Feedforward Processing in Early Visual Cortex Underlies the Ebbinghaus Illusion

Song Zhao; Yi Fang; Mengdie Zhai; Chengzhi Feng; Wenfeng Feng

doi:10.1111/cogs.70251

. 2026 Aug 3;50(8):e70251. doi: 10.1111/cogs.70251

Feedforward Processing in Early Visual Cortex Underlies the Ebbinghaus Illusion

Song Zhao ^1,^†, Yi Fang ^1,^†, Mengdie Zhai ^1,^†, Chengzhi Feng ¹, Wenfeng Feng ^1,^2,^✉

PMCID: PMC13430296 PMID: 42544078

Abstract

Low‐level occipital regions, including the primary visual cortex (V1), are known to play a pivotal role in generating the Ebbinghaus size illusion, in which a circle surrounded by small inducers looks larger than an identical circle surrounded by large inducers. However, a definitive answer is still lacking as to whether the low‐level visual cortex plays its role at the feedforward stage of processing. To resolve this issue, we measured event‐related potentials (ERPs) evoked by two equal‐size circles flashed on the left and right sides of human participants, with one side constantly displaying large surrounding inducers and the other side small inducers. Experiment 1 unveiled a significant lateralization in the evoked C1 component, a well‐established ERP index of afferent V1 activity, only when the circle within small inducers was perceived as larger but not when the circle within large inducers was perceived as larger. This illusion‐specific C1 lateralization, which closely resembled the C1 modulation evoked by physical differences in size, was further replicated in Experiment 2 even when the attentional bias toward small inducers was invalidated as an alternative account. Furthermore, Granger causality analysis revealed a one‐way transfer of information from V1‐representative electrodes to extrastriate‐representative electrodes during the C1 lateralization. Together, these findings offer the strongest evidence to date that the Ebbinghaus illusion begins at the feedforward stage of cortical visual processing, consistent with the prediction of the contour interaction theory.

Keywords: Ebbinghaus illusion, Size perception, Primary visual cortex, Feedforward, ERPs, C1, Granger causality

1. Introduction

The adage “seeing is believing” commonly suggests a congruence between visual perception and its subsequent beliefs. Nevertheless, visual illusions challenge this notion, demonstrating that one's subjective interpretation may diverge from the actual sensory input. One of the most striking instances is the Ebbinghaus illusion: a central circle surrounded by a ring of small circles is perceived as larger than a physically identical circle surrounded by a ring of large circles (Ebbinghaus, 1902). Visual illusions, like the Ebbinghaus illusion, have been furnishing a unique window into the psychophysiological mechanisms underlying our subjective experience of the external world (Cavanagh, 2024; Eagleman, 2001).

It is well established that anatomically early visual areas including primary visual cortex (V1) play a pivotal role in generating the Ebbinghaus illusion (Song, Schwarzkopf, & Rees, 2011; Schwarzkopf, Song, & Rees, 2011; Schwarzkopf & Rees, 2013; Kreutzer, Weidner, & Fink, 2015; Nakashima & Sugita, 2018; Chen, Qiao, Wang, & Jiang, 2018, 2022, 2024; Wang, Chen, & Jiang, 2021; Wu, Feng, Han, Chen, & Luo, 2023). For instance, the functionally defined V1 surface area representing the central visual field has been shown to be correlated with the strength of the Ebbinghaus illusion (Schwarzkopf et al., 2011; Schwarzkopf & Rees, 2013). Meanwhile, Song et al. (2011) found that the Ebbinghaus illusion was attenuated when the central circle (target) and the surrounding circles (inducers) were presented to different eyes, suggesting that monocular neurons, which are almost nonexistent in visual areas higher than V1 (Hubel & Wiesel, 1968; Zeki, 1978), take part in generating this illusion. Furthermore, the Ebbinghaus illusion was found to persist even when the surrounding inducers were suppressed from conscious awareness by continuous flash suppression, implying that it takes place in the early visual processing stream (Nakashima & Sugita, 2018; Chen et al., 2018). In addition, recent functional near‐infrared spectroscopy (fNIRS) and functional magnetic resonance imaging (fMRI) studies have consistently shown that the perceptually larger target (i.e., surrounded by small inducers) triggered greater activation in early visual areas compared to the physically identical but perceptually smaller target (i.e., surrounded by large inducers) even when the contribution from physical differences between the small and large inducers was controlled (Chen et al., 2022, 2024).

However, it remains unclear whether the anatomically early visual cortex can take part in the generation of the Ebbinghaus illusion in a rapid feedforward manner. This is because early visual areas, including V1, also receive a large amount of feedback signals from other high‐level brain regions when processing visual information (for review, see Briggs, 2020), and the existing psychophysical studies and brain imaging investigations with relatively low temporal resolution are inherently insufficient to dissociate the rapid feedforward processing (if any) from its subsequent feedback processing. It is noteworthy that although recent fMRI and fNIRS studies, by applying functional connectivity analyses to resting‐state brain activity, have found feedforward connections from the occipital cortex to other brain areas that could predict the Ebbinghaus illusion magnitude (Chen et al., 2022; Wu et al., 2023), a more recent study using task‐based fMRI data did not reveal such illusion‐related feedforward connections but a feedback connectivity from the parietal to occipital areas (Chen, Wu, Yu, & Sperandio, 2024). This discrepancy implies that those resting‐state feedforward connections may not account for the real‐time visual processing evoked by the Ebbinghaus configuration.

To determine whether the Ebbinghaus illusion occurs at the feedforward stage of cortical visual processing, we measured high temporal‐resolution event‐related potentials (ERPs) evoked by two equal‐size central circles briefly presented on the left and right sides, with one side continuously displaying large surrounding inducers and the other side small inducers (Fig. 1a). Here, we focused on the earliest cortical visual ERP—the C1 component (∼60–100 ms post‐stimulus onset), which has been suggested to originate predominantly in V1 (Jeffreys & Axford, 1972; Clark, Fan, & Hillyard, 1995; Di Russo, Martínez, Sereno, Pitzalis, & Hillyard, 2001; Kelly, Schroeder, & Lalor, 2013a,Kelly, Vanegas, Schroeder, & Lalor, 2013b; but see Ales, Yates, & Norcia, 2010) and widely accepted as an electrophysiological index of the first feedforward activation in the visual cortex (Martínez et al., 1999; Di Russo, Martínez, & Hillyard, 2003; Ding, Martinez, Qu, & Hillyard, 2014; Bombeke, Duthoo, Mueller, Hopf, & Boehler, 2016; Alilović, Timmermans, Reteig, van Gaal, & Slagter, 2019; Qin, Wiens, Rauss, & Pourtois, 2022). Our Experiment 1 found a lateralization in the C1 component elicited by the two equal‐size central circles only for trials on which the circle presented within small inducers was perceived as larger (wherein the illusion occurred) but not for trials on which the circle within large inducers was perceived as larger (wherein the illusion did not occur). Experiment 2 replicated this illusion‐specific C1 lateralization and further invalidated the attentional bias toward small inducers as an alternative account. These findings provide strong evidence that the Ebbinghaus illusion begins at the feedforward stage of cortical visual processing.

Fig. 1 — Task design and behavioral results in Experiment 1. (a) Schematic illustration of a trial with equal‐size test and standard circles and a trial with unequal‐size test and standard circles, presented in a block throughout which an annulus of large inducers was *fixed* on the left and an annulus of small inducers on the right. The standard circle size was constant, while the red‐blue colors and left‐right positions of the standard and test circles varied from trial to trial. Participants were required to report the color of the apparently large circle. (b) Grand‐averaged proportion of trials on which participants reported the test circle as larger than the standard circle, plotted as a function of the test circle size (% of the standard) separately for the condition where the test circle appeared within small inducers and the condition where the standard circle appeared within small inducers. Note that when the test and standard circles were equal in size, participants reported the test circle as larger much more often when it appeared within small inducers than when it appeared within larger inducers, indicative of a robust Ebbinghaus illusion. Error bars represent ± 1 SD.

2. Experiment 1

2.1. Methods

2.1.1. Participants

A total of 52 healthy and right‐handed human subjects gave their informed consent as approved by the Institutional Review Board of Soochow University to participate in Experiment 1, and monetary compensation was given for their participation. Each of them reported normal or corrected‐to‐normal vision without color blindness, and they were all naive as to the hypothesis of the study. Data from two participants were excluded either because of quit during the experiment or due to excessive electroencephalogram (EEG) artifacts (>40%; c.f., Zhao, Feng, Huang, Wang, & Feng, 2021; Zhao et al., 2023), leaving data of 50 subjects (32 female and 18 male; age range 18–27 years, mean age 21.7 years) for further analysis. The minimal sample size was set a priori to 50, which is larger than those used in previous studies focusing on modulations of the C1 component (for a recent review, see Qin et al., 2022). Subjects were asked for their gender but also given the options of “none of the above” and “prefer not to say,” and none of them chose these options. No information about race and ethnicity were collected. Experimental procedures were in agreement with the Declaration of Helsinki.

2.1.2. Stimuli, apparatuses, and task

The experiment was performed in a dark and sound‐attenuated chamber. Stimulus presentation was scripted using Presentation 18.0 (Neurobehavioral Systems, Berkeley, CA, USA). Visual stimuli were presented on a 27‐inch LCD monitor (ASUS PG279Q, resolution 1920 × 1080, refresh rate 120 Hz) on which the background color was set to gray. Subjects sat in front of the monitor with a viewing distance of approximately 80 cm and were required to maintain their eyes fixed on a small black cross (0.69° × 0.69°), which was continuously visible at the center of the screen throughout each experimental block.

The inducers of the Ebbinghaus configuration were also fixed on the screen throughout each block (Fig. 1a), which consisted of six large black filled circles (each 4.42° in diameter) distributed at equal distances around an invisible ring with a radius of 4.69° and eight small black filled circles (each 1.36° in diameter) distributed at equal distances around another invisible ring with a radius of 2.27°. The centers of the two rings of inducers were positioned 8.05° to the left and right of the fixation cross horizontally and 5.75° above the fixation cross vertically. Note that we presented these inducers (and hence the central circles; see below) in the upper visual field to better separate the C1 component from the subsequent P1 component, given that only the C1 elicited by upper‐field stimuli is negative in polarity that can be easily distinguished from the positive P1 (Luck, 2014). The left‐right positions of the small and large inducers were randomized across blocks with equal probability.

On a given trial, the central circles of the Ebbinghaus configuration consisted of a red‐filled circle and a blue‐filled circle (both 17.6 cd/m² in luminance), with one circle appearing at the center of the ring of large inducers and the other appearing at the center of the ring of small inducers simultaneously for 100 ms. Meanwhile, the size of one central circle was fixed at 2.30° in diameter (standard circle), while the size of the other (test circle) could be 1.38°, 1.84°, 2.30°, 2.76°, or 3.22° in diameter. Specifically, the test and standard circles were equal in size (i.e., 2.30°) on two‐fifths of the trials. On another two‐fifths of the trials, the test circle was either smaller (1.38° or 1.84°) or larger (2.76° or 3.22°) than the standard circle with equal probability. On the remaining one‐fifth of the trials, the test and standard circles were omitted. The left‐right positions and red‐blue colors of the standard and test circles were randomized from trial to trial. All types of trials were presented in a random order within each block, and the intertrial interval varied from 1800 to 2200 ms.

Participants were told to ignore the constant surrounding inducers and to indicate the color (red or blue) of the central circle that was perceived as larger regardless of its position by pressing one of two keyboard buttons (F or J). This orthogonal response procedure (i.e., reporting the target's color rather than its location) was used to minimize space‐related response bias (c.f., McDonald, Teder‐Sälejärvi, Di Russo, & Hillyard, 2005; Störmer, McDonald, & Hillyard, 2009). The assignment of buttons to colors was counterbalanced across participants, so that half of the participants pressed the button F with their left index finger to register a red‐color response and the button J with their right index finger to register a blue‐color response; for the other half of the participants, the response buttons were reversed. The experiment comprised 20 blocks of 80 trials each (10 small‐inducers‐left blocks and 10 small‐inducers‐right blocks), totaling 1600 trials. Participants could rest between blocks.

2.1.3. Electrophysiological recording and analysis

EEG was recorded continuously when subjects performed the behavioral task, using a SynAmps² amplifier (NeuroScan, El Paso, TX, USA) and a custom‐built 64‐electrode elastic cap. The electrodes on the cap were positioned according to a modified 10‐10 system montage (for details, see Zhao, Wang, Feng, Wang, & Feng, 2022). An additional electrode placed at the left mastoid served as the online reference. Horizontal eye movements were detected by a pair of bipolar electrodes positioned at the left and right outer canthi (horizontal electrooculogram, HEOG). Vertical eye movements and blinks were detected by another pair of bipolar electrodes placed above and below the left eye (vertical electrooculogram, VEOG). The impedances of all electrodes were kept below 5 kΩ. The online EEG and EOG signals were filtered by a band‐pass filter of 0.05–100 Hz and digitized at a sampling rate of 1000 Hz. Electrophysiological recording was carried out using SCAN 4.5 (NeuroScan).

All offline EEG and ERP analyses were carried out using the EEGLAB toolbox (Delorme & Makeig, 2004) and ERPLAB toolbox (Lopez‐Calderon & Luck, 2014) in MATLAB (The MathWorks, Natick, MA, USA). The raw EEG signals were first down‐sampled to 500 Hz and then low‐pass filtered (half‐amplitude cutoff = 33.75 Hz, transition band width = 7.5 Hz) using a Hamming‐windowed sinc FIR filter with zero‐phase shifted (two‐pass forward and reverse) to attenuate high‐frequency noise triggered by muscle activity or external electrical sources. The filtered EEG data were re‐referenced to the average of the left and right mastoid electrodes. Then, the EEG data were segmented into 400‐ms epochs time‐locked to the two central circles onset with a 100‐ms pre‐stimulus baseline and were baseline‐corrected. In terms of artifact rejection, the moving‐window peak‐to‐peak amplitude method was employed on all EEG electrodes and the VEOG electrode (window size: 200 ms, step size: 20 ms, threshold: 100 µV) to eliminate epochs contaminated by eye blinks, muscle activity, and sporadic artifacts of unknown origins. Additionally, the moving‐window step function method was applied to the HEOG channel (window size: 200 ms, step size: 20 ms, threshold: 25 µV) to discard epochs contaminated by horizontal eye movements. Among the included 50 participants (see Participants section of Experiment 1), 5.38 ± 0.70% (M ± SE, unless otherwise indicated) of the epochs were excluded after artifact rejection. The remaining valid epochs were then used to compute averaged ERP waveforms. Prior to further analysis, the ERPs were first collapsed across the two central circles’ color configurations (left‐red/right‐blue and the reverse) to enhance the signal‐to‐noise ratio.

For the crucial condition in which the test and standard circles were equal in size, the ERPs were averaged separately for the small‐inducers‐left and small‐inducers‐right trials, as well as for the trials on which subjects perceived the circle within small inducers to be larger and the trials on which subjects perceived the circle within large inducers to be larger. Then, the ERPs were collapsed across the small inducers location (left, right) and hemisphere of electrodes (left, right) to obtain ERPs recorded contralaterally and ipsilaterally relative to the small inducers location. The earliest C1 component was measured as the mean amplitude over three pairs of parieto‐occipital electrodes adjacent to midline (P1/P2, P3/P4, PO3/PO4)¹ within the time window of 78–98 ms post‐stimulus onset. Note that these time intervals and electrodes would not mismeasure the earliest N1 subcomponent, because this subcomponent is known to peak 100–150 ms at anterior electrodes, whereas the C1 typically peaks 80–100 ms at posterior midline electrodes (Luck, 2014). Meanwhile, the subsequent P1 component was also measured given its prominence in the waveforms. It was quantified as the mean amplitude within the time window of 120–140 ms over four pairs of lateral parieto‐occipital electrode sites (P5/P6, P7/P8, PO5/PO6, PO7/PO8). The measurement parameters above were determined in an unbiased manner using the method of collapsed localizer (Luck & Gaspelin, 2017). That is, ERPs were first collapsed across all conditions to be contrasted, and the time intervals and electrodes where each corresponding ERP component had its largest amplitude in the collapsed waveform were then selected for measuring the noncollapsed data. Notably, these measurement parameters are also consistent with the spatio‐temporal distributions of C1 and P1 observed in prior studies where bilateral stimuli were used (Störmer et al., 2009; Fu, Fedota, Greenwood, & Parasuraman, 2010a; Ding et al., 2014).

To ascertain whether the neural activity at early stages of visual information processing underlies the occurrence of the Ebbinghaus illusion, separate two‐way repeated‐measures ANOVAs were conducted on the mean amplitudes of the C1 and P1 elicited by the equal‐size circle pair, with the factors of perceptual outcome (reporting the circle within small/large inducers to be larger) and hemisphere (contralateral/ipsilateral relative to the location of small inducers).² After finding a significant two‐way interaction, specific comparisons between the contralateral versus ipsilateral amplitudes were further performed using paired t‐tests separately for each perceptual outcome. Note that although trials with the two perceptual outcomes may not be entirely equivalent to the illusion‐present and illusion‐absent trials (due to the existence of random error in response), the difference between them should indicate the factor underlying the presence/absence of the illusion anyway. Additionally, to determine whether the inducers‐dependent early ERP lateralizations (if any) could further account for the interindividual variability in the Ebbinghaus illusion magnitude, Pearson correlation analyses were performed. The magnitude of the inducers‐dependent ERP lateralization for each participant was calculated as the amplitude difference between the contralateral and ipsilateral ERPs evoked by the equal‐size circle pair on trials where the circle within small inducers was reported as larger. The magnitude of the Ebbinghaus illusion for each participant was determined in the equal‐size condition by the probability of reporting the test circle within small inducers as larger minus the probability of reporting the test circle within large inducers as larger (for details, see Behavioral results section of Experiment 1).

Lastly, given that both the C1 and P1 components have been shown to be sensitive to physical differences in size (Zani & Proverbio, 1995; Kornmeier, Pfäffle, & Bach, 2011; Gebodh, Vanegas, & Kelly, 2017; Zhang et al., 2024), we also compared the C1 and P1 amplitudes elicited by the larger‐size test circles (2.76° and 3.22°) versus those elicited by the smaller‐size test circles (1.38° and 1.84°) using separate paired t‐tests. To facilitate these analyses, ERPs to the unequal‐size pairs of test and standard circles were first averaged according to the test circle size (larger/smaller than the standard circle) and its location (left/right) regardless of the small inducers location, and then collapsed across the test circle location and hemisphere of recording to generate ERPs contralateral and ipsilateral to the test circle location. The C1 and P1 amplitudes to the larger versus smaller test circles were all measured over the hemisphere contralateral to the test circle location (i.e., the hemisphere ipsilateral to the fixed‐size standard circle).

In view of the intrinsic hardship in supporting the absence of an effect with conventional null hypothesis significance tests, Bayes‐based repeated‐measures ANOVAs, paired t‐tests, or correlation analyses were further performed using JASP 0.13.1 (JASP Team, 2020) when there were nonsignificant results (i.e., p > .05). A Bayes factor (BF₁₀ ) value lower than 0.333 would be regarded as substantial evidence for the null hypothesis (c.f., Dienes, 2014; Wagenmakers et al., 2018).

2.2. Results

2.2.1. Behavioral results

To check whether the Ebbinghaus illusion was successfully induced in the current task design, we calculated the proportion of trials on which subjects reported the test circle as larger than the standard circle at each test circle size level (i.e., 60%, 80%, 100%, 120%, and 140% of the standard). These calculations were done separately for the condition where the test circle appeared within small inducers and for the condition where the test circle appeared within large inducers (i.e., where the standard circle appeared within small inducers; Fig. 1b). Data points of the two conditions were fitted separately using a four‐parameter Boltzmann sigmoidal function, Y = L + (U − L)/{1 + exp[(C₅₀ − X)/S]}, where Y is the proportion of the response, X is the test size level, L and U are the lower and upper asymptotes, C₅₀ is the test size level at which the proportion of response is halfway between the upper and lower asymptotes, and S is the slope. The goodness of fit was high for each function (test circle within small inducers: R ² = .97 ± .07; test circle within large inducers: R ² = .97 ± .06).

On the crucial trials where the test and standard circles had the same physical size (i.e., at the test size level of 100%), subjects reported the test circle to be larger much more frequently when it was presented within small inducers (probability: 0.679 ± 0.012) than when it was presented within larger inducers (0.314 ± 0.011; see Fig. 1b), as revealed by a paired t‐test (t(49) = 16.293, p < .001, d = 2.304). Meanwhile, the probability of reporting the test circle as larger was significantly higher than the chance level (0.5) when the test circle appeared within small inducers (t(49) = 15.530, p < .001, d = 2.196) but significantly lower than the chance level when the test circle appeared within large inducers (t(49) = −16.315, p < .001, d = −2.307), as revealed by one‐sample t‐tests. Furthermore, the point of subjective equality (PSE)—the test size at which subjects judged the test circle to be larger on half of the trials—was estimated from the psychophysical curves of Fig. 1b to be 94.28 ± 0.47% when the test circle appeared within small inducers and 106.00 ± 0.38% when the test circle appeared within large inducers, which differed significantly (t(49) = −15.252, p < .001, d = −2.157). Meanwhile, the PSE was substantially smaller than 100% (reflecting an overestimation of the test circle size) when the test circle appeared within small inducers (t(49) = −12.102, p < .001, d = −1.711) but substantially larger than 100% (reflecting an underestimation of the test circle size) when the test circle appeared within large inducers (t(49) = 15.966, p < .001, d = 2.258). Taken together, these behavioral results indicate that the Ebbinghaus illusion was highly prominent in the current task, as expected.

It is worth mentioning that simple reaction times have been shown to be sensitive also to the Ebbinghaus illusion, with faster responses to the central circle perceived as illusorily larger (Sperandio, Savazzi, & Marzi, 2010). However, the current experimental design precludes us from using this measure to probe the Ebbinghaus illusion, because here the circle surrounded by small inducers and the circle surrounded by large inducers were presented simultaneously (rather than in isolation), and our participants were required to make a binary choice (rather than an indiscriminate speeded response).

2.2.2. ERPs to the equal‐size circle pair

To determine whether the Ebbinghaus illusion begins at the feedforward stage of cortical visual processing, the mean amplitudes of the earliest C1 component (78–98 ms) elicited by the equal‐size pair of test and standard circles (Fig. 2) were subjected to a repeated‐measures ANOVA with two factors of perceptual outcome (reporting the circle within small/large inducers as larger) and hemisphere (contralateral/ipsilateral relative to the small inducers location). Because the briefly presented test and standard central circles were physically equal in size and the small and large inducers were constantly displayed, any ERP lateralization in response to the two central circles should be attributed to the influence of contextual inducers. The results yielded that although neither the main effect of perceptual outcome (F(1, 49) = 0.218, p = .643, η ² _p = 0.004, BF₁₀ = 0.203) nor the main effect of hemisphere (F(1, 49) = 2.087, p = .155, η ² _p = 0.041, BF₁₀ = 0.193) was significant, the two‐way interaction was significant (F(1, 49) = 4.167, p = .047, η ² _p = 0.078). Further specific comparisons showed that the C1 amplitude contralateral to small inducers (−1.12 ± 0.13 µV) was substantially greater than the C1 amplitude ipsilateral to small inducers (i.e., contralateral to large inducers; −1.02 ± 0.14 µV) when subjects reported the circle within small inducers as larger (t(49) = −2.971, p = .005, d = −0.420; Fig. 2a,c). Conversely, there was no difference between the contralateral and ipsilateral C1 amplitudes (−1.10 ± 0.15 µV and −1.12 ± 0.15 µV) when subjects judged the circle within large inducers as larger, with the Bayes factor showing substantial evidence for the null hypothesis (t(49) = 0.260, p = .796, d = 0.037, BF₁₀ = 0.159; Fig. 2b,c). These findings signify that the afferent C1 activity underlies the occurrence of the Ebbinghaus illusion on a trial‐by‐trial basis, thereby supporting the hypothesis that this illusion begins at the feedforward sweep of visual processing.

Fig. 2 — C1 lateralization underlying the occurrence of the Ebbinghaus illusion in Experiment 1. Grand‐averaged ERPs elicited by the equal‐size circle pair recorded at the representative electrodes P3/P4 contralateral and ipsilateral to the side of small inducers, and scalp topographies of the contralateral, ipsilateral, and contralateral minus ipsilateral amplitudes during the C1 component's interval, are shown separately for trials wherein the circle within small inducers was perceived as larger (a) and trials wherein the circle within large inducers was perceived as larger (b). The shaded areas on waveforms and white dots on scalp topographies depict the time window (78–98 ms) and electrodes (P1/P2, P3/P4, PO3/PO4) over which the C1 mean amplitudes were measured. For raw C1 topographies on the small‐inducers‐left and small‐inducers‐right trials, see Fig. S1. (c) Computed C1 mean amplitudes displayed as functions of perceptual outcome and recording hemisphere, with single‐participant data depicted by scatter dots and grand‐averaged data marked by black symbols. Error bars represent ± 1 SE. **: p < .01; n.s.: nonsignificant. Note that the C1 contralateral to small inducers was significantly larger than its ipsilateral counterpart only when participants reported the circle within small inducers to be larger. (d) Scatter plot with fitted line indicating that the magnitude of this C1 lateralization could not further predict the interindividual variability in the Ebbinghaus illusion magnitude (quantified as the probability of reporting the test circle within small inducers as larger minus the probability of reporting the test circle within large inducers as larger in the equal‐size condition). The semi‐transparent area around the fitted line represents a 95% confidence band.

We also conducted a brain−behavior correlation analysis for data in the equal‐size condition to explore whether the inducers‐dependent C1 lateralization (measured as the contralateral minus ipsilateral C1 amplitude difference on trials where the circle within small inducers was reported as larger; see Fig. 2a) can further predict the between‐subject variability in the Ebbinghaus illusion magnitude (measured as the probability of reporting the test circle within small inducers as larger minus the probability of reporting the test circle within large inducers as larger; see Fig. 1b). However, no reliable correlation was found between the two measures, with the Bayes factor providing substantial evidence for the null hypothesis (r(48) = −.050, p = .731, BF₁₀ = 0.187; Fig. 2d). No correlation was found even when the behavioral Ebbinghaus illusion magnitude was quantified alternatively as the PSE difference between the condition where the test circle appeared within large inducers and the condition where the test circle appeared within small inducers (r(48) = −.024, p = .871, BF₁₀ = 0.179).

After the C1 component, the P1 component's mean amplitudes (120–140 ms) were also analyzed with the 2 (perceptual outcome) × 2 (hemisphere) ANOVA (Fig. 3). The results revealed that the main effect of perceptual outcome was not significant (F(1, 49) = 1.559, p = .218, η ² _p = 0.031, BF₁₀ = 0.397). Importantly, the main effect of hemisphere was highly significant (F(1, 49) = 22.777, p < .001, η ² _p = 0.317), whereas the two‐way interaction was not significant, with the Bayes factor furnishing substantial evidence for the absence of this interaction (F(1, 49) = 0.073, p = .787, η ² _p = 0.001, BF₁₀ = 0.204). This pattern of results reflect that the P1 amplitude contralateral to small inducers was larger than the P1 amplitude ipsilateral to small inducers, regardless of whether the circle within small inducers was reported as larger (contralateral: 1.45 ± 0.24 µV; ipsilateral: 1.11 ± 0.26 µV; Fig. 3a,c) or the circle within large inducers was reported as larger (contralateral: 1.34 ± 0.25 µV; ipsilateral: 1.02 ± 0.25 µV; Fig. 3b,c). On the other hand, the brain−behavior correlation analysis showed that the interindividual variability in the Ebbinghaus illusion magnitude could be positively predicted by the inducers‐contingent P1 lateralization on trials where the circle within small inducers was perceived as larger (r(48) = .322, p = .022; Fig. 3d). Notably, such a correlation was found even for the P1 lateralization measured on trials where the circle within large inducers was perceived as larger (r(48) = .331, p = .019). Even when the Ebbinghaus illusion magnitude was measured as the aforementioned PSE difference, the same pattern of results was found (for trials where the circle within small inducers was perceived as larger: r(48) = .388, p = .005; for trials where the circle within large inducers was perceived as larger: r(48) = .401, p = .004). Hence, these findings imply that in contrast to the C1 component, the subsequent P1 is associated more with one's general predisposition to perceive the Ebbinghaus illusion than with the presence/absence of the illusion at a given moment.

We have reasoned that any ERP lateralization in response to the equal‐size circle pair here should be attributed to illusion‐related processing, because the static contextual inducers (see Fig. 1a) were expected to evoke no prominent ERP response. Nonetheless, one may still be concerned that there could be subtle lateralized ERP effects owing to physical differences between the small and large inducers even when these inducers were constantly displayed, which might have confounded our C1 and P1 lateralization effects reported above. Hence, we reanalyzed the C1 and P1 amplitudes after subtracting ERPs recorded on the randomly interleaved “circle‐pair‐absent” trials (see Section 2.1.2), in order to examine whether the same pattern of results could be replicated after the potential confounds driven by inducers‐related physical differences were eliminated. As expected, this is exactly what we found, demonstrating that the aforementioned C1 and P1 lateralization effects were mainly driven by the Ebbinghaus‐illusion‐related processing per se (for details, see Supplementary Materials, Section B).

In addition, in view of recent evidence showing that early visual ERPs peaked earlier in response to perceptually larger disks than perceptually smaller disks of matched retinal size in the context of size constancy (Noviello et al., 2024), we carried out an exploratory analysis examining whether the peak latency of our C1 and P1 components can also track the difference in perceived size. However, the pattern of our peak latency results does not provide support for such a prediction (for details, see Supplementary Materials, Section C).

2.2.3. ERPs to the unequal‐size circle pairs

Given that both the C1 and P1 amplitudes have been found to increase monotonously with stimulus size (Zani & Proverbio, 1995; Kornmeier et al., 2011; Gebodh et al., 2017; Zhang et al., 2024), the above findings imply that the pattern of early neural modulations responsible for the Ebbinghaus illusion seems similar to that produced by physical differences in size. To verify this speculation, we further compared the C1 and P1 to the unequal‐size circle pairs recorded contralaterally to the test circle (Fig. 4) between the visual displays containing a larger‐size (2.76° or 3.22°) test circle versus those containing a smaller‐size (1.38° or 1.84°) test circle. Because each of the visual displays contained a fixed‐size standard circle, any ERP differences revealed in these comparisons can be ascribed to the sizes of the test circles. As expected, the contralateral C1 amplitude was found to be significantly greater for the larger‐size test circles (−1.14 ± 0.16 µV) than for the smaller‐size test circles (−0.88 ± 0.14 µV; t(49) = −2.492, p = .016, d = −0.352; Fig. 4a,c), and the same was true for the early phase of the contralateral P1 (110–130 ms, larger test circles: 1.16 ± 0.23 µV; smaller test circles: 1.01 ± 0.21 µV; t(49) = 2.094, p = .041, d = 0.296; Fig. 4b,c). These results substantiate the similarity between the illusion‐related pattern of cortical activity and that evoked by physical size differences, suggesting that the Ebbinghaus illusion is processed as if the circle surrounded by small inducers were “physically larger” than the identical circle surrounded by large inducers.

Fig. 4 — Similar C1 and P1 effects stemming from physical differences in size in Experiment 1. Grand‐averaged ERPs to the unequal‐size circle pairs containing larger‐size versus smaller‐size test circles, recorded at the electrodes P3/P4 (a) and PO7/PO8 (b) contralateral to the test circle location. Note that these ERPs were collapsed across the small inducers location (surrounding the test or standard circle) to counterbalance any effects caused by the contextual inducers. (c) Scalp topographies of the C1 and P1 size effects, calculated by subtracting the contralateral ERPs to displays containing smaller‐size test circles from the contralateral ERPs to displays containing larger‐size test circles. The gray boxes on waveforms and white dots on scalp topographies denote the time windows and electrodes over which the mean amplitudes of the C1 (78–98 ms, P1/P2, P3/P4, PO3/PO4) and P1's early phase (110–130 ms, P5/P6, P7/P8, PO5/PO6, PO7/PO8) were measured, respectively.

2.3. Discussion

The core finding of Experiment 1 was that when the briefly presented left and right circles were equal in size, the evoked C1 amplitude contralateral to small inducers was greater than its ipsilateral counterpart only on trials wherein the circle presented within small inducers was judged as larger (which contained the illusion trials) but not on trials wherein the circle within large inducers was judged as larger (which contained the nonillusion trials). This illusion‐specific C1 lateralization persuaded us to conclude that the Ebbinghaus illusion starts at the first feedforward sweep of cortical visual processing. However, before this conclusion can be fully embraced, a critical interpretation issue must be addressed. Specifically, although we used an orthogonal response procedure (wherein participants reported the color, rather than the location, of the apparently larger circle) to minimize space‐related response bias, given the robustness of the Ebbinghaus illusion as revealed by our behavioral results, participants might have gradually realized that they reported the circle with small inducers more frequently during the task, which could in turn lead to more attention being directed to the side of small inducers. Relevantly, attending to one side of bilaterally symmetric brief visual stimuli is known to result in an enlarged ERP amplitude beginning at the P1 component's interval over the occipital scalp contralateral to the attended side (Luck, Heinze, Mangun, & Hillyard, 1990; Hillyard & Anllo‐Vento, 1998; McDonald et al., 2005; Störmer et al., 2009). Although this suggests that only the P1 lateralization, rather than the earliest C1 lateralization, observed in our Experiment 1 might have been confounded by the potential attentional bias toward the side of small inducers, in light of other evidence implying that spatial attention may modulate the C1 component under certain circumstances (e.g., Kelly, Gomez‐Ramirez, & Foxe, 2008; Fu et al., 2009, 2010b; Dassanayake, Michie, & Fulham, 2016), it is still uncertain whether or not the current C1 effect was confounded by this attentional bias.

We examined this alternative account in Experiment 2 in the following two ways. First, we required participants to report the color of the apparently larger circle (just like Experiment 1) in half of the experimental blocks and to report the color of the apparently smaller circle in the other half of the blocks. Logically, if the attentional bias toward small inducers exists in the former response task, there must be a reversed attentional bias toward large inducers in the latter response task, and collapsing data across the two tasks would basically cancel out this attentional bias (c.f., Anton‐Erxleben, Henrich, & Treue, 2007; Han, Tan, Zhuang, & Qian, 2022). Hence, if the C1 and P1 lateralization effects observed in Experiment 1 were mainly driven by this attentional bias, we should predict that these ERP effects would disappear in Experiment 2 after the data are collapsed across the two opposite response tasks. In contrast, a replication of these ERP effects in Experiment 2 after data collapse would invalidate such an attentional bias account. Second, we introduced a new condition to Experiment 2 in which a task‐irrelevant unilateral green circle, serving as the probe stimulus, was occasionally presented within either the small or large inducers (i.e., on either the left or right side; see Fig. 5a). It is well known that a visual stimulus presented on the attended side elicits a larger P1 amplitude (and even a larger C1 amplitude in some cases) than the identical stimulus presented on the unattended side (Hillyard & Anllo‐Vento, 1998; Martínez et al., 1999; Di Russo et al., 2003; Kelly et al., 2008; Fu et al., 2009, 2010b; Dassanayake et al., 2016; Baumgartner, Graulty, Hillyard, & Pitts, 2018; Alilović et al., 2019). Accordingly, if there is any significant residual attentional bias toward the side of small inducers after the ERP data are collapsed across the two opposite response tasks, we should expect that the probe‐elicited P1 (and probably the C1) would be greater when the unilateral probe is presented within small inducers than when it is presented within large inducers.

Fig. 5 — Task design and behavioral results in Experiment 2. (a) Same schematic illustration as Fig. 1a but for a trial with equal‐size test and standard circles and a new type of trial with a task‐irrelevant unilateral probe circle, presented in a block throughout which an annulus of small inducers was *fixed* on the left and an annulus of large inducers on the right. Subjects in Experiment 2 were required to report the color of either the apparently large circle or the apparently small circle in separate blocks. (b) Same psychophysical curves as Fig. 1b showing the robustness of the Ebbinghaus illusion but for the probabilities of perceiving the test circle as larger in Experiment 2, which were collapsed across the “which was larger” and “which was smaller” tasks to counterbalance the potential attentional bias toward the side of small inducers in the former task. Error bars represent ± 1 SD.

3. Experiment 2

3.1. Methods

3.1.1. Participants

For Experiment 2, a total of 52 new healthy subjects who did not participate in Experiment 1 were recruited. All subjects reported normal or corrected‐to‐normal vision without color blindness and were naïve as to the hypothesis of the experiment. Data from one participant were excluded due to excessive EEG artifacts (>40%), leaving 51 subjects (36 female and 15 male; age range 18–28 years, mean age 21.9 years; all right‐handed) in the final sample. The same informed consent as Experiment 1 was obtained from all participants.

3.1.2. Stimuli, apparatuses, and tasks

In Experiment 2, the equipment, stimuli, and trial procedure were identical to Experiment 1 but with the following three exceptions. First, the central‐circles‐absent trials in Experiment 1 were replaced by the trials on which a task‐irrelevant green filled circle (probe circle) was presented equiprobably within either the small or large inducers for 100 ms (Fig. 5a). The probe circle, with a diameter and luminance equal to those of the standard circle (i.e., 2.30° and 17.6 cd/m²), was presented on one‐third of the trials. Accordingly, the test and standard circles, when presented, were equal in size on another one‐third of the trials, and were unequal in size (test < standard or test > standard) on the remaining one‐third of the trials. Second, participants here were required to report the color of the apparently larger central circle in half of the blocks and to report the color of the apparently smaller central circle in the other half of the blocks, while ignoring the surrounding inducers as well as the unilateral probe circle. The order of the two opposite response tasks were counterbalanced across participants. Third, Experiment 2 consisted of 28 blocks (seven blocks for each of the four combinations divided according to response task [reporting the apparently larger or smaller circle's color] and small inducers location [left or right]), each containing 96 trials, resulting in 2688 trials in total.

3.1.3. Electrophysiological recording and analysis

The EEG recording and ERP analysis were operated in the same manner as Experiment 1, except as otherwise noted. Among the remaining 51 participants (see Participants section of Experiment 2), 5.78 ± 1.14% of the epochs were excluded after artifact rejection. Prior to being statistically examined by repeated‐measures ANOVAs with the factors of perceptual outcome (perceiving the circle within small/large inducers as larger) and hemisphere (contralateral/ipsilateral relative to the small inducers location), the ERPs (C1 and P1) elicited by the equal‐size pair of test and standard circles were first collapsed across the two opposite response tasks to cancel out the potential attentional bias toward small inducers (see Discussion section of Experiment 1). Note that according to this operation, the ERPs on trials with the first perceptual outcome were obtained by averaging the ERPs on trials where the circle within small inducers was reported as larger across tasks with the ERPs on trials where the circle within large inducers was reported as smaller. Similarly, the ERPs on trials with the second perceptual outcome were computed by averaging the ERPs on trials where the circle within large inducers was reported as larger across tasks with the ERPs on trials where the circle within small inducers was reported as smaller.

The ERPs elicited by the task‐irrelevant unilateral probe circle were first averaged according to the probe location (within small/large inducers) and its left‐right position while also being collapsed across the two opposite response tasks. Then, the ERP waveforms were further collapsed across the probe position (left, right) and hemisphere of recording (left, right) to obtain waveforms recorded contralaterally and ipsilaterally with respect to the probe circle. To ascertain if there were any residual attentional bias toward the small inducers location (see Discussion section of Experiment 1), separate two‐way repeated‐measures ANOVAs with the factors of probe location (within small/larger inducers) and hemisphere (contralateral/ipsilateral relative to the probe circle) were conducted on the mean amplitudes of the probe‐elicited C1 and P1 components. They were measured with the same time windows and electrodes as for the C1 and P1 elicited by the equal‐size pair of test and standard circles, except that the probe‐elicited ipsilateral P1 was measured within a delayed window of 134–154 ms to better capture its peak. In case of a significant two‐way interaction, specific contrasts were further performed between the two probe location conditions using paired t‐tests separately for each hemisphere.

3.1.4. Granger causality analysis

Because the attentional bias toward small inducers, a potential confounding factor of the current study, was expected to be minimized in Experiment 2, here we employed Granger causality analysis to further evaluate whether the C1 lateralization on the illusion‐present trials was primarily attributable to a feedforward information flow from V1 to extrastriate cortex. EEG preprocessing for Granger causality analysis followed the same procedures as those used in the above ERP analysis (see Section 2.1.3 for details), except that the data were segmented into 1000‐ms epochs time‐locked to the onset of the two central circles with a 500‐ms pre‐stimulus interval, and that the contralateral‐minus‐ipsilateral responses on the illusion‐present trials were obtained on a single‐trial basis. To facilitate the latter, we determined which subcondition constituting the illusion‐present trials had the fewest number of trials and randomly sampled an equivalent number of trials for each remaining subcondition, before collapsing the single‐trial responses across subconditions. This procedure was iterated 1000 times, and the collapsed single‐trial responses were averaged across iterations to improve data stability.

Then, time‐frequency distributions of the single‐trial contralateral‐minus‐ipsilateral responses were obtained using short‐time Fourier transform with a fixed 200‐ms Hanning window. The resulting time‐frequency distributions were baseline‐corrected at each frequency by subtracting the average power within the −200 to −100 ms interval from the power at each post‐stimulus time point. In light of previous literature indicating that theta oscillations are associated with feedforward processing in V1 (Kienitz et al., 2021), as well as our time‐frequency analysis confirming that neural oscillations within the C1 time window (58–98 ms) were predominant in the theta band (4–8 Hz), our Granger causality analysis focused on the time series during 58–98 ms within 4–8 Hz at V1‐representative electrodes (P3/P4) and extrastriate‐representative electrodes (PO7/PO8). Causality analysis was then performed using the Multivariate Granger Causality (MVGC) toolbox (Barnett & Seth, 2014). First, a vector auto regressive model was constructed to characterize the dynamic interactions between the selected electrodes (from P3/P4 to PO7/PO8, from PO7/PO8 to P3/P4). The best model order was selected according to the Akaike information criterion (AIC). Subsequently, the Granger causality values were computed pairwise based on the auto‐covariance sequence to assess directed interactions between the selected electrodes. In principle, the Granger causality value measures the degree to which the prediction error is reduced after incorporating information from past time points of the source variable into the prediction of the current time point of the target variable (Barnett & Seth, 2014). Finally, we employed two built‐in F‐tests in the MVGC toolbox to assess whether the observed causality values were significantly greater than the chance level of zero (Fan, Wang, Shao, Zhang, & He, 2020). For more procedural details regarding how our Granger causality analysis was performed using the MVGC toolbox, please see the corresponding MATLAB code uploaded to the OSF repository.

3.2. Results and discussion

3.2.1. Behavioral results

In Experiment 2, the general analytic procedure for behavioral data were identical to those used in Experiment 1, except that the data were first collapsed across the two opposite response tasks before statistical tests. Specifically, for each of the 10 combinations of the test size (60%, 80%, 100%, 120%, 140% of the standard) and test circle location (within small/large inducers), the probability of reporting the test circle as larger in the “which was larger” task was first averaged together with the probability of reporting the standard circle as smaller in the “which was smaller” task, in order to obtain the collapsed probability of reporting the test circle as larger shown in Fig. 5b.

In close agreement with Experiment 1, the collapsed probability of reporting the test circle as larger was also much higher when the test was presented within small inducers (0.688 ± 0.011) than when it was presented within larger inducers (0.312 ± 0.012) on the crucial trials where the test and standard were physically equal in size (t(50) = 16.811, p < .001, d = 2.354). Furthermore, the former one was also higher than the chance level (t(50) = 16.795, p < .001, d = 2.352), whereas the latter one was also lower than the chance level (t(50) = −16.232, p < .001, d = −2.273). In parallel, the estimated PSE was once again smaller when the test appeared within small inducers (93.84 ± 0.42%) than when it appeared within large inducers (106.17 ± 0.60%; t(50) = −15.061, p < .001, d = −2.109), with the former and the latter being significantly smaller and larger than 100%, respectively (t(50) = −14.529, p < .001, d = −2.034; t(50) = 10.253, p < .001, d = 1.436). Therefore, these results demonstrate that the Ebbinghaus illusion was robust even when the response criteria (which was larger vs. which was smaller) were counterbalanced across tasks.

3.2.2. ERPs to the equal‐size circle pair

After being collapsed across the two opposite response tasks, the mean C1 amplitudes (78–98 ms) evoked by the equal‐size pair of circles were examined with the same 2 (perceptual outcome) × 2 (hemisphere) ANOVA as used in Experiment 1. As expected, there was a significant two‐way interaction (F(1, 50) = 4.345, p = .042, η ² _p = 0.080), with the two main effects being nonsignificant (perceptual outcome: F(1, 50) = 0.381, p = .540, η ² _p = 0.008, BF₁₀ = 0.229; hemisphere: F(1, 50) = 2.760, p = .103, η ² _p = 0.052, BF₁₀ = 0.232). Further specific contrasts revealed again that the C1 amplitude was significantly larger over the hemisphere contralateral to small inducers (−1.22 ± 0.14 µV) than over the hemisphere ipsilateral to small inducers (−1.12 ± 0.14 µV) only on trials where the circle within small inducers was perceived as larger (i.e., where the circle within large inducers was perceived as smaller; t(50) = −3.685, p < .001, d = −0.516; Fig. 6a,c), but not on trials where the circle within large inducers was perceived as larger (i.e., where the circle within small inducers was perceived as smaller; contralateral: −1.22 ± 0.13 µV; ipsilateral: −1.22 ± 0.14 µV; t(50) = −0.055, p = .957, d = −0.008, BF₁₀ = 0.153; Fig. 6a,c). In addition, the brain−behavior correlation analysis also showed no reliable correlation between the C1 lateralization on trials with the first perceptual outcome and the Ebbinghaus illusion magnitude (r(49) = .218, p = .124, BF₁₀ = 0.552; Fig. 6d), which was the case even when the Ebbinghaus illusion magnitude was measured alternatively by PSE (r(49) = .244, p = .085, BF₁₀ = 0.739).

Fig. 6 — Same as Fig. 2 but for the illusion‐specific C1 lateralization replicated in Experiment 2, where the ERP data were collapsed across the “which was larger” and “which was smaller” tasks to counterbalance the potential attentional bias toward the side of small inducers in the former task. Error bars represent ± 1 SE. ***: p < .001; n.s.: nonsignificant.

The same two‐way ANOVA conducted on the subsequent P1 amplitudes (120–140 ms) only revealed, as expected, a significant main effect of hemisphere (F(1, 50) = 43.829, p < .001, η ² _p = 0.467). The main effect of perceptual outcome (F(1, 50) = 0.091, p = .764, η ² _p = 0.002, BF₁₀ = 0.160) and the two‐way interaction (F(1, 50) = 0.059, p = .810, η ² _p = 0.001, BF₁₀ = 0.237) were both far from significance, with their Bayes factors providing substantial evidence for the null hypothesis. These results reflect once again that the contralateral versus ipsilateral P1 lateralization was highly prominent irrespective of whether the circle within small inducers was perceived as larger (contralateral: 1.46 ± 0.24 µV; ipsilateral: 1.09 ± 0.25 µV; Fig. 7a,c) or the circle with large inducers was perceived as larger (contralateral: 1.44 ± 0.24 µV; ipsilateral: 1.06 ± 0.26 µV; Fig. 7b,c). Moreover, the brain−behavior correlation analysis also confirmed that individuals with a greater magnitude of the overall P1 lateralization (collapsed across the two perceptual outcomes) exhibited a stronger tendency to perceive the Ebbinghaus illusion (r(49) = .320, p = .022; Fig. 7d), which held true even when the Ebbinghaus illusion magnitude was quantified as PSE (r(49) = .323, p = .021). Taken together, even though the potential attentional bias toward the side of small inducers in Experiment 1 (if any) had been minimized in Experiment 2 by collapsing the ERP data across the two opposite response tasks, we still replicated the C1 and P1 lateralization effects as well as their associations with different aspects of the behavioral Ebbinghaus illusion. Thus, it demonstrates that the attentional bias toward small inducers is inadequate to account for the main findings of the present study.

Fig. 7 — Same as Fig. 3 but for the P1 lateralization responsible for the interindividual variability in the Ebbinghaus illusion magnitude in Experiment 2, where the ERP data were collapsed across the two opposite response tasks to counterbalance the potential attentional bias toward small inducers in the “which was larger” task. Error bars represent ± 1 SE. *: p < .05; ***: p < .001.

3.2.3. ERPs to the unilateral probe circle

Moreover, to ascertain whether there was any attentional bias toward small inducers after the data were collapsed across tasks, the C1 and P1 components elicited by the task‐irrelevant unilateral probe circle newly added in Experiment 2 were analyzed with separate two‐way ANOVAs with the factors of probe location (within small/larger inducers) and hemisphere (contralateral/ipsilateral relative to the probe circle). For the C1 component (Fig. 8a), there was a significant main effect of hemisphere (F(1, 50) = 45.680, p < .001, η ² _p = 0.477), with the C1 amplitude contralateral to the probe being overall smaller than its ipsilateral counterpart (contralateral: −0.14 ± 0.10 µV and −0.21 ± 0.09 µV, ipsilateral: −0.45 ± 0.08 µV and −0.56 ± 0.07 µV, for the probes with small and larger inducers, respectively). This pattern is in accordance with previous reports of the C1 topography in response to unilateral stimuli presented in the upper visual field (Di Russo et al., 2001, 2003; Baumgartner et al., 2018). However, neither the main effect of probe location (F(1, 50) = 1.161, p = .286, η ² _p = 0.023, BF₁₀ = 0.381) nor its interaction with hemisphere (F(1, 50) = 0.547, p = .463, η ² _p = 0.011, BF₁₀ = 0.225) was significant, with the latter's Bayes factor showing substantial evidence for the null hypothesis. These null findings suggest that even if we assume there existed any bias of spatial attention, it would not affect the C1 activity, consistent with the “majority view” that attention does not modulate the first feedforward stage of cortical visual processing (Hillyard & Anllo‐Vento, 1998; Martínez et al., 1999; Di Russo et al., 2003; McDonald et al., 2005; Störmer et al., 2009; Fu et al., 2010a; Ding et al., 2014; Baumgartner et al., 2018; Alilović et al., 2019).

For the P1 component (Fig. 8B), in contrast, not only the two main effects (probe location: F(1, 50) = 11.839, p = .001, η ² _p = 0.191; hemisphere: F(1, 50) = 16.025, p < .001, η ² _p = 0.243) but also the two‐way interaction (F(1, 50) = 33.826, p < .001, η ² _p = 0.404) were significant. Further analyses of the interaction showed that although there was no substantial difference in P1 amplitude between the probes within small (0.67 ± 0.18 µV) and large (0.63 ± 0.19 µV) inducers over the hemisphere contralateral to the probe (t(50) = 0.479, p = .634, d = 0.067, BF₁₀ = 0.170), the P1 amplitude was significantly smaller, instead of larger, for the probe within small inducers (1.12 ± 0.18 µV) than for the probe with large inducers (1.64 ± 0.18 µV) over the hemisphere ipsilateral to the probe (t(50) = −6.106, p < .001, d = −0.855). Notably, if this P1 effect was indeed indicative of a residual bias of spatial attention in Experiment 2, it would be an attentional bias toward the side of large inducers instead of the side of small inducers, because the P1 component is known to be greater in response to spatially attended visual stimuli than in response to spatially unattended stimuli (Hillyard & Anllo‐Vento, 1998; Martínez et al., 1999; Di Russo et al., 2003; Baumgartner et al., 2018; Alilović et al., 2019). Crucially, note that the existence of such a residual attentional bias toward large inducers, despite being unexpected, would only result in the observed significant P1 lateralization to the equal‐size circle pair (see Fig. 7) underestimating rather than overestimating the true P1 lateralization effect. Hence, the analyses of the probe‐evoked ERPs in Experiment 2 further invalidate the attentional bias toward small inducers as an alternative explanation for our main findings.

3.2.4. Initial phase of the C1 to the equal‐size circle pair

It is noteworthy that some previous studies considered the initial phase of the C1 component (i.e., the time range before it peaks) as a purer index of the afferent V1 activity (e.g., Foxe & Simpson, 2002; Hagler, 2014; Gebodh et al., 2017; Alilović et al., 2019). Accordingly, we further tested whether the illusion‐specific C1 lateralization in response to the equal‐size pair of central circles had already been evident during the C1's initial phase, with its mean amplitude remeasured over 58–78 ms, an interval immediately preceding the original measurement interval (see Fig. 6). Indeed, the same pattern of results was found, as reflected by a significant perceptual outcome × hemisphere interaction (F(1, 50) = 5.789, p = .020, η ² _p = 0.104) as well as two nonsignificant main effects (perceptual outcome: F(1, 50) = 0.796, p = .377, η ² _p = 0.016, BF₁₀ = 0.414; hemisphere: F(1, 50) = 0.266, p = .608, η ² _p = 0.005, BF₁₀ = 0.151). Specifically, the C1's initial phase was also significantly greater over the hemisphere contralateral to small inducers (−0.49 ± 0.06 µV) than over the hemisphere ipsilateral to small inducers (−0.43 ± 0.06 µV) only when the circle within small inducers was perceived to be larger (t(50) = −2.120, p = .039, d = −0.297). In contrast, when the circle within large inducers was perceived to be larger, the initial C1 contralateral to small inducers (−0.32 ± 0.10 µV) was even numerically smaller than that ipsilateral to small inducers (−0.41 ± 0.09 µV), although the difference did not reach significance (t(50) = 1.738, p = .088, d = 0.243, BF₁₀ = 0.616). Therefore, these additional analyses provide stronger evidence that the generation of the Ebbinghaus illusion is associated with the first feedforward stage of cortical visual processing.

3.2.5. Granger causality results

Finally, to further examine whether the C1 lateralization on trials where the circle within small inducers was perceived as larger was driven by a feedforward information flow from V1 to extrastriate visual cortex, Granger causality analysis was performed between the V1‐representative electrodes (P3/P4) and extrastriate‐representative electrodes (PO7/PO8), based on the contralateral‐minus‐ipsilateral EEG oscillations within the theta band (4–8 Hz) during the C1 time window (58–98 ms) on these illusion‐present trials. The optimal model order selected according to the AIC was 13. The results showed that the information flow from the electrodes P3/P4 to PO7/PO8 was significantly greater than zero (causality value = 0.0092, p < .001), whereas the information flow from the electrodes PO7/PO8 to P3/P4 did not reach significance (causality value = 0.0029, p = .095).³ This pattern of results suggests a unidirectional information transfer from V1 to extrastriate cortex during the C1 time window, hence furnishing converging support that the Ebbinghaus illusion starts at the first feedforward stage of cortical visual processing.

4. General discussion

Previous investigations have reported convergent evidence that low‐level visual regions including V1 are involved in representing the Ebbinghaus size illusion (Song et al., 2011; Schwarzkopf et al., 2011; Schwarzkopf & Rees, 2013; Kreutzer et al., 2015; Nakashima & Sugita, 2018; Chen et al., 2018, 2022, 2024; Wang et al., 2021; Wu et al., 2023). However, it remains largely undetermined whether the low‐level visual cortex can take part in generating this illusion at the feedforward stage of processing, because low‐level areas also receive a large amount of slower feedback signals from other high‐level brain regions when processing visual information (for review, see Briggs, 2020). The existing psychophysical and brain imaging studies of the Ebbinghaus illusion, given their relatively low temporal resolution, are intrinsically insufficient to dissociate the rapid feedforward processing (if any) from its subsequent feedback processing.

To resolve this issue, we recorded high temporal‐resolution ERPs to the test and standard circles symmetrically flashed on the left and right sides, with one side constantly displaying large surrounding inducers and the other side small inducers during a given block. Our Experiment 1 unveiled that when the test circle size was physically equal to the standard circle size, the evoked earliest visual ERP—the C1 component—was larger over the hemisphere contralateral to small inducers than over the hemisphere ipsilateral to small inducers (i.e., contralateral to large inducers) only for trials on which the circle within small inducers was perceived as larger (wherein the Ebbinghaus illusion occurred) but not for trials on which the circle within large inducers was perceived as larger (wherein the illusion did not occur). Moreover, this illusion‐specific C1 lateralization closely resembled the C1 modulation evoked by physical differences in size. Importantly, this illusion‐specific C1 lateralization was further replicated in Experiment 2 even when the response criteria (i.e., reporting the apparently larger vs. smaller circle) were counterbalanced across tasks to minimize the potential attentional bias toward the side of small inducers. Actually, the pattern of ERPs to the task‐irrelevant unilateral probe was completely opposite to what the attentional bias toward small inducers would predict, thereby invalidating this alternative account for our C1 results. Given that the C1 wave has been shown to originate predominantly in V1 (i.e., the striate cortex: Jeffreys & Axford, 1972; Clark et al., 1995; Di Russo et al., 2001; Kelly et al., 2013a, 2013b; but see Ales et al., 2010) and widely accepted as a neural index of afferent activation in the visual cortex (Martínez et al., 1999; Di Russo et al., 2003; Ding et al., 2014; Bombeke et al., 2016; Alilović et al., 2019; Qin et al., 2022), the current findings furnish strong evidence that the anatomically early visual cortex begins to take part in producing the Ebbinghaus illusion at the feedforward stage of processing. In accordance with this proposal, our Granger causality analysis of the illusion‐present trials also revealed a unidirectional information flow from V1‐representative to extrastriate‐representative electrodes within the C1 lateralization.

It is noteworthy that by applying functional connectivity analyses to resting‐state brain activity, recent fMRI and fNIRS studies have already found feedforward connections from the low‐level visual cortex to other brain areas that could predict the Ebbinghaus illusion magnitude (Chen et al., 2022; Wu et al., 2023). However, a more recent study using task‐based fMRI data did not yield those illusion‐related feedforward connections but a feedback connectivity from the parietal to occipital areas (Chen et al., 2024). This discrepancy may suggest that the feedforward connections estimated by resting‐state data cannot account for the real‐time visual processing evoked by the Ebbinghaus configuration, or that the stimulus‐evoked feedforward processing might be too rapid to be captured by fMRI signals in the study of Chen et al. (2024). In any case, a definitive answer is still lacking as to whether there exists a feedforward locus of cortical visual processing in the Ebbinghaus illusion. Here, by recording instant ERPs elicited by the equal‐size pair of targets presented within small and large inducers, we provide the first unequivocal evidence for the feedforward locus in the Ebbinghaus illusion by showing that the lateralization of the afferent C1 component occurred in an illusion‐specific manner, and that only the Granger‐causal connectivity from V1‐representative to extrastriate‐representative electrodes (but not vice versa) was significant during the C1 lateralization. Hence, the current C1 lateralization effect, in conjunction with the P1 lateralization effect (see below), enhances our understanding about the temporal dynamics of neural activity underlying the Ebbinghaus illusion.

Similar to the earliest C1, the subsequent P1 component elicited by the equal‐size target pair was also found to be larger over the hemisphere contralateral to small inducers than over its ipsilateral counterpart across our Experiments 1 and 2. Given that the P1 component has been consistently localized to extrastriate visual cortex (Clark et al., 1995; Di Russo et al., 2001, 2003; Ding et al., 2014; Miller, Shapiro, & Luck, 2015), the current P1 lateralization is in accord with recent brain imaging studies showing that the target within small inducers elicited stronger fMRI and fNIRS signals in the extrastriate region than the identical target within large inducers (Chen et al., 2022, 2024). However, the current P1 lateralization was further shown to be independent of whether the target within small or large inducers was perceived as larger on a given trial, whereas its overall magnitude was positively predictive of the interindividual variability in the Ebbinghaus illusion magnitude. These interesting findings demonstrate that, in contrast to the C1, the P1 is associated more with how frequently one would perceive the Ebbinghaus illusion than with the presence/absence of the illusion at a given moment. That is, the early sensory processing indexed by the P1 seems necessary but not sufficient for triggering the Ebbinghaus illusion. However, unlike the C1 component, there is no general consensus in the ERP literature regarding whether the P1 component reflects a pure feedforward processing (pros: Zhang & Luck, 2009; Luck & Kappenman, 2011; Roth‐Paysen, Bröcker, Bruchmann, & Straube, 2022; cons: Foxe & Simpson, 2002; Nikolaev, Gepshtein, Kubovy, & van Leeuwen, 2008). Therefore, it is currently uncertain whether the P1 results reported here can also be treated as compelling evidence for the early feedforward locus in the Ebbinghaus illusion. Nevertheless, these P1 results do showcase how the sensory analysis in extrastriate cortex serves as a prerequisite for the earlier processing in striate cortex to initiate an illusory size perception, which is consistent with prior findings highlighting the interactions between multiple brain regions in producing the Ebbinghaus illusion (Kreutzer et al., 2015; Chen et al., 2022; von Gal et al., 2023; Chen et al., 2024; Chen & Jiang, 2024).

In addition to the brain dynamics of the Ebbinghaus illusion, our ERP findings also have new implications for clarifying its psychological mechanisms, which have been vigorously debated for more than 50 years. Specifically, the “size contrast” account proposes that the Ebbinghaus illusion is driven by relatively high‐level cognitive comparisons between the sizes of the central target and surrounding inducers (Massaro & Anderson, 1971; Coren & Miller, 1974; de Fockert, Davidoff, Fagot, Parron, & Goldstein, 2007; Gold, 2014). In contrast, the “contour interaction” account argues that this illusion stems from low‐level sensory interactions, so that the small inducers’ contours (which are typically adjacent to the central target) attract the central target's contour, whereas the large inducers’ contours (which are typically more distant from the target; e.g., see our Fig. 5a) repel the target's contour (Girgus, Coren, & Agdern, 1972; Jaeger, 1978; Jaeger & Grasso, 1993; Sherman & Chouinard, 2016; Todorović & Jovanović, 2018). Obviously, our findings of inducers‐contingent C1 and P1 effects, given their short latency, are consistent with the prediction of the low‐level contour interaction account. However, it does not mean that these ERP effects are sufficient to invalidate the size contrast account, because the current study was not designed to dissociate the two accounts, which requires extra attempts to manipulate the relative size of inducers versus target and the distance between inducers versus target independently (for a detailed discussion of the difficulties in manipulating the two factors orthogonally, see Todorović & Jovanović, 2018). Given that there is growing evidence suggesting that contour interactions and size contrasts may jointly give rise to the Ebbinghaus illusion (Roberts, Harris, & Yates, 2005; Kirsch & Kunde, 2021; Chen & Jiang, 2024), manipulating the above two factors independently based on the current experimental design, although difficult, should be put on the agenda.

It is worth mentioning that under the current experimental design, we were constrained from further disentangling whether the observed C1 and P1 lateralizations signify the representation of the target within small inducers being enlarged, the representation of the target within large inducers being shrunk, or both of them. Indeed, the larger C1 and P1 over the hemisphere contralateral (relative to ipsilateral) to the target within small inducers can also be interpreted as smaller C1 and P1 over the hemisphere contralateral to the target within large inducers. Ascertaining this issue is also important because it has long been suggested that the size overestimation of the target within small inducers and the size underestimation of the target within large inducers may involve different illusion‐producing processes (Jaeger & Pollack, 1977; Jaeger, 1978; Saneyoshi, 2018; Chen et al., 2022). Further inspection of our data revealed that the C1 was uniquely smaller in numerical terms over the hemisphere ipsilateral to the small inducers (i.e., contralateral to the large inducers) on the illusion‐present trials across Experiments 1 and 2, suggesting that our C1 lateralization might stem mainly from the representation of the target within large inducers being shrunk. However, it is strongly noteworthy that this speculation is based on the assumption that the scalp‐recorded C1 reflects the projection of neural transmission in a contralateral manner, which is not necessarily true because: ERPs do not always reflect brain activity right beneath the recorded electrode; and the C1 evoked by unilateral stimuli in the upper visual field tends to be more ipsilaterally distributed (Di Russo et al., 2001, 2003; Baumgartner et al., 2018). Notwithstanding, we note that the possible “ipsilateral projection” does not necessarily generalize to the C1 evoked by bilateral stimuli. If it did generalize, it would imply that on our illusion‐present trials, the circle within small inducers (i.e., the perceptually larger circle) elicited a smaller C1 than the circle within large inducers (i.e., the perceptually smaller circle). This implication would be clearly at odds with existing findings in the Ebbinghaus illusion literature, where perceptually larger central targets have been shown to elicit stronger activation in early visual cortex (Chen et al., 2022, 2024), and, therefore, seems less likely to hold. Crucially, although we were constrained from disentangling for sure the exact origin of the current illusion‐specific C1 lateralization, its reliable occurrence across Experiments 1 and 2 at least indicates that the differential processing of the two central circles under the Ebbinghaus illusion emerges as early as the feedforward stage of cortical visual processing, which still supports our core conclusion. Nonetheless, future research with refined paradigms that can circumvent the current difficulties in interpreting the C1 lateralization is definitely required, and presenting the standard circle and large/small inducers at the center of the upper visual field prior to the test circle onset seems to be a promising solution (for similar designs, see Chen et al., 2018, 2022).⁴

Another limitation of the current study is that although we have controlled for the response‐related spatial attentional bias in Experiment 2 by collapsing data across two opposite response tasks, a more subtle form of attentional bias might remain unaccounted for. Specifically, no matter whether the task was to report the color of the apparently larger or smaller circle, participants might be consistently aware that they more frequently perceived the circle within small inducers as larger, and the circle within large inducers as smaller. This could lead some participants to still pay more attention to the side of small inducers while others to the side of large inducers, even after the response‐related attentional bias we focused on has been counterbalanced. Unfortunately, it is impossible to know how many participants fell into the former group and how many into the latter in the current study. However, our probe‐elicited P1 results in Experiment 2 indicate that there was an unexpected, residual attentional bias toward the side of large inducers even after ERP data had been collapsed across two opposite response tasks, which strongly suggests that it may well be the subtle attentional bias mentioned above. If that is the case, our probe‐elicited C1 results would indicate, at least in the current study, that this subtle attentional bias had not yet affected stimulus processing at the C1 stage, and, therefore, would not confound our illusion‐related C1 lateralization, although it is currently still debated whether attention modulates the C1 component (Wolf, Bruchmann, Pourtois, Schindler, & Straube, 2022; Qin, Crespi, Proverbio, & Pourtois, 2023; Pan, Zhao, Luo, Chen, & Cai, 2024). Nevertheless, further investigation is warranted to determine whether our probe‐elicited P1 effect signifies this subtle attentional bias, and how this attentional bias can be effectively controlled.

In addition, there were several factors that might have also contributed to our illusion‐specific C1 lateralization. First, given that stimuli with higher salience have been shown to elicit larger C1 amplitudes (Zhang et al., 2012), it seems possible that the generation of the Ebbinghaus illusion was accompanied concurrently by changes in relative salience of the two central circles, which might have more or less facilitated the observed C1 lateralization on the illusion‐present trials. Second, in light of previous studies showing that perceptual load may interact with involuntary attention to modulate the C1 component (Fu et al., 2009, 2010b), it is also possible that the perceptual load here differed intrinsically between the small‐ and large‐inducers sides—and that this subjective difference could be even more pronounced on the illusion‐present trials—which might also have added to the observed illusion‐specific C1 lateralization. Third, although we did not manipulate attentional load throughout the current study, trial‐by‐trial fluctuations in attentional load might also have played a role. For example, the attentional load might be relatively balanced between the small‐ and large‐inducers sides on the illusion‐absent trials but less so on the illusion‐present trials. Indeed, several investigations have reported that attentional load may affect the C1 component under certain circumstances (Rauss, Pourtois, Vuilleumier, & Schwartz, 2009, 2012; Wolf et al., 2022; Qin et al., 2023; but see Fu et al., 2010a; Ding et al., 2014 for negative results). Given that all of the aforementioned three factors could covary with the occurrence of the Ebbinghaus illusion, a challenge for the future is to determine whether they are causally involved in the illusion or merely confounding factors.

Author contributions

Song Zhao: Conceptualization, data curation, formal analysis, funding acquisition, investigation, project administration, software, supervision, visualization, writing—original draft, writing—review and editing; Yi Fang: Conceptualization, formal analysis, investigation, validation, visualization, writing—original draft; Mengdie Zhai: Conceptualization, formal analysis, methodology, software, validation, writing—original draft, writing—review and editing; Chengzhi Feng: Methodology, resources, writing—original draft; Wenfeng Feng: Conceptualization, data curation, funding acquisition, project administration, resources, supervision, writing—original draft, writing—review and editing.

Conflicts of interest

There are no conflicts of interest to declare.

Data and code availability statement

The experimental stimuli, data, and analysis scripts that support the current findings are available at https://osf.io/wjpzh/overview.

Supporting information

Supplementary Information

COGS-50-e70251-s001.docx^{(248.7KB, docx)}

Acknowledgments

This study was supported by the National Key Research and Development Program of China (no. 2021ZD0202600 to Wenfeng Feng) and the National Natural Science Foundation of China (no. 32171048 to Wenfeng Feng; no. 32200851 to Song Zhao).

Notes

Although averaging ERP amplitudes across adjacent electrodes has the disadvantage of losing spatial information, it has the advantages of maximizing signal‐to‐noise ratio and statistical power (Luck, 2014; Zhang & Kappenman, 2024) and reducing the number of factors in a given multi‐factor ANOVA (thereby controlling the overall Type I error rate: Luck & Gaspelin, 2017), which are more important in ERP research.

We also tentatively conducted three‐way ANOVAs with a new factor “electrode” included (for the C1 component, three levels: P1/2, P3/4, PO3/4; for the P1 component, four levels: P5/6, P7/8, PO5/6, PO7/8), and the results are detailed in Supplementary Materials, Section A.

When P1/P2, which are more adjacent to midline, were used as the V1‐representative electrodes, the same pattern of results was found: the information flow from P1/P2 to PO7/PO8 was significantly greater than zero (causality value = 0.0110, p < .001), whereas the information flow from PO7/PO8 to P1/P2 did not reach significance (causality value = 0.0030, p = .273).

⁴

We thank one of the anonymous reviewers for providing us with the basic idea for this solution (design). According to our understanding, each trial under this design may start with the presentation of an annulus of large inducers, an annulus of small inducers, or no inducers at the center of the upper visual field with equal probability, which will be constantly visible (if presented) throughout each trial. After a variable delay, a standard circle is presented at the center of the ring of inducers and remains visible until the trial ends. Following another delay, a test circle—either smaller or larger than the standard circle—is presented below the Ebbinghaus configuration, and participants may be required to adjust the size of the test circle to match that of the standard circle without time limit. In terms of data analysis, the C1 at posterior midline electrodes evoked by the standard circle can be compared across the small‐inducers, large‐inducers, and no‐inducers conditions to disentangle whether any C1 modulation reflects an enlargement of the target representation within small inducers, a shrinkage of the target representation within large inducers, or both. Note that under the proposed design: (a) pilot experiments may be required to help maximize the proportion of the illusion‐present trials for the small‐inducers and large‐inducers conditions, thereby ensuring sufficient sensitivity for the proposed between‐condition comparisons of the C1; (b) the Ebbinghaus configuration should remain on screen (rather than disappear) when the test circle appears, in order to ensure that the behavioral illusion effect arises from comparing the test circle with the perceptual representation of the standard circle, rather than with its working memory representation.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary Information

COGS-50-e70251-s001.docx^{(248.7KB, docx)}

Data Availability Statement

The experimental stimuli, data, and analysis scripts that support the current findings are available at https://osf.io/wjpzh/overview.

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PERMALINK

Feedforward Processing in Early Visual Cortex Underlies the Ebbinghaus Illusion

Song Zhao

Yi Fang

Mengdie Zhai

Chengzhi Feng

Wenfeng Feng

Abstract

1. Introduction

Fig. 1.

2. Experiment 1

2.1. Methods

2.1.1. Participants

2.1.2. Stimuli, apparatuses, and task

2.1.3. Electrophysiological recording and analysis

2.2. Results

2.2.1. Behavioral results

2.2.2. ERPs to the equal‐size circle pair

Fig. 2.

Fig. 3.

2.2.3. ERPs to the unequal‐size circle pairs

Fig. 4.

2.3. Discussion

Fig. 5.

3. Experiment 2

3.1. Methods

3.1.1. Participants

3.1.2. Stimuli, apparatuses, and tasks

3.1.3. Electrophysiological recording and analysis

3.1.4. Granger causality analysis

3.2. Results and discussion

3.2.1. Behavioral results

3.2.2. ERPs to the equal‐size circle pair

Fig. 6.

Fig. 7.

3.2.3. ERPs to the unilateral probe circle

Fig. 8.

3.2.4. Initial phase of the C1 to the equal‐size circle pair

3.2.5. Granger causality results

4. General discussion

Author contributions

Conflicts of interest

Data and code availability statement

Supporting information

Acknowledgments

Notes

References

Associated Data

Supplementary Materials

Data Availability Statement

ACTIONS

PERMALINK

RESOURCES

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