Authors: Qi Sun, Xiu-Mei Gong, Lin-Zhe Zhan, Si-Yu Wang, Liang-Liang Dong
Categories: Article, biological motion perception, orientation perception, serial dependence, speed perception, visual perception
Source: Journal of Vision
Doi: 10.1167/jov.23.13.2
Although visual feature estimations are accurate and precise, overall estimation errors (i.e., the difference between estimates and actual values) tend to show systematic patterns. For example, estimates of orientations are systematically biased away from horizontal and vertical orientations, showing an oblique illusion. Additionally, many recent studies have demonstrated that estimations of current visual features are systematically biased toward previously seen features, showing a serial dependence. However, no study examined whether the overall estimation errors were correlated with the serial dependence bias. To address this question, we enrolled three groups of participants to estimate orientation, motion speed, and point-light-walker direction. The results showed that the serial dependence bias explained over 20% of overall estimation errors in the three tasks, indicating that we could use the serial dependence bias to predict the overall estimation errors. The current study first demonstrated that the serial dependence bias was not independent from the overall estimation errors. This finding could inspire researchers to investigate the neural bases underlying the visual feature estimation and serial dependence.
Keywords: visual perception, serial dependence, orientation perception, speed perception, biological motion perception
Accurately estimating visual features is critical for humans' and animals' survival. For instance, accurately perceiving our self-motion direction (i.e., heading) can help us avoid obstacles; accurately perceiving the speed of moving objects can help us avoid unpredictable and sudden dangers; accurately perceiving predators' motion directions can help animals escape from being predated. To make it, perceptual systems have been evolving for millions of years (Martin & Gordon, 2001).
Although the perceptual performances are accurate, they show systematic estimation errors. The most well-known estimation error is the oblique illusion in orientation perception (Appelle, 1972; Caelli, Brettel, Rentschler, & Hilz, 1983; Cicchini, Mikellidou, & Burr, 2017; Furmanski & Engel, 2000; Mikellidou, Cicchini, Thompson, & Burr, 2015; Orban, Vandenbussche, & Vogels, 1984; Wei & Stocker, 2017). Specifically, the cardinal orientations (i.e., horizontal and vertical orientations) can be estimated accurately and precisely, but the orientations tend to be overestimated as the orientations deviate from the cardinal orientations (Gentaz et al., 2001). The systematic estimation errors are also observed in other features (e.g., the center bias) (D'Avossa & Kersten, 1996; Sun, Yan, Wang, & Li, 2022; Sun, Zhang, Alais, & Li, 2020; Wang, Gong, Sun, & Li, 2022; Warren & Saunders, 1995; Xu, Sun, Zhang, & Li, 2022) and peripheral bias (Crane, 2012; Cuturi & MacNeilage, 2013; Gu, Fetsch, Adeyemo, DeAngelis, & Angelaki, 2010) in self-motion direction perception from optic flow, meaning that the perceived self-motion directions are systematically biased toward or away from the straight-ahead direction; the facing-to-viewer bias in biological motion (i.e., BLM) perception (Schouten, Troje, Brooks, van der Zwan, & Verfaillie, 2010; Schouten, Troje, & Verfaillie, 2011; Shen et al., 2018; Vanrie, Dekeyser, & Verfaillie, 2004; Weech, McAdam, Kenny, & Troje, 2014; Weech & Troje, 2018), meaning that the perceived BLM directions are faced observers; the central tendency in color (Olkkonen, McCarthy, & Allred, 2014; Olkkonen & Allred, 2014) and numerosity (Anobile, Burr, Gasperini, & Cicchini, 2019; Pomè, Thompson, Burr, & Halberda, 2021; Xiang, Graeber, Enke, & Gershman, 2021) perception, meaning that the perceived colors or the numerosity sizes are compressed toward the center of stimulus distribution; static bias in motion speed perception (Durgin, Gigone & Scott, 2005; Pelah, Thurrell, & Berry, 2002; Sotiropoulos, Seitz, & Seriès, 2011; Stone & Thompson, 1992; Thompson, 1982; Thompson, Stone, & Swash, 1996; Thompson, Brooks, & Hammett, 2006), meaning that the observers tend to underestimate the motion speeds.
Aside from the systematic estimation error (i.e., overall estimation errors), recent studies have revealed that perceived visual features are systematically biased by previously seen features, named as serial dependence (Fischer & Whitney, 2014; Kiyonaga, Scimeca, Bliss, & Whitney, 2017; see Pascucci et al., 2023 for a review). Fischer and Whitney (2014), for example, showed a serial of oriented Gabors, and after each Gabor, participants rotated a response bar to report their perceived orientation. The results showed that the perceived orientations were systematically biased toward the orientation of previous n^th^ trial (n = 1, 2, etc.). They named the bias as attractive serial dependence, which could help observers keep the temporal continuity of the physical environment. Such attractive serial dependence was also observed in other visual features, such as orientation (Ceylan, Herzog, & Pascucci, 2021; Cicchini et al., 2017; Cicchini, Mikellidou, & Burr, 2018; Fischer & Whitney, 2014; Fritsche, Mostert, & de Lange, 2017; Pascucci et al., 2019; Samaha, Switzky, & Postle, 2019), spatial position (Bliss, Sun, & D'Esposito, 2017; Manassi, Liberman, Kosovicheva, Zhang, & Whitney, 2018), expression, identity, and attractiveness of faces (Kim, 2021; Liberman, Fischer, & Whitney, 2014; Taubert, Van der Berg, & Alais, 2016; Xia, Leib, & Whitney, 2016; Yu, Yang, & Ying, 2023; Yu & Ying, 2021), numerosity (Kim, Burr, Cicchini, & Alais, 2020; Fornaciai & Park, 2018), and self-motion direction (Wang et al., 2022; Xu et al., 2022). In contrast, some studies have found the opposite trend (i.e., repulsive serial dependence meaning that the perceived features of current trials are repelled away from the previously seen features, such as orientation) (Alais, Leung, & Van der Burg, 2017; Kang & Choi, 2015; Bae & Luck, 2017). Researchers generally propose that repulsive serial dependence can help observers maximize the discrimination sensitivity. Recently, Rafiei, Chetverikov, Hansmann-Roth, and Kristjánsson (2021) have pointed out that attractive and repulsive serial dependence can co-exist in visual perception, which are modulated by observers’ attention.
After reviewing the previous studies, we found that few studies systematically investigated the relationship between overall estimation errors and serial dependence. The overall estimation errors are induced by various factors (e.g., stimulus uncertainty, neural fatigue, response methods, and past experience). However, the serial dependence primarily reflects the estimation bias induced by one past event which can be one component of past experience. Therefore one question naturally slipping into our minds is whether serial dependence bias can directly predict the overall estimation error. According to the above logic, we can intuitively conclude that serial dependence bias can predict the overall estimation error. Then, another question is how much of the overall estimation error does the serial dependence bias account for? The account proportion can reflect the dependence strength between the serial dependence bias and the overall estimation error. So far, Sun and his collaborators have conducted two studies to simultaneously examine the overall estimation error (i.e., center bias) and serial dependence in heading perception from optic flow (Sun et al., 2020; Xu et al., 2022). However, they discussed the overall estimation error and the serial dependence bias independently, overlooking their dependent relationship.
In the current study, we systematically investigated whether the serial dependence bias in visual perception could directly predict the overall estimation error by examining the overall estimation errors and the serial dependence biases in the perception of orientation (Experiment 1), speed (Experiment 2), and BLM direction (Experiment 3). In each visual feature, we fitted the serial dependence bias as a function of the overall estimation errors. If the serial dependence were one part of the overall estimation errors, then the fitting function would be significant. In addition, the fitting function could give us the proportion of serial dependence bias in the overall estimation error. Revealing the dependence between the serial dependence bias and the overall estimation error can provide psychophysical evidence for the claim that the cortical areas involved in the processing of visual features are also engaged in the serial dependence. In addition, the dependence strength can provide clues about the involvement strength of these cortical areas in the serial dependence.
Twenty-one participants (nine males, 12 females; age 18–25 years) were recruited from Zhejiang Normal University. All participants were naïve to the experimental purpose and had normal or corrected-to-normal vision. The experiment was approved by the Scientific and Ethical Review Committee in the Department of Psychology of Zhejiang University. We got participants’ written consent forms before they conducting the experiment.
The orientation stimuli were Gabor patches (Figure 1, a Gaussian windowed sinusoidal grating with 1.5% Michelson contrast and 0.023 cycles/degree; 8.27° H × 8.27° V); presented on a gray background (RGB: [110 110 110]; 67.45 cd/cm^2^). The orientation of each Gabor was randomly selected from a range of [–85°, 90°] with a step of 5°, a total of 36 orientations.
Figure 1. (A) Gabor patches with different orientations were used in the orientation estimation experiment. Negative and positive values indicated the orientations were counter-clockwise or clockwise relative to the vertical Gabor (i.e., 0°). (B) Mosaic mask display used in orientation and speed estimation tasks. (C) Response display used in orientation estimation task in which a gray bar was positioned on the display center. Participants adjusted the orientation of the bar to indicate their perceived orientation.
The displays were programmed in MATLAB using the Psychophysics Toolbox 3. The monitor was a 27-inch Dell monitor (resolution: 2560 H × 1440 V pixels; refresh 120 Hz), the graphics card was NVIDIA GeForce GTX 1660Ti.
On each trial, a Gabor was presented for 50 ms (inspired by Wei and Stocker (2016), internal noise could be modulated by changing the presentation time of stimulus. A short duration of 50 ms made the activity of the neurons less active and thus provided more space to manipulate the internal noise), followed by a 200-ms blank display. Then, a 300-ms mosaic mask (Figure 1B) was presented. After the mask, a response bar (Figure 1C) was on the display. The center of the bar was fixed on the display center. Participants used a mouse to adjust the bar's orientation to match their perceived Gabor orientation and click the left button to confirm their estimates. After a 200 ms-blank display, the next trial started.
The current experiment consisted of 1080 trials (36 orientations × 30 trials). All trials were randomly presented and divided into 15 blocks. Before conducting the experiment, participants’ heads were fixed by a chin-rest. The viewing distance was 56 cm. Additionally, each participant was given 20 practice trials randomly selected from the above 1080 trials to familiarize the participants with the experiment. The whole experiment lasted for about 50 minutes.
We recorded participants’ perceived orientation and calculated the overall estimation error, which was the difference between the perceived orientation and actual orientation. If participants failed to estimate the orientation accurately, then the overall estimation error would be significantly different from zero. In particular, if the overall estimation error shared the same sign as the actual orientation, then participants overestimated the orientation; in contrast, if the sign of the overall estimation error was opposite to the actual orientation, then participants underestimated the orientation. According to the previous studies, it was expected an oblique bias in the current experiment, showing that the orientations smaller than 45° were overestimated; the orientations larger than 45° were underestimated. A one-sample t-test was used to examine this proposal with 0° as the baseline.
To examine whether serial dependence was present in the orientation estimation, we first calculated the relative orientation. The relative orientation was the difference in the actual orientation between the previous first trial (n − 1^th^ trial, n = 2, 3, etc.) and the current trial (nth trial). Then, the estimation bias was the mean estimation error of the current trials in each relative orientation. For example, the −170° relative orientation had two the difference between the −85° previous trial and the 85° current trial (i.e., −85° to 85° = −170°) or the difference between the −80° previous trial and the 90° current trial (i.e., −80° to 90° = −170°), so the orientation bias was the mean of orientation errors of 85° and 90° current trials. Like the previous studies (e.g., Frische & Whitney, 2014), we fitted the estimation bias (EB) as a first derivative of Gaussian function (DoG) of the relative orientation (RO), given
in which α~EB~ indicates the amplitude of the DoG curve. In addition, a positive α~EB~ indicates that the perceived orientation is biased toward the previously seen orientation, showing an attractive serial dependence; in contrast, a negative α~EB~ indicates that the perceived orientation is repelled away from the previously seen orientation, showing a repulsive serial dependence. To test the significance level of α~EB, a bootstrapping test was conducted. Specifically, we sampled the data with replacement for 10,000 times and fitted the sampled data with Equation 1, which generated a distribution of αEB~ and got its 95% confidence interval (CI). If 0 was smaller than the lower bound of the 95% CI, then α~EB~ was positive, indicating an attractive serial dependence; vice versa.
In the above data analysis, the independent variable of overall estimation error was the actual orientation, whereas the independent variable of serial dependence bias was the relative orientation. If we wanted to develop the relationship between the overall estimation error and serial dependence bias, the independent variables should be consistent between the two analyses. Therefore we grouped all participants’ feature estimates in each experiment. We first selected the current trials with the same orientation as the previous first trials. Then the mean estimation errors of these trials were calculated, serving as the baseline errors (BE). After that, we chose the current trials whose orientations differed from the previous 1^st^ trials and calculated their mean estimation errors, which was named as the edited overall estimation errors (EOEE). Finally, we calculated the residual estimation error (REE) by using the EOEE to minus the BE. The REE could be proposed to be purely induced by serial dependence. If the estimation error induced by serial dependence was one part of the overall estimation errors, we would find some common patterns between the residual estimation error and the edited estimation error.
To capture the trends of the EOEE against the AO, we fitted a cubic function, given by Equation 2:
and to capture the trends of the REE against the AO, we fitted a linear function, given
in which α~REE~ was the slope. A negative α~REE~ means that the fitting line passes through the second and fourth quadrants of the coordinate. When the actual orientation of current trial is counter-clockwise (x-axis, e.g., −85°), there are more previous trials with clockwise orientations (e.g., −80° to 90°) than orientations (−85°). If the perceived orientation is biased toward the clockwise orientation, then there was a positive residual estimation error (y-axis), showing an attractive serial dependence. In contrast, a positive α~REE~ shows a repulsive serial dependence.
Finally, to examine whether the serial dependence bias could predict the overall estimation error, we fitted the EOEE as a linear function of the REE, given
in which Sf was the slope. If the serial dependence bias were one part of the overall estimation error, the linear function could fit the data well. Meanwhile, the R^2^ of the linear function could suggest how much error the serial dependence could explain the overall estimation error.
Before examining the relationship between the overall estimation errors and the serial dependence bias, we examined how overall estimation errors (the difference between perceived and actual features) changed with actual features, and whether serial dependence was present in the orientation perception. Figure 2A plots the overall estimation error against the actual feature and clearly shows that the orientations within the range (−45°, 45°) are systematically overestimated, whereas the orientations beyond that range are systematically underestimated. One sample t-test showed that the orientations (±30° to ±5°, 35° to 45°) were all significantly overestimated (areas with solid rectangles in Figure 2A) (ts(20) > 2.38, ps < 0.027); the orientations (±60° to ±85°, −45° to −55°) were all significantly underestimated (areas with dashed rectangles in Figure 2A) (ts(20) > 2.62, ps < 0.016). These results indicated an oblique illusion in our orientation estimation task, consistent with the previous studies (Appelle, 1972; Caelli et al., 1983; Furmanski & Engel, 2000; Gentaz et al., 2001; Orban et al., 1984; Wei & Stocker, 2017).
Figure 2. Results of orientation estimation. (A) The overall estimation error is against the actual orientation. The dots are the mean overall estimation error averaged across all participants. Error bars are the standard error across all participants. Areas with rectangles indicate the overall estimation errors are significantly different from zero (one sample t-test). (B) The estimation bias is against the relative orientation – the difference in the actual orientation between the previous first trial and the current trial. The solid red line is the best fitting result of DoG function (Equation 1). (C) The edited overall estimation error against the actual orientation. The blue squares correspond to participants’ raw data. The light blue dots are the mean edited overall estimation error. The solid blue line is the best fitting result of the cubic function (Equation 2). (D) The residual estimation error is against the actual orientation. The red squares correspond to participants’ raw data. The light red dots are the mean residual estimation error. The solid red line is the best-fitting result of the linear function (Equation 3).
Figure 2B plots the estimation bias against the relative feature. A DoG curve well explained more than 41% of the estimation bias. Especially, the amplitude of the DoG curve was significantly larger than 0 (95% CI, 2.58-4.82), suggesting that an attractive serial dependence was present in orientation estimation.
As mentioned in Data analysis, the above analysis hindered us to develop the relationship between the overall estimation errors and the estimation biases due to the different independent variables (actual orientation vs. relative orientation). Therefore to address the problem, in each experiment, we first selected the current trials that shared the same feature orientations as the previous first trials and calculated the mean estimation errors of these current trials. The estimation errors served as the baseline estimation errors. Next, we selected the current trials whose orientations differed from the previous first trials and calculated the mean estimation errors of these current trials, named as the edited overall estimation errors. Last, we used the edited overall estimation errors to minus the baseline estimation errors to get the residual estimation errors, which were proposed to be purely induced by serial dependence.
Figure 2C plots the edited overall estimation error against the actual orientation. It clearly showed that the result patterns of the edited overall estimation error were similar to the residual estimation error, which were well predicted by our cubic function (Equations 2, R^2^ = 0.94), showing an oblique illusion in the orientation estimation task.
Figure 2D plots the residual estimation error against the actual orientation. A linear function well predicted this trend with a negative slope (α~REE~ = −0.036) (R^2^ = 0.43), indicating an attractive serial dependence. However, the attractive trend seemed to be evidently lower than that in Figure 2B, which implied that the similarity of the consecutively presented features affected the serial dependence. The more similar the features, the more attractive the serial dependence (Cicchini et al., 2018; Fischer et al., 2020; Manassi, Liberman, Kosovicheva, Zhang, & Whitney, 2018; Manassi, Kristjánsson, & Whitney, 2019; Manassi & Whitney, 2022; Turbett, Palermo, Bell, Burton, & Jeffery, 2019; Turbett, Palermo, Bell, Hanran-Smith, & Jeffery, 2021).
Last, the linear function between the edited overall estimation error and the residual estimation error showed that the residual estimation error explained about 21.26% of the edited overall estimation errors (p < 0.018). Therefore we can use the serial dependence bias to deduce the overall orientation estimation error. This result implies that the cortical areas involved in the orientation estimation play a role in the serial dependence in the orientation perception. John-Saaltink, KoK, Lau, and de Lange (2016) found that primary visual cortex (V1) was involved in the serial dependence, supporting our proposal.
Experiment 1 found that in the orientation perception, the serial dependence bias accounted for about 21.26% of the overall estimation error. In the current experiment, we adopted another low-level visual feature, motion speed, to re-examine the finding of Experiment 1.
Eighteen participants (6 males, 12 females; age 18–25 years) were recruited from Zhejiang Normal University. All participants were naïve to the experimental purpose and had normal or corrected-to-normal vision. The experiment was approved by the Scientific and Ethical Review Committee in the Department of Psychology of Zhejiang University. We got participants’ written consent forms before they conducting the experiment.
The stimuli and apparatus were the same as Experiment 1. However, in the current experiment, only a vertical Gabor patch was presented (the Gabor with 0° in Figure 1A). The Gabor was not static but laterally moved at a speed of 0.88°/s, 1.54°/s, 2.20°/s, 2.85°/s, 3.51°/s, 4.17°/s, 4.83°/s ,5.49°/s, or 6.15°/s (Movies 1–4 are examples given in OSF (https://osf.io/kytp3/?view_only=22bdaf9669cf4a8f98779a2b6be4ee8c) for the speeds of 0.88°/s, 3.15°/s, 6.15°/s, and 7.02°/s).
Each trial started with a 200 ms vertical and dynamic Gabor, followed by a 200-ms mosaic mask (Figure 1B). After the mask, participants were asked to move a mouse-controlled vertical probe on a horizontal line. The left and right end-points of the line corresponded to speeds of 0°/s and 7.02°/s. When participants clicked the mouse, a 200-ms blank display was presented, and the next trial started.
The current experiment consisted of 270 trials (9 speeds × 30 trials). All trials were randomly presented. Before conducting the experiment, participants’ heads were fixed by a chin-rest. The viewing distance was 56 cm. Additionally, each participant was given 40 practice trials randomly selected from the above 270 trials to familiarize the participants with the experiment. The whole experiment lasted for about 20 min.
The data analysis methods were similar to Experiment 1, except that we directly calculated the edited overall estimation error (EOEE) and the residual estimation error (REE). We fitted the EOEE or REE as a quadratic function of the actual speed (AS), given
Then, we fitted the EOEE as a linear function of the REE, given by Equation 4. The R^2^ of the linear function indicated the proportion of the overall estimation error explained by the serial dependence bias. Please see Appendix Figures A1A and A1B for the results of overall estimation error and estimation bias.
Figure 3A plots the edited overall estimation error against the actual speed, which is well predicted by a quadratic function (Equation 1, solid blue line, R^2^ = 0.98). The curve showed that when the actual speed was lower than 3.51°/s, the estimation error was positive, suggesting that the speed was overestimated; whereas, when the actual speed was higher than 3.51°/s, the estimation error became negative, suggesting that the speed was underestimated. Together, the data showed that the perceived speeds were systematically compressed towards the 3.51°/s, the center of the range of the speed stimuli, showing a central tendency that has been observed in the other features, such as line length (Ashourian & Loewenstein, 2011; Duffy, Huttenlocher, Hedges, & Crawford, 2010; Huttenlocher et al., 2000), facial expressions (Roberson et al., 2007; Corbin et al., 2017), absolute size (Huttenlocher, Hedges, & Vevea, 2000), time interval (Jazayeri & Shadlen, 2010; Ryan, 2011), and color (Olkkonen & Allred, 2014; Olkkonen et al., 2014).
Figure 3. Results of speed estimation. (A) The edited overall estimation error against the actual orientation. The blue squares correspond to participants’ raw data. The light blue dots are the mean edited overall estimation error. The solid blue line is the best fitting result of the quadratic function (Equation 5). (B) The residual estimation error is against the actual orientation. The red squares correspond to participants’ raw data. The light red dots are the mean residual estimation error. The solid red line is the best-fitting result of the quadratic function (Equation 6).
Figure 3B plots the residual estimation error against the actual speed, which was also well predicted by a quadratic function (Equation 2, solid red line, R^2^ = 0.92). The curve trend is similar to that in Experiment 1 (a linear function with a negative slope, see Figure 2D), showing an attractive serial dependence in the speed perception.
Last, a linear function fitting between the edited overall estimation error and the residual estimation error showed that the residual estimation error explained about 86.49% of the edited overall estimation errors (p < 0.001). Therefore, in the speed perception, we can also use the serial dependence bias to deduce the overall orientation estimation error, implying that the cortical areas involved in the speed estimation play a role in the serial dependence in the speed perception.
In addition, we noticed that the explained proportion in speed perception was more than that in the orientation perception, which might suggest that the cortical areas involved in the speed perception were more engaged in serial dependence than the cortical areas involved in the orientation perception. Moreover, previous studies have shown that some post-perceptual stages (e.g., attention, working memory) were involved in the serial dependence with non-speed stimuli (Bae & Luck, 2017; Bliss et al., 2017; Fischer & Whitney, 2014; Kim et al., 2020; Kiyonaga et al., 2017; Rafiei et al., 2021; Sun, Zhan, Zhang, Jia, & Gong, 2023; Xu et al., 2022). Hence, we boldly proposed that the high-level cortical areas involved in attention and working memory (e.g., prefrontal cortex) (Bichot, Xu, Ghadooshahy, Williams, & Desimone, 2019; Curtis & D'Esposito, 2003; Maunsell & Treue, 2006; Rossi, Pessoa, Desimone, & Ungerleider, 2009; Funahashi, 2017) were more involved in the serial dependence of non-speed stimuli than speed stimuli, which could be tested in future studies.
Experiments 1 and 2 adopted low-level visual features (orientation and speed) and found that the serial dependence bias can explained certain proportion of the overall estimation error. In the current study, we examined whether the above finding could also be applied in the middle-level visual features (e.g., point-light-walker direction).
Thirty-six participants (19 males, 17 females; age 18–24 years) were recruited from Zhejiang Normal University. All participants were naïve to the experimental purpose and had normal or corrected-to-normal vision. The experiment was approved by the Scientific and Ethical Review Committee in the Department of Psychology of Zhejiang University. We got participants’ written consent forms before conducting the experiment.
A serial of point-light-walker (PLW) stimuli (Figure 4A) were presented on a blank display. The PLW stimuli were generated from BML kit (see https://www.biomotionlab.ca/). Each walker was about 3.07° V × 8.58° H and consisted of 16 white dots that indicated walkers’ head, clavicles, bell button, left and right angles, knees, hips, hands, elbows, and shoulder joints. We changed several parameters of the online PLW generator, others were kept default. Specifically, the parameter Camera.Perspective was changed into Disabled; Walker.Speed was set to 1; Camera.Azimuth that controlled the walking direction was randomly selected from a range of [–90° 90°] with a step of 9°. Negative and positive values indicated that the PLW's direction was biased to the left or right sides of the observer. 0° indicated that the PLW moved toward the observer.
Figure 4. (A) Point-light walkers (PLWs) were generated from BML kit (see https://www.biomotionlab.ca/) and moved along different directions. Lines were invisible in the experiment. (B) Participants were asked to report the PLW direction by adjusting a purple probe on a circle.
The monitor was ASUS ROG PG279Q (resolution: 2560 H × 1440 V pixels; refresh 60 Hz), and the graphics card was NIVIDA P620.
On each trial, a PLW was presented at the display center for one second, followed the response display in which a white circle was presented and a purple probe was on the circle (Figure 4B). Participants were asked to move the mouse to change the probe's position on the circle. The bottom point, left and right mid-points corresponded to the 0°, −90° and 90° PLW direction. After participants’ response, the next trial started.
The current experiment consisted of 420 trials (21 orientations × 20 trials). All trials were randomly presented and divided into four blocks. Before conducting the experiment, participants’ heads were fixed by a chin-rest. The viewing distance was 56 cm. Additionally, each participant was given 10 practice trials randomly selected from the above 420 trials to familiarize the participants with the experiment. The whole experiment lasted for about 30 minutes.
The data analysis methods were similar to Experiment 2, except that we fitted the EOEE or REE as a cubic function of the actual PLW direction (AD), given
Then we fitted the EOEE as a linear function of the REE, given by Equation 4. The R^2^ of the linear function indicated the proportion of EOEE explained by the REE. Please see Appendix Figures A1C and A1D for the results of overall estimation error and estimation bias.
Figure 5A plots the edited overall estimation error against the PLW direction, which is well predicted by a cubic function (Equation 7, solid blue line, R^2^ = 0.54). The curve showed that when the PLW moved leftward (negative values), the edited overall estimation error was also leftward, meaning that the perceived PLW direction was biased toward the left lateral motion direction (−90°), vice versa. We named the bias as the lateral-motion bias, different from the center bias in self-motion direction (e.g., Sun et al., 2020; Xu et al., 2022), oblique illusion in orientation (Appelle, 1972; Caelli et al., 1983; Furmanski & Engel, 2000; Mikellidou, Cicchini, Thompson, & Burr, 2015; Orban, Vandenbussche, & Vogels, 1984).
Figure 5. Results of PLW direction estimation. (A) The edited overall estimation error against the actual PLW direction. The blue squares correspond to participants’ raw data. The light blue dots are the mean edited overall estimation error. The solid blue line is the best-fitting result of the cubic function (Equation 7). (B) The residual estimation error is against the actual PLW direction. The red squares correspond to participants’ raw data. The light red dots are the mean residual estimation error. The solid red line is the best-fitting result of the cubic function (Equation 2).
Figure 5B plots the residual estimation error against the actual PLW direction, which is also well predicted by a cubic function (Equation 8, solid red line, R^2^ = 0.71). The overall trend of the curve is similar to that in Experiment 1 (a linear function with a negative slope, see Figure 2D), showing an overall attractive serial dependence in the PLW direction perception. Note that, the attractive serial dependence is evident for the peripheral PLW directions (>45°). When the PLW direction is smaller than 45°, the serial dependence shows a repulsive trend. Previous studies have proposed that the main function of attractive serial dependence is to help observers keep the world stability and continuity; in contrast, the repulsive serial dependence can improve observers’ discriminative abilities (Alais et al., 2017; Gepshtein, Lesmes, & Albright, 2013). Hence, we proposed that for the PLW directions deviating less from the straightforward direction (0°), observers focused more on the discrimination than the world continuity; however, for the peripheral PLW directions, observers focused more on the world continuity than the discrimination.
Again, a linear function fitting between the edited overall estimation error and the residual estimation error showed that the residual estimation error explained about 25.80% of the edited overall estimation errors (p = 0.053, marginally significant). Therefore, in the PLW direction perception, we can also use the serial dependence bias to deduce the overall orientation estimation error, implying that the cortical areas involved in the PLW direction estimation play a role in the serial dependence in the speed perception.
In the current study, we conducted three visual feature estimation experiments (orientation, speed, and point-light-walker direction) to systematically examine whether the serial dependence bias could predict the overall estimation error (the difference between the perceived and actual features). The simple linear regression fitting results showed that the serial dependence bias could explain over 20% of the overall estimation error, directly demonstrating that the serial dependence bias was not independent of the overall estimation error. Especially, the trend of serial dependence bias against the actual features was similar to that of the estimation error against the actual feature, which encouraged us to boldly deduce the serial dependence bias based on the estimation error.
The above finding is one contribution of the current study. Previous studies generally examined the estimation error and serial dependence independently (Sun et al., 2020; Xu et al., 2022). The overall estimation error indicates our perceptual mistakes, a negative aspect of our perception; in contrast, the attractive serial dependence indicates our perceptual stability, a positive aspect of our perception (Fischer et al., 2020; Fornaciai & Park, 2018; Manassi & Whitney, 2022; Manassi et al., 2018). The positive relationship between the overall estimation error and serial dependence bias in the current study highlights that the serial dependence bias can also be a mistake of our visual perception, inspiring researchers to discuss the negative aspects of serial dependence.
In addition, the positive relationship between the overall estimation error and the serial dependence bias indicates that the feature perception and the serial dependence share some common neural basis. In other words, the cortical areas involved in the feature estimation are engaged in serial dependence on these features, which has been demonstrated by John-Saaltink et al. (2016). They found that the primary visual cortex (V1) was involved in the serial dependence and estimation of orientations. However, no study has directly examined the cortical areas, such as V1, V2 (Orban, Kennedy, & Bullier, 1986), and MT (Maunsell & van Essen, 1983) for the speed estimation, and MT/MST and STS for the biological motion perception (Puce & Perrett, 2003), are involved in the serial dependence in these features. Our current study provides direct psychophysical evidence for the involvement of these areas in serial dependence.
Importantly, the proportion of the overall estimation error predicted by the serial dependence bias may indicate the involvement degree of these cortical areas engaging in feature estimation in serial dependence. The more proportion the serial dependence explained, the more engaged these cortical areas. Hence, we could propose that the cortical areas of speed estimation were involved more than the cortical areas of orientation and PLW direction estimation in serial dependence. Moreover, previous studies have showed that serial dependence occurs at both perceptual and post-perceptual stages (Ceylan et al., 2021; Pascucci et al., 2019; Fornaciai & Park, 2020). Some post-perceptual cognitive abilities (e.g., working memory, attention) are involved in serial dependence (Bae & Luck, 2017; Bliss et al., 2017; Frische & Whitney, 2014; Kim et al., 2020; Kiyonaga et al., 2017; Rafiei et al., 2021; Xu et al., 2022; Sun et al., 2023). The cortical areas mentioned in the above paragraph are mainly perceptual areas. The remaining unexplained proportion highlights the involvement of post-perceptual cortical areas in the serial dependence, such as prefrontal cortex, parietal cortex for attention (Behrmann, Geng, & Shomstein, 2004; Bichot et al., 2019; Maunsell & Treue, 2006; Rossi et al., 2009), and prefrontal cortex area for working memory (Courtney, Petit, Maisog, Ungerleider, & Haxby, 1998; Curtis & D'Esposito, 2003; Funahashi, 2017). These proposals can be examined in the future studies.
The current study started with the orientation estimation experiment, which was the most frequently tested visual feature in the serial dependence studies. Whereas, the ranges of the relative orientation in these studies were generally within the range of −90° to 90° (Ceylan et al., 2021; Cicchini et al., 2017; Cicchini et al., 2018; Fritsche & de Lange, 2019; Fischer & Whitney, 2014; Gallagher & Benton, 2022; John-Saaltink, Kok, Lau, & De Lange, 2016; Kondo, Murai, & Whitney, 2022; Liberman, Zhang, Whitney, 2016; Manassi, Liberman, Chaney, & Whitney, 2017; Samaha et al., 2019; Sheehan & Serences, 2022; except Manassi et al., 2018). They found that the serial dependence existed in a certain relative orientation range (i.e., the range of the continuity field). Once the relative orientation was beyond the range of the continuity field (e.g., ∼37.8°, Fischer & Whitney, 2014; ∼20°, Cicchini et al., 2017), serial dependence disappeared. However, we extended the range of the relative orientation into the whole circle range (i.e., [–180°, 180°]) and revealed that the size of serial dependence fluctuated. Specifically, the size of serial dependence first increased and then decreased, consistent with the previous studies. However, what differentiated from the previous studies was that serial dependence increased again when the relative orientation continuously increased, which indicated that the continuity field could cover the whole circle range. We proposed that the different continuity field findings could be due to different stimulus ranges, because in one-going project, we shrunk the relative orientation range into −90° to 90° and found that the continuity field of the attractive serial dependence was very narrow (Figure 6A). Additionally, the attractive serial dependence changed into repulsive serial dependence when the relative orientation was beyond the continuity field, consistent with the Samaha et al. (2019). Therefore, with the current and previous studies, we can conclude that the continuity field is in serial dependence of visual perception but the range of the continuity field is modulated by our experimental design (e.g., stimulus ranges).
Figure 6. (A) Results of serial dependence in one ongoing orientation project. The x-axis was the relative orientation that was the difference in the actual orientation between the previous first and current trials. The y-axis was the overall estimation error that was the difference between the estimate and the actual orientations. Each dot was the mean overall estimation error averaged across 16 participants. Error bars were the standard errors across 16 participants. Shaded areas indicated that the mean overall estimation error was significantly different from 0°. (B) Schematic illustration of one stimulus used in this project. In each display, one oriented gray bar was randomly presented on a shaded area. The squares and shaded areas were invisible in the experiment. After the display, participants were asked to report their perceived orientation by adjusting a bar (Figure 1C).
Additionally, aside from extending the orientation range, we also tested two types of new visual speed and PLW direction. Before the current study, no study examined the serial dependence in the speed perception. The current study revealed that the speed estimates were biased toward the previously experienced speed, showing an attractive serial dependence (the right panels in Figures 3B and 5B). However, we found that the serial dependence bias increased with the increase of the relative speed. There was no continuity field as the relative speed less than 5.27°/s. The trend suggested that if there was a continuity field of speed perception, then the range of continuity field would be larger than 5.27°/s. In the future studies, we can extend the speed range to depict the range of the speed continuity field.
Moreover, so far, for the serial dependence in the PLW direction estimation, only two abstracts have been published in vision science society (VSS) conferences (Chaney, Liberman, & Whitney, 2016; Li et al., 2021). Chaney et al. (2016) found that the estimation of the PLW direction was biased toward the previous PLW direction, showing an attractive serial dependence. In the current study, we supported their findings with similar data analysis methods (see Appendix Figure A1D) and showed that the range of the continuity field was less than 90°. However, after updating the data analysis methods, the strength of the serial dependence was reduced (the right panel in Figure 5B), which might be due to the variability of participants (see Appendix Figure A2C). Appendix Figure A2C shows that although the residual estimation errors (red dots) are positively correlated with the edited overall estimation errors (blue dots). The trends vary among participants in the PLW direction experiment, different from the similar trends in the orientation and speed experiments (Appendix Figures A2A, A2B).
For the overall estimation errors (Figure 2A, Appendix Figures A1A, A1C), first, we well reproduced the oblique illusion in the orientation estimation. Because several studies have discussed the oblique illusion mechanisms, we, here, do not repeat them (Appelle, 1972; Li et al., 2003; Orban et al., 1984; Vogels & Orban, 1985). Second, we found that the speed estimates were systematically compressed toward the center of the speed range (i.e., 3.51°/s), showing a central tendency revealed in many different physical features (e.g., Anobile et al., 2019; Bae & Luck, 2020; Manassi & Whitney, 2022; Olkkonen & Allred, 2014; Olkkonen et al., 2014; Pomè et al., 2021; Xiang et al., 2021). However, previous studies proposed that the speed perception was consistent with a Bayesian inference account (Jogan & Stocker, 2015; Stocker & Simoncelli, 2006). In these studies, the researchers proposed that speeds tended to be underestimated because the stationary took the highest proportion in the prior (Stocker & Simoncelli, 2006; Weiss, Simoncelli, & Adelson, 2002). However, recently, Merz, Soballa, Spence, and Frings (2022) proposed that the speed prior could be dynamically changed rather than 0°/s. In the experiment, they showed participants a black point randomly positioned on a circle. The point moved clockwise along the circle for 250 ms at a certain speed (e.g., 12.6 pix/s, 15.71 pix/s, 31.41 pix/s, 62.8 pix/s, 125.7 pix/s, 502.7 pix/s, 1005.3 pix/s and 2010.6 pix/s). Participants were asked to reproduce the beginning or end position of the point when the point disappeared. They found that at low speeds, participants reported that the beginning position was shifted backward or the end position was shifted forward, indicating an overestimation of speeds. In contrast, at fast speeds, participants reported that the beginning position was shifted forward or the end position was shifted backward, indicating an underestimation of speeds. These result patterns were consistent with our central tendency. Hence, Merz's and our studies suggested that the prior of speed perception could be dynamic.
Third, previous PLW perception studies generally showed a facing-to-viewer bias, meaning that participants tended to report the PLW was facing the viewer (Schouten et al., 2010; Schouten et al., 2011; Shen et al., 2018; Vanrie et al., 2004; Weech et al., 2014; Weech & Troje, 2018). Accordingly, we expected a facing-to-viewer bias, showing the underestimation of the PLW direction. However, our data showed that PLW direction perception was fluctuating (the left panel in Appendix Figure 1C). We proposed that the different findings could be due to the different research methods or purposes. In the facing-to-viewer studies, the researchers asked participants to report whether the PLW was facing or back to them (two-alternative-choice task). Our study was a PLW direction estimation task. However, we did not find PLW studies with same tasks to make comparisons. Additionally, previous studies also found that compared with male observers, female observers were more likely to judge the PLW face to the viewer (Brooks et al., 2008; Schouten et al., 2010). Hereby, we divided the participants’ estimates into three groups and found that 13 participants showed strong back-to-viewer bias (Appendix Figure A3A), and there were ten males. Nine participants showed strong facing-to-viewer bias (Appendix Figure A3B), and there were 8 females. This finding supported the idea that the bias of PLW perception could be modulated by observer sex (Brooks et al., 2008; Schouten et al., 2010).
To sum up, aside from extending the serial dependence in speed and PLW direction perceptions, the current study reveals that the estimation bias caused by serial dependence is one part of the overall estimation errors in visual perception, highlighting that we cannot treat them as two independent mechanisms like previous studies (e.g., Sun et al., 2020; Xu et al., 2022). The perceptual estimation and serial dependence share some common neural basis, which inspires us to examine the role of the cortical areas involved in the feature estimation in serial dependence.
The authors thank Fan-Huan You (master student in our lab) for proofreading the papers.
Supported by the National Natural Science Foundation of China, China (No. 32200842) to Qi Sun.
Commercial none.
Corresponding Qi Sun.
Email: sunqi_psy@zjnu.edu.cn.
Address: Zhejiang Normal University, Wucheng District, Jinhua 321004, PRC.
Figure A1. Results of speed estimation and PLW direction. (A) and (C) The overall estimation error is against the actual speed or PLW direction. The dots are the mean overall estimation error averaged across all participants. Error bars are the standard error across all participants. (B) and (D) The estimation bias is against the relative speed and PLW direction – the difference in the actual speed and PLW direction between the previous first trial and the current trial. The solid red line is the best fitting results of the quadratic function (Equation 5) in (B) or the DoG function (Equation 1) in (D).
Figure A2. Results of each participant in the orientation (A), speed (B) and PLW direction (C) experiments. The x-axis is the actual visual feature. Y-axis is two-folded: one is the edited estimation error in the blue dots; the other is the residual estimation error in the red dots.
Figure A3. We divided the data of the PLW estimation experiment into three groups based on participants’ data trends. We found that (A) 13 participants (three females, 10 males) overestimated the PLW direction, showing a back-to-viewer bias; (B) nine participants (eight females, one male) underestimated the PLW direction, showing a facing-to-viewer bias; (C) 14 participants (six females, eight males) did not show a regular estimation trend.