +30°/+45° and 15° with 30°/45° flanker directions. The data were calculated as the difference between intact and scrambled flanker conditions for each of the six flanker directions. The results showed a significantly stronger effect for the 30° flanker direction compared with 15°: mean difference = 2.30°, t(29) = 2.62, р = 0.014, Cohen's d = −0.553, indicating tuning of the effect across flanker directions within the range of 15° to 30°. 
We performed one-sample t-tests to test whether the effect under the scrambled condition differed significantly from zero. The results indicate that there was no significant effect for any of the six directions. The outcomes demonstrate that the spatial context effect depends more on global rather than local processing of the surrounding stimuli. 
In the adaptation task, a one-sample t-test was first performed to test whether the aftereffect was significantly different from zero. The aftereffect data used here were generated by calculating the average repulsive aftereffect produced by the adaptation direction of +30° and the repulsive aftereffect produced by the adaptation direction of 30°. The results showed a significant effect: t(29) = 2.49, р = 0.019, Cohen's d = 0.456. This result is consistent with the result we obtained in our previous study on smaller samples (Chen et al., 2023). 
Experiment 2. Tuning of effects across different walking flanker deviation magnitudes
In Experiment 1, we observed an assimilative effect of the spatial context on perceived walking direction, with a degree of tuning apparent across the (limited) range of flanker walking directions tested. It is known that other spatial effects in vision, such as the tilt illusion (Clifford, 2014), demonstrate tuning that depends on the angular difference between the center stimulus and its surrounding stimuli. Experiment 2 was designed to measure the tuning of spatial contextual modulation effects across a wide range of walking directions of the flankers. To account for the tuning effect of the walking flanker deviation magnitude that we observed, we introduced a simple function that describes the characteristics of angular tuning. 
Methods
Participants
The sample consisted of 40 undergraduate students (12 males, 28 females), with a mean age of 18.3 ± 0.6 years. A target sample size of at least 35 participants was chosen prior to data collection based on a power analysis conducted using G*Power 3.1. The expected effect size used in the power analysis was obtained from the data for the spatial context task in Experiment 1 (two-tailed; Cohen's d = 0.630; α = 0.05; 1 – β = 0.95; required sample size, 35). Two additional participants completed the experiment but were excluded from the analysis for not completing the task as instructed. 
Apparatus and stimuli
Stimuli were the same as in the spatial context task from Experiment 1 but were displayed with stereoscopic presentation using a 3D monitor. This was done because some participants reported “flipped” experiences during piloting of the wider test angles used in Experiment 2, which included stimuli walking both toward and away from the viewer (i.e., walking at an angle greater than ±90°). In particular, when viewed on a typical two-dimensional monitor, a point-light stimulus walking away from the viewer could be mistakenly perceived as walking toward the viewer, and vice versa (Vanrie, Dekeyser, & Verfaillie, 2004) (for examples, see the bottom and top panels of Figure 3A). We previously found that these “flipped” experiences are less common when viewing the point-light stimuli stereoscopically (Chen et al., 2023). All 3D stimuli were generated in MATLAB using Psychtoolbox with a binocular disparity of 6° of visual angle. The stimuli were presented on a 19-inch True3Di stereoscopic monitor (Redrover, Seoul, Republic of Korea) with a refresh rate of 60 Hz and pixel resolution of 1680 × 1050. Participants viewed the monitor from a distance of 57 cm through a pair of polarized 3D glasses, such that each eye received a different image from corresponding regions of visual space. 
Figure 3.
 
Stimuli and results for Experiment 2. (A) Examples of the center test stimulus flanked by differing orientations of flankers toward +15°, +90°, and +165° from top to bottom. (B) Data from Experiment 2 averaged across participants (n = 40). Mean illusion as a function of the flanker deviation magnitude from 15° to 165°. The error bars represent ±1 SEM across participants for each flanker deviation magnitude. Asterisks (*) indicate flanker deviation magnitudes for which the mean illusion was significantly different from zero, determined using a Holm–Bonferroni-adjusted alpha threshold. The red curved line represents the best fitted line to the response data, describing the tuned component of the assimilative effect of flankers on perceived walking direction. The dashed line represents the untuned component of the assimilative effect.
Figure 3.
 
Stimuli and results for Experiment 2. (A) Examples of the center test stimulus flanked by differing orientations of flankers toward +15°, +90°, and +165° from top to bottom. (B) Data from Experiment 2 averaged across participants (n = 40). Mean illusion as a function of the flanker deviation magnitude from 15° to 165°. The error bars represent ±1 SEM across participants for each flanker deviation magnitude. Asterisks (*) indicate flanker deviation magnitudes for which the mean illusion was significantly different from zero, determined using a Holm–Bonferroni-adjusted alpha threshold. The red curved line represents the best fitted line to the response data, describing the tuned component of the assimilative effect of flankers on perceived walking direction. The dashed line represents the untuned component of the assimilative effect.
Experimental design
The experimental design was similar to the spatial context task in Experiment 1 except that only two different types of condition were used: a walker alone in the center of the screen and a walker flanked by two other walkers, one on each side. Each participant completed 90 trials in each run, with each condition (flankers plus/minus direction, no flankers) presented 30 times in a random order. The walking direction of the test stimulus across the 30 trials shown for each condition was dictated by the staircase used in Experiment 1. The contextual effect was measured for 11 flanker deviation magnitudes, ranging from 15° to 165° in 15° intervals. The 11 runs were presented in randomized order to each participant. 
Results
Overview of data
In Experiment 2, we investigated the tuning of the spatial context effect across a wide range of flanker walking directions. Figure 3B shows the mean illusion (magnitude and direction) as a function of flanker deviation magnitude across participants (n = 40). For each flanker deviation magnitude between 15° and 165°, the effect of the flankers on the perceived walking direction of the test was calculated by averaging the attractive illusion of the rightward-oriented and leftward-oriented flankers (e.g., ±15°), such that positive values of the illusion measure indicate an assimilative effect. As can be seen in Figure 3B, the magnitude of illusion intensified with an increase in flanker deviation magnitude and peaked at 30°, then weakened as the flanker deviation magnitude further increased, indicating that the magnitude of the illusion tended to vary with the direction difference between the flankers and the tests. 
Statistical analysis
For the illusion data, a one-way repeated-measures ANOVA was first conducted. The main effect of flanker deviation magnitude was not significant, F(10, 390) = 1.53, p = 0.167, ηp2 = 0.038, suggesting that differences in the magnitude of the assimilative effect across flanker walking directions are relatively modest. Additional one-sample t-tests were conducted for each flanker deviation magnitude to identify the directions in which the illusion differed significantly from zero. To determine the significance of the one-sample t-tests, the p values for each test were compared with an alpha threshold, which was adjusted using the Holm–Bonferroni method. Out of the 11 flanker deviation magnitudes, significant effects were observed in seven directions: 15°, t(39) = 4.05, р = 2 × 10−4,Cohen's d = 0.640; 30°, t(39) = 4.10, р = 2 × 10−4, Cohen's d = 0.649; 45°, t(39) = 3.57, р = 0.001, Cohen's d = 0.566; 75°, t(39) = 3.35, р = 0.002, Cohen's d = 0.528; 105°, t(39) = 3.59, р = 0.001, Cohen's d = 0.566; 135°, t(39) = 2.88, р = 0.006, Cohen's d = 0.451; 165°, t(39) = 2.77, р = 0.009, Cohen's d = 0.438. Together, these results show that the surrounding walkers had an effect across a wide range of walking directions. The data illustrated in Figure 3B exhibit a distinct pattern, whereby a strong context effect occurred within a small range of flanking directions near the direction of the test stimulus and appeared weakened beyond this range. 
To capture the unique trend observed in the response data, we employed a Gaussian derivative to fit the data:  
\begin{eqnarray*}f(x)=A\ast x \ast \exp \left(-1/2\left(\frac{x}{\sigma}\right)^{2}\right)+C\end{eqnarray*}
where A controls the overall amplitude of the curve, σ controls the width of the curve, and C shifts the entire curve up or down. 
We fit the function to the averaged data across participants by adjusting the values of the three free parameters and minimizing the sum of squares between the observed data and the predicted values from the fit using the “nlinfit” function in MATLAB. This determined the best-fitting values for the three parameters: (a) the amplitude of the curve, A, which represents the tuned component of the assimilative effect; (b) the vertical offset, C, which represents the untuned component of the assimilative effect; and (c) the parameter σ, which affects the overall shape and characteristics of the curve and corresponds to the flanker deviation magnitude at the peak of the tuned component. The fitted curve is shown in Figure 3B. The best-fitting parameters are C = 0.78°, A = 0.84°, and σ = 31.6°. The fit accounts for 70.5% of the total variance. We further performed bootstrapping on the fits to obtain confidence intervals for these parameters. The bootstrapping procedure involved resampling the participant data with replacement 1000 times, recalculating the mean aftereffect for each condition (flanker deviation magnitude), and refitting the model. The resulting 95% bootstrapped confidence intervals for the parameters of the Gaussian derivative are as follows: A, 0.40–1.44; σ, 21.8–46.4; and C, 0.48–1.05. Importantly, neither the confidence interval for A (magnitude of the tuned component) nor the confidence interval for C (magnitude of the untuned component) includes zero, indicating significant differences from zero for both parameters. The results demonstrate that the shape of the Gaussian derivative function can account well for the tuning of the perceptual assimilation effect across flanker directions, with both tuned and untuned components apparent in the data. 
Discussion
The present study investigated the spatial contextual effect of perceived walking direction in the presence of flankers. We made a comparison between spatial and temporal contextual modulation in Experiment 1. We found an attractive effect in the spatial task, replicating the study by Cheng et al. (2022), whereas a repulsive effect was found in the adaptation (temporal) task, replicating our previous study (Chen et al., 2023). These attractive effects of the spatial context and repulsive effects of the temporal context occurred in the same observers for judgments about the walking direction of the same test stimuli. Comparison with the control condition (scrambled flankers) confirmed that spatial contextual modulation relies on global rather than local processing. In Experiment 2, we found a characteristic tuning effect across flanker directions, in which the magnitude of the illusion changed with the flanker deviation magnitude, with the peak effect occurring at around 30°. We will discuss what these findings suggest regarding the neural mechanisms of spatial contextual modulation in perceived walking direction. 
Tuning of spatial contextual modulation of perceived walking direction
Cheng et al. (2022) recently reported an attractive effect of spatial context in the walking direction. The current study replicated this attractive effect and further examined how the effect is tuned to the surrounding walking direction. In particular, in Experiment 2, we compared the effect across the full 360° range of the flankers’ walking directions. The characteristic tuning we found suggests that the magnitude of the angle between test and flanker directions determines the strength of the attractive effect. Specifically, as can be seen in Figure 3B, within a small range of flanker deviation magnitude near the walking direction of the target stimulus, the effect rapidly increased to a peak, then exhibited a slow decrease as the flanker walking direction increased further, and eventually became stable. By fitting a Gaussian derivative to the data, we identified both tuned and untuned components of the assimilative effect in the angular tuning profile. 
How can the tuning of the spatial context effect be understood with respect to the underlying neural mechanisms? The schematic in Figure 4 illustrates how the angular tuning profile of the spatial context effect might have arisen with reference to the activation of neurons in the visual system that respond to the (perceived) walking direction of a presented stimulus. In particular, the figure depicts hypothetical population response profiles (i.e., the excitatory responses occurring across a population of direction-tuned neurons to a given stimulus walking direction). As depicted in the figure, in response to a given directional stimulus, the population of neurons exhibits a “hill” of activity, with the location of the hill indicating the direction of motion. It is assumed that the neurons in the population have similar individual tuning curves (i.e., the same direction bandwidth) but different preferred directions spanning the full 360° of possible walking directions. When flankers are added at another location within the spatial receptive field of the same neural population, they provide excitatory input that shifts the hill of activity to an extent that depends on both the difference in target-flanker direction and the bandwidth of individual neurons (i.e., the width of their tuning across walking directions). This account assumes that, despite their spatial separation on screen, the flanker and target walkers fall within the same spatial receptive field of neurons coding for walking direction. The simultaneous presentation of the flanker and target walkers results in a summative effect on the population response, leading to a nonlinear dependence of the perceived walking direction of the target on the angle of the flankers. By measuring the shift in the perceived walking direction of the target as a function of the difference between the target stimulus and flanker, the direction bandwidth of the neurons in the population can be inferred and hence the minimum number of such neurons necessary to span the full 360° of possible walking directions. 
Figure 4.
 
Schematic illustration of hypothetical population response profiles. The figure illustrates the response of a hypothetical population of direction-tuned neurons as a function of the neuronal preferred direction. The predicted population responses to a target stimulus with 0° walking direction (solid black line), flankers (solid blue line), and target with flankers (solid red line) for flanker directions of 0°, 15°, 30°, 45°, and 60° are displayed from top to bottom. The black dashed line indicates the peak population response when the target is presented alone; the red dashed line indicates the peak when the target is presented with flankers. The shift in the position of the peak when flankers are present versus absent provides a prediction of the magnitude of the assimilative effect on the perceived walking direction of the target stimulus. Importantly, summation of the responses to the test and flankers only causes a shift in the position of the peak population response when the walking direction of the flankers is near enough to the test. In this example, the predicted assimilative effect peaks for 30° flankers (and occurs more weakly for flankers with walking direction either less averted or more averted than 30°). This dependence on the angular difference between the flankers and target is related to the individual tuning curves of neurons in the population, such that a given neuron may respond strongly to the walking direction of the target but also respond weakly to the (different) walking direction of the flanking stimulus, and thus the predicted assimilative effect varies with the width of individual neuronal tuning curves. As a result, characteristics of neuronal tuning can be inferred from the tuning of behavioral effects across flanker walking directions.
Figure 4.
 
Schematic illustration of hypothetical population response profiles. The figure illustrates the response of a hypothetical population of direction-tuned neurons as a function of the neuronal preferred direction. The predicted population responses to a target stimulus with 0° walking direction (solid black line), flankers (solid blue line), and target with flankers (solid red line) for flanker directions of 0°, 15°, 30°, 45°, and 60° are displayed from top to bottom. The black dashed line indicates the peak population response when the target is presented alone; the red dashed line indicates the peak when the target is presented with flankers. The shift in the position of the peak when flankers are present versus absent provides a prediction of the magnitude of the assimilative effect on the perceived walking direction of the target stimulus. Importantly, summation of the responses to the test and flankers only causes a shift in the position of the peak population response when the walking direction of the flankers is near enough to the test. In this example, the predicted assimilative effect peaks for 30° flankers (and occurs more weakly for flankers with walking direction either less averted or more averted than 30°). This dependence on the angular difference between the flankers and target is related to the individual tuning curves of neurons in the population, such that a given neuron may respond strongly to the walking direction of the target but also respond weakly to the (different) walking direction of the flanking stimulus, and thus the predicted assimilative effect varies with the width of individual neuronal tuning curves. As a result, characteristics of neuronal tuning can be inferred from the tuning of behavioral effects across flanker walking directions.
In a previous study that modeled the effect of adaptation on the sensory coding of walking direction (Chen et al., 2023), we fitted a population coding model similar to that which underlies the schematic presented in Figure 4 but with sensory adaptation modeled as a selective change in the gain on direction-selective neurons (or sensory channels) following prolonged exposure to an adapting stimulus. We found that the tuning of perceptual aftereffects provided insights into the width and number of direction-selective channels involved in sensory coding of walking direction. Specifically, we estimated that the width of these channels was approximately 60° full-width at half height, such that at least six of these channels would be necessary to cover the full 360° range of walking directions. In the current study, the characteristic tuning of spatial-context effects also provides insights into the width of the involved channels, as described in the previous paragraph, and the current data imply a channel structure consistent with the tuning of perceptual aftereffects measured in Chen et al. (2023). In particular, the best-fitting parameter σ, with a value of 31.6°, corresponds to a channel width of approximately 74° full-width at half height. The width of the tuning for spatial effects appears consistent with the interaction of signals from test and flankers with a single channel. This similarity in the peak tuning across inducer walking directions in the adaptation and flanker tasks is consistent with these qualitatively different perceptual effects being mediated via the same direction-selective sensory channels. 
The untuned component of the assimilative effect may be partly due to response bias, as the direction of surrounding stimuli has the potential to bias the participants’ response, regardless of any perceptual effects. Additionally, the untuned component may be attributed to the decisional stage. According to the response competition paradigm (Eriksen, 1995), when making a left/right decision in the presence of (irrelevant) left/right walking flankers, such interference could occur at the decisional rather than the perceptual stage. In the study by Thornton and Vuong's (2004), they examined the perception of a central target walker (±90°) when flanked by two walkers in a linear configuration or more in a clock-face configuration. These flankers were walking either congruently (±90°) or incongruently (±90°) with the direction of the target. The authors found that, when the direction of the central target walker was incongruent with the flankers, participants exhibited slower decision making compared with congruent conditions. An unbiased two-interval procedure used in the measurement of tilt illusion (Patten & Clifford, 2015) could be employed in future studies to test these hypotheses. Specifically, to avoid response bias, participants would be required to respond to stimuli presented in two sequential temporal intervals, indicating the interval in which the walking direction of the target walker is closest to direct. The flankers in each interval would walk at the same magnitude of angular deviation, leftward in one interval and rightward in the other. This procedure would help control for response bias by making the response (first vs. second interval) orthogonal to the stimulus manipulation (leftward vs. rightward flanker walking direction). 
Attractive versus repulsive effects of spatial contextual modulation
For low-level attributes, such as orientation, the spatial context can have a repulsive effect on perception of a target as well as an assimilative effect. For example, in the tilt illusion, an oriented surround stimulus exhibits both repulsive and attractive effects on the perceived orientation of a central target, depending on the difference in angle between the test and surrounding stimuli (Clifford, 2014). However, in our experiments that examined contextual modulation of perceived walking direction by the spatial context, we observed attraction over a wide range of directions of the surrounding stimulus, without any indication of repulsive effects of the flanking walkers. This is in accordance with research investigating other high-level contextual effects, such as facial attractiveness (Walker & Vul, 2014) and facial age (Awad et al., 2020), which only observed attractive effects of the spatial context (albeit without measuring tuning across a wide range of inducers). The difference in contextual modulation presented in low-level and high-level attributes suggests that the processing of high-level walking direction in contextual modulation might be mediated by interactions between representations of the high-level attributes, rather than simply inherited from low-level processing interactions. Neurophysiological studies in macaque found neurons sensitive to biological motion stimuli in the superior temporal polysensory area (Bruce Desimone, & Gross, 1981) and lower superior temporal region (Nelissen, Vanduffel, & Orban, 2006). In contrast, by recording neurons from the monkey's visual cortex, Hubel and Wiesel (1968) revealed that the primary visual cortex (V1) is the first site of visual processing hierarchy where neurons consistently exhibit selectivity for orientation. Importantly, it has been observed across many studies that the receptive fields in low-level visual processing tend to be relatively small compared with neurons at later stages of visual processing that respond to more complex perceptual features such as biological motion (Spillmann, Dresp-Langley, & Tseng, 2015). There is also some behavioral evidence in humans consistent with relatively large receptive fields for mechanisms in the visual system encoding perceived walking direction—namely, that perceptual aftereffects following adaptation to walking direction generalize to test stimuli presented in regions of the visual field separated by 5° of visual angle or more (Jackson & Blake, 2010). Thus, larger receptive fields of neurons processing walking direction might enhance assimilation due to multiple stimuli falling within the same receptive field. Indeed, the model presented in the previous section accounts for the tuning of the assimilation effect under the assumption that the test and flanker stimuli fall within the same spatial receptive field of neurons coding for walking direction, having a summative effect on the population response. In contrast, smaller receptive fields in earlier stages of the visual system, such as V1, may offer more scope for competitive local interactions between neurons representing basic visual features in adjacent areas of space, mediated by lateral inhibition. Similarly, the repulsive effect observed in tilt illusion has been explained in terms of lateral inhibition between neural mechanisms tuned to different orientations (Blakemore et al., 1970). 
The magnitude of attractive effect observed in Experiment 2 appears comparatively smaller than that observed in Experiment 1, as can be seen in Figures 2B and 3B. However, independent samples t-tests were conducted to compare the attractive effect between Experiment 1 and 2 across flanker deviation magnitudes of 15°, 30°, and 45°, and the results indicate that the differences between the two experiments are not significant: for 15°, Experiment 1 versus Experiment 2 (mean difference = 0.52°), t(36) = 0.967, р = 0.349; for 30°, Experiment 1 versus Experiment 2 (mean difference = 1.03°), t(25) = 1.52, р = 0.140; for 45°, Experiment 1 versus Experiment 2 (mean difference = 1.14°), t(121) = 1.34, р = 0.183. The primary difference between Experiments 1 and 2 lies in the presentation of stimuli. Stimuli in Experiment 2 were presented stereoscopically in 3D, whereas in Experiment 1 they were presented in two dimensions. This discrepancy may account for the observed differences, as the additional depth cues provided by binocular disparities offer more reliable and robust information for participants to perceive walking direction (Bülthoff, Bülthoff, & Sinha, 1998; Jackson & Blake, 2010). 
Spatial versus temporal contextual modulation
In Experiment 1, we found that the same observers experienced an attractive effect of the spatial context on perceived walking direction while also exhibiting a repulsive effect of the temporal context on perceived walking direction. This is consistent with the direction of effects reported previously in the small number of studies that have examined the effect of adaptation (Chen et al., 2023) and spatial context (Cheng et al., 2022) on perceived walking direction, but here it was demonstrated in the same observers using the same test and adapting/flanking stimuli. The opposing direction of effects exerted by the temporal context and spatial context suggests that these two effects are likely to be driven by fundamentally different neural processes resulting in differences in magnitude and direction, albeit likely within the same mechanisms (as evidenced by similarities in the inferred width of the sensory channels coding direction, as discussed earlier). Specifically, the repulsive effect of adaptation can be explained as a temporary and selective change in the gain on sensory channels responsible for encoding walking direction, which biases the population response of the system away from the direction adapted to (Chen et al., 2023). And, the assimilative spatial effect can be attributed to the summation of excitatory responses due to the presence of multiple stimuli that fall within the same receptive field, as described earlier. 
By comparing the contextual effects of low-level attributes such as brightness, size, orientation, and motion, Yang, et al. (2013) found relatively little correlation among them, indicating distinct underlying mechanisms. The direction of adaptation effects is found to be consistent for both low-level and high-level stimuli, as evidenced by repulsive effects observed in tilt adaptation (Clifford, 2014) and walking direction adaptation (Chen et al., 2023), respectively. These effects can both be explained by the adjustment of gain on neural populations coding for orientation and walking direction, whereas the opposite direction of effects observed in spatial context between tilt illusion and walking direction suggests the existence of a more conceptually distinct mechanism underlying the effect of spatial context for low-level and high-level stimuli. In future work, it would be particularly interesting to investigate whether contextual effects in high-level attributes, such as facial age, gaze direction, and walking direction, exhibit correlations. 
Local versus holistic effects of biological motion
We observed attractive context effects on walking direction perception, which is consistent with recent findings from Cheng et al. (2022). However, we found a slightly different result under the scrambled condition. In the study by Cheng et al. (2022), they tested the spatial context effect using ±15° oriented flankers and employed scrambled surrounding stimuli to investigate the impact of local motion. They found a marginally significant effect, concluding that local motion played a partial role in the contextual attraction effect. The marginally significant attractive effects reported by Cheng et al. (2022) were 0.20° and 0.27° for leftward and rightward walking flankers, respectively, under the scrambled condition. As can be seen in Figure 2B, our observed attractive effect under the scrambled flanker condition at ±15° flanker direction was comparable to these values (0.40° for leftward and 0.32° for rightward), albeit not statistically significant. In our study, as shown in Figure 2B and further statistical analysis, the significantly larger effects observed for intact flankers compared with scrambled flankers for ±30° and +45° flanker directions indicate that the contextual modulation of walking direction depends more on a global level conveyed by the surrounding visual features at these three flanker directions; the non-significant effect found in the scrambled flankers condition constitutes a lack of evidence for dependence on local level cues. There is research supporting the view that contextual modulation relies more on processing of coherent (global) pattern. Herzog and Koch (2001) devised a novel illusion known as the “shine-through illusion,” in which a briefly presented vernier (two abutting lines), followed by a standard grating (comprising more than seven aligned elements), creates a subjective perception of the vernier shining through the grating. This illusion serves as a sensitive tool for investigating contextual effects between the center (target) and surrounding stimuli. Herzog and Fahle (2002) employed the shine-through illusion, and by varying the orientation, number, and intensity of the contextual elements they did not observe any consistent differences in the performance of vernier discrimination, concluding that the contextual modulation cannot be solely explained by local low-level features but by the global spatial structure of the context. 
Conclusions
In summary, our study confirms the attractive effect found in the contextual modulation of perceived walking direction (Cheng et al., 2022) and provides further characterization and comparison between spatial and temporal contextual effects. We measured the angular tuning of spatial contextual modulation, finding that the effect of the surround on perception of a central target changes in magnitude with the direction of the surrounding walkers but is consistently assimilative rather than repulsive, and we discovered the existence of tuned and untuned components of this effect by fitting the resulting data. The tuning of the assimilative effect can be explained with reference to the summation of excitatory responses caused by the target and flanking walkers across a population of neurons tuned to walking direction but differing in preferred direction. Given that the untuned component we observed may reflect a systematic response bias, future research may benefit by using an unbiased method for measuring the contextual effect of high-level attributes such as walking direction. Based on the current results, we can conclude that spatial and temporal contextual modulations of walking direction are likely mediated by dissociable neural processes, resulting in assimilative versus repulsive effects on perception, respectively, for the same motion stimuli when measured in the same observers. Interestingly, however, the similarity that we observed in the peak tuning of spatial and temporal effects across the walking direction of the inducers suggests that both effects may operate on the same population of sensory neurons coding for walking direction. Mechanisms underlying the assimilative effect for walking direction also likely differ significantly from those mediating spatial interactions in lower level vision, reflected in assimilative effects of flankers on perceived walking direction compared with the repulsive effects that tend to occur in the tilt illusion, for example. This could be a consequence for spatial contextual modulation produced by larger spatial receptive fields in higher level vision compared with lower level vision. 
Acknowledgments
Supported by Australian Research Council Discovery Projects (DP200100003 to CJP and CWGC; DP160102239 to CWGC) and by an Australian Government Research Training Program Scholarship (to CC). Data, analysis scripts, and plot are available online at the Open Science Framework site (https://osf.io/ygrhn/?view_only=be9020d6f6d0457aab588defb1e11581). 
Commercial relationships: none. 
Corresponding author: Chang Chen. 
Email: chang.chen2@unsw.edu.au. 
Address: School of Psychology, University of New South Wales, Sydney, NSW 2052, Australia. 
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Figure 1.
 
(A) Illustration of the classic Ebbinghaus illusion (contrast effect). The central circle surrounded by smaller circles (on the right side) appears larger than the one of the same size surrounded by larger circles (on the left side). (B) Illustration of an assimilation effect. The inner of two concentric circles appears larger than a single circle of the same size as the inner one.
Figure 1.
 
(A) Illustration of the classic Ebbinghaus illusion (contrast effect). The central circle surrounded by smaller circles (on the right side) appears larger than the one of the same size surrounded by larger circles (on the left side). (B) Illustration of an assimilation effect. The inner of two concentric circles appears larger than a single circle of the same size as the inner one.
Figure 2.
 
(A) Illustration of different conditions in the spatial context task in Experiment 1. Shown from top to bottom are the test stimulus presented alone in the center of the screen, the center test stimulus flanked by two other intact walker stimuli (walking toward −30°), and the center test stimulus flanked by two other scrambled stimuli. (B) Mean illusion as a function of the flanker direction in the spatial context task. The stimulus orientation perceived as walking directly toward the observer was estimated by finding the PSE between walking directions that the participant judged as leftward versus rightward. The magnitude of the illusion is reported as the difference in the PSEs between the test stimulus presented with and without flankers such that illusions of the opposite sign as the flanker direction correspond to perceptual assimilation. The error bars represent ±1 SEM across participants for each flanker direction. (The plot of the mean PSE as a function of the walking direction can be found online at the OSF repository.) (C) Mean aftereffect as a function of adapting walking direction. Aftereffects of the same sign as the adapting direction correspond to perceptual repulsion. The error bars represent ±1 SEM across participants for each adapting direction.
Figure 2.
 
(A) Illustration of different conditions in the spatial context task in Experiment 1. Shown from top to bottom are the test stimulus presented alone in the center of the screen, the center test stimulus flanked by two other intact walker stimuli (walking toward −30°), and the center test stimulus flanked by two other scrambled stimuli. (B) Mean illusion as a function of the flanker direction in the spatial context task. The stimulus orientation perceived as walking directly toward the observer was estimated by finding the PSE between walking directions that the participant judged as leftward versus rightward. The magnitude of the illusion is reported as the difference in the PSEs between the test stimulus presented with and without flankers such that illusions of the opposite sign as the flanker direction correspond to perceptual assimilation. The error bars represent ±1 SEM across participants for each flanker direction. (The plot of the mean PSE as a function of the walking direction can be found online at the OSF repository.) (C) Mean aftereffect as a function of adapting walking direction. Aftereffects of the same sign as the adapting direction correspond to perceptual repulsion. The error bars represent ±1 SEM across participants for each adapting direction.
Figure 3.
 
Stimuli and results for Experiment 2. (A) Examples of the center test stimulus flanked by differing orientations of flankers toward +15°, +90°, and +165° from top to bottom. (B) Data from Experiment 2 averaged across participants (n = 40). Mean illusion as a function of the flanker deviation magnitude from 15° to 165°. The error bars represent ±1 SEM across participants for each flanker deviation magnitude. Asterisks (*) indicate flanker deviation magnitudes for which the mean illusion was significantly different from zero, determined using a Holm–Bonferroni-adjusted alpha threshold. The red curved line represents the best fitted line to the response data, describing the tuned component of the assimilative effect of flankers on perceived walking direction. The dashed line represents the untuned component of the assimilative effect.
Figure 3.
 
Stimuli and results for Experiment 2. (A) Examples of the center test stimulus flanked by differing orientations of flankers toward +15°, +90°, and +165° from top to bottom. (B) Data from Experiment 2 averaged across participants (n = 40). Mean illusion as a function of the flanker deviation magnitude from 15° to 165°. The error bars represent ±1 SEM across participants for each flanker deviation magnitude. Asterisks (*) indicate flanker deviation magnitudes for which the mean illusion was significantly different from zero, determined using a Holm–Bonferroni-adjusted alpha threshold. The red curved line represents the best fitted line to the response data, describing the tuned component of the assimilative effect of flankers on perceived walking direction. The dashed line represents the untuned component of the assimilative effect.
Figure 4.
 
Schematic illustration of hypothetical population response profiles. The figure illustrates the response of a hypothetical population of direction-tuned neurons as a function of the neuronal preferred direction. The predicted population responses to a target stimulus with 0° walking direction (solid black line), flankers (solid blue line), and target with flankers (solid red line) for flanker directions of 0°, 15°, 30°, 45°, and 60° are displayed from top to bottom. The black dashed line indicates the peak population response when the target is presented alone; the red dashed line indicates the peak when the target is presented with flankers. The shift in the position of the peak when flankers are present versus absent provides a prediction of the magnitude of the assimilative effect on the perceived walking direction of the target stimulus. Importantly, summation of the responses to the test and flankers only causes a shift in the position of the peak population response when the walking direction of the flankers is near enough to the test. In this example, the predicted assimilative effect peaks for 30° flankers (and occurs more weakly for flankers with walking direction either less averted or more averted than 30°). This dependence on the angular difference between the flankers and target is related to the individual tuning curves of neurons in the population, such that a given neuron may respond strongly to the walking direction of the target but also respond weakly to the (different) walking direction of the flanking stimulus, and thus the predicted assimilative effect varies with the width of individual neuronal tuning curves. As a result, characteristics of neuronal tuning can be inferred from the tuning of behavioral effects across flanker walking directions.
Figure 4.
 
Schematic illustration of hypothetical population response profiles. The figure illustrates the response of a hypothetical population of direction-tuned neurons as a function of the neuronal preferred direction. The predicted population responses to a target stimulus with 0° walking direction (solid black line), flankers (solid blue line), and target with flankers (solid red line) for flanker directions of 0°, 15°, 30°, 45°, and 60° are displayed from top to bottom. The black dashed line indicates the peak population response when the target is presented alone; the red dashed line indicates the peak when the target is presented with flankers. The shift in the position of the peak when flankers are present versus absent provides a prediction of the magnitude of the assimilative effect on the perceived walking direction of the target stimulus. Importantly, summation of the responses to the test and flankers only causes a shift in the position of the peak population response when the walking direction of the flankers is near enough to the test. In this example, the predicted assimilative effect peaks for 30° flankers (and occurs more weakly for flankers with walking direction either less averted or more averted than 30°). This dependence on the angular difference between the flankers and target is related to the individual tuning curves of neurons in the population, such that a given neuron may respond strongly to the walking direction of the target but also respond weakly to the (different) walking direction of the flanking stimulus, and thus the predicted assimilative effect varies with the width of individual neuronal tuning curves. As a result, characteristics of neuronal tuning can be inferred from the tuning of behavioral effects across flanker walking directions.
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