Article

Role of Orientation
Processing in the Eggs Illusion

Perception
2019, Vol. 48(12) 1197–1213! The Author(s) 2019
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DOI: 10.1177/0301006619878954
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Kun Qian
Institute of Decision Science for a Sustainable Society,
Kyushu University, Fukuoka, Japan

Hiroyuki Mitsudo
Faculty of Human-Environment Studies, Kyushu University,
Fukuoka, Japan

Abstract
In the eggs illusion, small patches perceptually deform when placed at the midpoints between theintersections of a regular grid. In this study, we explored the role of orientation processing in theillusion, by manipulating some spatiotemporal stimulus parameters using three psychophysicalexperiments. In Experiment 1, we manipulated grid luminance and presentation duration as independent variables and found that the illusion occurred even with a brief presentation of approximately 200 to 300 ms. In Experiments 2 and 3, besides presentation duration, we alsosystematically varied the orientation information of the stimulus. In addition to the original grid
pattern, stimuli with only horizontal or vertical bars were employed in Experiment 2. The magnitude of the illusion was significantly weakened under the bar conditions. In Experiment 3, we varied
the orientation of the bars stepwise and revealed that the local orientation information around thecircular patches and the relative orientation information provided by the orthogonal bars of thegrid are contributing factors to the illusion. Based on these results, we discussed the role oforientation processing in generating the eggs illusion.
Keywords
visual illusion, shape perception, orientation processing
Date Received: 19 June 2019; accepted: 6 September 2019

Introduction
Two-dimensional, regular grid patterns can produce visual illusions concerning brightness,such as the Hermann grid illusion (Brewster, 1844; Hermann, 1870), Bergen’s illusion
Corresponding author:
Kun Qian, Institute of Decision Science for a Sustainable Society, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka
8190395, Japan.
Email: qk@kyudai.jp

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Perception 48(12)(Bergen, 1985), and the blanking phenomenon (McAnany & Levine, 2004). Schrauf andcolleagues (Schrauf, Lingelbach, Lingelbach, & Wist, 1995; Schrauf, Lingelbach, & Wist,
1997) reported a striking brightness illusion produced by a grid, in which white patches
located at the intersections of a gray grid appear darkened and scintillating. The scintillating
grid illusion is influenced by the luminance contrast and size relationship among the stimulus elements (i.e., white circular patches, gray grid, and black background squares; Schrauf
et al., 1997). Spatial and temporal characteristics of the scintillating grid illusion have been
also explored. In the spatial domain, orientation information is important for generating thescintillating grid illusion, because the illusory effect is weakened by changing orientation
information, such as curving (Levine & McAnany, 2008), breaking (Qian, Kawabe,
Yamada, & Miura, 2012), or partially removing (Qian, Kawabe, Yamada, & Miura,2010) the grid. Another spatial feature is the retinal location, because the scintillating
grid illusion typically occurs in the retinal periphery and is enhanced by voluntary eye
movements (Schrauf et al., 1997; VanRullen & Dong, 2003). In the temporal domain,
Schrauf, Wist, and Ehrenstein (2000) reported that the scintillating grid illusion occurs
even at brief presentations. Considering these results, Qian et al. (2012) emphasized thatorientation processing greatly contributes to the scintillating grid illusion and proposed atheoretic mechanism of the scintillating grid illusion based on the activities of S1-type simple
cells in the primary visual cortex.
Whereas the scintillating grid illusion is related to the perception of brightness, the eggs
illusion—a grid-induced illusion relating to geometric shape—has been recently discovered(Qian & Mitsudo, 2016). In this illusion, unlike in the scintillating grid illusion, white circular
patches are located at the midpoints between adjacent intersections of a gray grid pattern.
In this configuration, the patches are perceived as elliptic (Figure 1). In the first investigationof this illusion, Qian and Mitsudo (2016) showed that the occurrence and magnitude of theeggs illusion were influenced by the patch size and grid luminance. The effect of both variables
suggests a similarity between the eggs illusion and the scintillating grid illusion, because thestrength of the scintillating grid illusion was also affected by the size of the white patches andthe luminance magnitude of the grid (Qian, Yamada, Kawabe, & Miura, 2009; Schrauf et al.,1997). This similarity is surprising because the visual attributes of the two illusions are quite
different. The eggs illusion involves shape perception, whereas the scintillating grid illusion
involves brightness perception. In addition to the scintillating grid illusion, Qian and Mitsudo(2016) also discussed other perceptual phenomena (e.g., the apparent size illusion [Helmholtz,
1867; van Erning, Gerrits, & Eijkman, 1988], the shape-contrast effect [Suzuki & Cavanagh,
1998], and the Orbison illusion [Orbison, 1939]), which might be related to the eggs illusion.
Nevertheless, the mechanisms underlying the eggs illusion remain unclear.
As to the scintillating grid illusion, Qian et al. (2012) suggested that orientation processing
is important. Considering some common features between the scintillating grid and eggs
illusions (Qian & Mitsudo, 2016), in this study, we investigated the role of orientation processing on the eggs illusion to provide insights into its underlying mechanisms. Based on theprevious studies of the scintillating grid illusion, we manipulated the spatiotemporal featuresof the eggs illusion to explore the processing of orientation information. Schrauf et al. (2000)
found that a brief presentation (around 200 ms) enhanced the scintillating grid illusion.
To examine the temporal properties of the eggs illusion and their relationship with orientation
processing, in all experiments of this study, we systematically varied the presentation durationand stimulus configuration of the pattern that produces the eggs illusion. Especially inExperiments 2 and 3, we varied the spatial configuration to thoroughly investigate the roleof orientation information, to examine the interactions between spatial and temporal properties, and finally to compare them with those of the scintillating grid illusion.

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Figure 1. The eggs illusion. White circular disks located on a gray grid are perceived as egg-like ellipses.

Experiment 1a: Presentation Duration Alters the Eggs Illusion
In this experiment, we manipulated the presentation duration of the eggs illusion. To examine the magnitude of the illusion, we used the same method as in Experiment 1 of Qian and
Mitsudo (2016). We manipulated the presentation duration in the range of 40 to 2,000 ms,
according to previous research on the scintillating grid illusion (Schrauf et al., 2000).
We predicted that the eggs illusion had similar temporal properties to those of the scintillating grid illusion and occurred under conditions of brief exposure.

Methods
Observers. Ten observers participated in Experiment 1a (eight men and two women; mean
age ¼ 29.9 years; SD ¼ 4.5 years). All observers, with normal or corrected-to-normal visualacuity, were naı̈ve to the purpose of the experiment. The experiments in this study wereapproved by the Ethics Committee for Psychological Studies in Institute of Decision Science
for a Sustainable Society, Kyushu University, Japan (No. 2017/2–3). Written informed
consent was provided by each participant at the beginning of the experiment.
Apparatus and stimuli. Stimuli were generated by a computer (Apple, Mac Pro, MB871J/A)
and displayed on a 21-in. CRT monitor (EIZO, FlexScan F931, 1,152  870 pixels, 75 Hz).
The experiment was conducted using MATLAB R2017a with Psychtoolbox (Brainard,
1997; Pelli, 1997). Observers viewed the monitor binocularly with a chin-and-foreheadrest, at a viewing distance of 60 cm. The experiment was conducted in a darkened room.

1200

Perception 48(12)The test stimulus consisted of a black background, a grid, and an array of perfectly
circular white patches. The luminance values of the black background and the white patches
were 1 cd/m2 and 94 cd/m2, respectively. The gray grid was composed of 11 horizontal and
11 vertical bars spaced equally (each bar subtended 25  35.40 of visual angle). The distance
between adjacent bars was 1.73 . Ten white circular patches with a diameter of 39.80 werearranged on each bar. Each patch was positioned at the midpoint between the two adjacentintersections of the bars. All stimuli were drawn using the antialiasing method.
The luminance of the grid and the presentation duration of stimuli were varied as independent variables. The luminance of the grid was selected from 7, 13, and 28 cd/m2, and thepresentation duration of stimuli was selected from 40, 133, 280, 413, 693, 973, 1,400, and
2,000 ms. These parameter values were similar to those used in previous studies (Qian &Mitsudo, 2016; Schrauf et al., 2000).
The display for response consisted of a 9-point scale (Figure 2). Two circular patches witha diameter of 44.40 and a luminance value of 94 cd/m2 were presented under the leftmost
point of the scale. Four different sets of elliptic patches were similarly presented under thethird, fifth, seventh, and ninth points from the left of the scale. In a column, two elliptic
patches had the same shape but were orthogonal to each other (i.e., vertically or horizontallyoriented). All eight ellipses in the four sets had an identical minor-axis length of 44.40 (thesame as the diameter of the circular patches in the leftmost set). The major-axis lengths ofthe ellipses in the third, fifth, seventh, and ninth sets from the left were 48.00 , 50.40 , 54.00 , and57.60 , respectively (corresponding to aspect ratios of 1.08, 1.14, 1.22, and 1.30).
Procedure. At the beginning of each trial, a black background was presented for 1 s, followed
by a fixation cross (1.1  1.1 of visual angle, 94 cd/m2) that was presented for 200 ms.
After the presentation of the fixation cross, the test stimulus was presented for one of theeight durations (40–2,000 ms). Observers were instructed to view the stimulus without

Figure 2. The response display of Experiment 1a. Observers were asked to make a judgment by moving
the square indicator horizontally. Circular and elliptic patches under the response scale were references forthe shape judgment.

Qian and Mitsudo

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keeping their eyes on a particular position, particularly when the presentation duration waslong. After the disappearance of the test stimulus, a black-and-white random-dot pattern
was displayed for 493 ms. The response display appeared after the disappearance of therandom-dot mask. Observers were asked to choose the patch from the nine given options
that was closest to the perceived shape of the patches in the test stimulus. If the patch shapes
were perceptually different across locations, observers were instructed to choose the one
closest to the averaged shape. The observers were not required to respond fast. The next trial
automatically started 500 ms after observer’s response.
Three levels of grid luminance and eight levels of presentation duration yielded 24 conditions. Each condition was tested 5 times. In total, 120 experimental trials were conductedin a randomized order. Approximately 10 practice trials were randomly selected from the
24 experimental conditions.

Results and Discussion
Figure 3 shows the perceived aspect ratios as a function of presentation duration averaged
over the 10 observers in Experiment 1a, with three curves each for the three grid luminancevalues. A two-way within-participant analysis of variance (ANOVA) was performed on themean aspect ratios, with the factors of grid luminance and presentation duration. We foundsignificant main effects of grid luminance—F(2, 18) ¼ 35.303, p < .0001, g2p ¼ .797—and presentation duration—F(7, 63) ¼ 5.162, p < .001, g2p ¼ .365—and a significant interaction—F(14, 126) ¼ 8.15, p < .0001, g2p ¼ .475. Tests of simple main effects revealed that the effectof the presentation duration was significant for all grid luminance conditions—7 cd/m2:
F(7, 189) ¼ 3.117, p < .005; 13 cd/m2: F(7, 189) ¼ 3.749, p < .001; 28 cd/m2: F(7, 189) ¼
12.419, p < .0001. The simple main effect of grid luminance was significant when the presentation duration was equal to or longer than 280 ms—40 ms: F(2, 144) ¼ 0.197, p ¼ .822;
133 ms: F(2, 144) ¼ 0.357, p ¼ .7; 280 ms: F(2, 144) ¼ 12.873, p < .0001; 413 ms: F(2, 144) ¼
28.425, p < .0001; 693 ms: F(2, 144) ¼ 26.109, p < .0001; 973 ms: F(2, 144) ¼ 40.463,
p < .0001, 1,400 ms: F(2, 144) ¼ 24.333, p < .0001, 2,000 ms: F(2, 144) ¼ 20.143, p < .0001.

Figure 3. Results of Experiment 1a. The mean perceived aspect ratios of the patches, averaged over the
10 observers, are shown as a function of presentation duration. Error bars denote standard errors ofthe mean. A higher perceived aspect ratio indicates a stronger magnitude of the eggs illusion. Note: Pleaserefer to the online version of the article to view the figures in colour.

1202

Perception 48(12)Multiple comparisons with Ryan’s method (Ryan, 1960) showed that perceived aspect ratios
were significantly different for each pair of all grid-luminance combinations (ps < .001)
and for seven pairs of presentation-duration combinations as follows: 40–280 ms, 40–
413 ms, 40–693 ms, 133–280 ms, 133–413 ms, 280–2,000 ms, and 413–2,000 ms (ps < .05).
The present results found that both grid luminance and presentation duration affected
the magnitude of the eggs illusion. The significant main effect of grid luminance is consistent
with Qian and Mitsudo (2016), showing that a brighter grid made circular patches appear
more elliptic. Furthermore, we found that the effect of grid luminance on the illusioninteracted with presentation duration. For presentation durations equal to or shorter
than 133 ms, no significant differences existed between the three levels of grid luminance.
However, for presentation durations longer than 133 ms (i.e., 280–2,000 ms), the simple
main effect of grid luminance was significant. The results of multiple comparisons suggestthat the illusory deformation was almost saturated at a presentation duration of around
280 ms, because no significant differences were found between 280 ms and 413, 693, 973, or
1,400 ms. Under conditions with grid luminance values of 13 cd/m2 and 28 cd/m2, the illusory deformation was enhanced at short stimulus configurations (280 ms). A significant
difference between 280 and 2,000 ms suggested that the illusion was weakened when thestimuli were presented for longer durations (a few seconds). Similar to the scintillating grid
illusion, these results showed that the eggs illusion also occurs at brief presentations.
Furthermore, the values of perceived aspect ratio were evidently greater than 1, even atbrief presentation durations of 40 and 133 ms. We questioned if the observers saw theillusion at short presentation durations of 40 and 133 ms. Our informal observations indicate that the illusion is imperceptible at very short presentations, and thus, we consider thatthe observers’ settings obtained at 40 and 133 ms resulted from their common response bias
against selecting the leftmost position of the response scale (i.e., a perfect circle). To address
this issue, we conducted Experiment 1b using a cancellation method.

Experiment 1b: Cancellation of the Eggs Illusion Under Various
Temporal Conditions
Based on the results of Experiment 1a, it was debatable whether the illusion disappeared underconditions of brief exposure (133 ms) because the obtained values of the perceived aspect ratio
were greater than 1. Therefore, to investigate whether such values were a result of a response
bias, we used a cancellation method which has also been employed in Qian and Mitsudo (2016,
Experiment 2). In this method, the perfectly circular small patches were replaced by ellipses withseveral aspect ratios relative to grid orientation. If the reported aspect ratios were related to a
response bias, but not to the eggs illusion, the obtained aspect ratios will be less systematically
influenced by the aspect ratio of the small patches in the test pattern.

Methods
The methods employed in Experiment 1a were used, except for those described here.
Observers. Sixteen observers participated in Experiment 1b (6 men and 10 women; mean
age ¼ 24.9 years; SD ¼ 5.6 years). Of them, two took part in Experiment 1a as well.
Apparatus and stimuli. The luminance value of the grid was 28 cd/m2, as it generated thestrongest illusion in Experiment 1a. In the experiment, instead of manipulating the grid
luminance, the aspect ratio of the white patches was altered as an experimental variable inQian and Mitsudo

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Experiment 1b. In addition to the perfect circle, elliptic patches were employed inExperiment 1b. The physical aspect ratio of the patches varied with respect to the local
grid orientation, resulting in the following seven levels: 0.87, 0.91, 0.96, 1.00 (perfect circle),
1.05, 1.09, and 1.14. The diameter of the perfect circles was 39.80 . To control the patch size,
the area of the patches was maintained constant across different patches as in Qian and
Mitsudo (2016, Experiment 2). Regarding the elliptic patches, the lengths of the axis along
the local grid orientation were 37.20 , 38.00 , 39.00 , 40.80 , 41.60 , and 42.50 , whereas the lengthsof the other axis were 42.70 , 41.70 , 40.70 , 38.90 , 38.10 , and 37.40 , respectively. In addition to thepatch shape, the presentation duration was also examined as the other experimental variable
in Experiment 1b. Since the aim of Experiment 1b was to confirm the illusion under a brief
stimulus exposure, we reduced the levels of presentation duration, yielding to the following
three durations: 40, 280, and 693 ms.
For the response display, the nine-point scale used in Experiment 1a was changed to a 6point scale. Under each point of the scale, there was a pair of sample patches with the same
aspect ratio. Although the sample patches at the leftmost point of the scale were two perfectcircles with a diameter of 39.80 , two ellipses with the same aspect ratio but with different
orientations (longer vertical axis or longer horizontal axis) were located under each scalepoint between the second and the sixth scale points from the left end. The sizes (shorter  longer axes) of the five pairs of ellipses were 39.00  40.80 , 38.00  41.60 , 37.20  42.50 ,36.40  43.40 , and 35.40  44.30 . Consequently, the corresponding aspect ratios of the sample
patches were 1.00, 0.96, 0.91, 0.88, 0.84, and 0.80, respectively.
Procedure. Observers were asked to choose one of the six alternatives that was closest to thepatches they perceived in the test stimulus. No feedback on response accuracy was provided.
Three conditions of presentation durations were varied across blocks with five repetitions ina randomized order. Each block consisted of 21 trials (7 patch shapes  3 repetitions), a
total of 315 experimental trials (21 trials  15 blocks) were tested for each observer.
Data analysis. To analyze how perceived patch shape is related to local grid orientation, we
fitted data from different aspect ratios with a three-parameter Gaussian curve (mean, SD,
and peak amplitude). The fitting procedure was the same as that used in Experiment 2 of
Qian and Mitsudo (2016).

Results and Discussion
Figure 4 shows the perceived aspect ratios averaged over the 16 observers. A two-way
within-participant ANOVA was conducted on the mean perceived aspect ratios with factorsof presentation duration and patch aspect ratio. The results of ANOVA revealed significant
main effects of presentation duration—F(2, 30) ¼ 62.442, p < .0001, g2p ¼ .806—and patch
aspect ratio—F(6, 90) ¼ 63.474, p < .0001, g2p ¼ .809—and a significant interaction—F(12,180) ¼ 16.995, p < .0001, g2p ¼ .531. Tests of simple main effects showed that the effect ofpresentation duration was significant for all patch aspect ratios—0.87 aspect ratio: F(2,210) ¼ 39.053, p < .0001; 0.91 aspect ratio: F(2, 210) ¼ 16.391, p < .0001; 0.96 aspect ratio:
F(2, 210) ¼ 11.222, p < .0001; 1.00 aspect ratio (perfect circle): F(2, 210) ¼ 28.897, p < .0001;
1.05 aspect ratio: F(2, 210) ¼ 50.912, p < .0001; 1.09 aspect ratio: F(2, 210) ¼ 70.713,
p < .0001; 1.14 aspect ratio: F(2, 210) ¼ 95.099, p < .0001. The simple main effect of patch
aspect ratio was significant for all presentation duration conditions—40 ms: F(6, 270) ¼
3.427, p < .005; 280 ms: F(6, 270) ¼ 46.541, p < .0001; 693 ms: F(6, 270) ¼ 70.246, p < .0001.

Perception 48(12)Mean perceived aspect ratio(minor axis / major axis)

1204
1

Presentation duration (ms)

0.96

40
280
693

0.92
The mean of 1 SEs
across conditions

0.88

0.84

SD = 0.448
SD = 0.550

0.076
0.060

0.80
0.87

0.91

0.96

1

1.05

1.09

1.14

Aspect ratio (vertical / horizontal)

Figure 4. Results of Experiment 1b. The mean perceived aspect ratios averaged over the 16 observers areshown as a function of physical aspect ratio. Corresponding patch shapes are illustrated along the graph axes.
Best-fitting Gaussian curves and amplitude peaks of each fitting curve are displayed in the graph.

To examine how the obtained aspect ratios were systematically related to the patch aspectratio, a Gaussian function with three free parameters (i.e., the mean, SD, and peak amplitude) was fitted to the perceived aspect ratios. Because fitting was unstable or impossible forsix observers in the 40-ms condition, we estimated the three parameters of the Gaussian
curve for the 14 observers at presentation durations of 280 and 693 ms (fitting for datafrom two observers were excluded because of their unreliable fitting results). As shown in
Figure 4, the mean values of the fitted Gaussian curve were shifted to smaller aspectratios at presentation durations of 280 and 693 ms, suggesting that somewhat elongatedpatches were required to cancel or weaken the illusory eggs effect. The SD values of theGaussian curve were comparable to those of Qian and Mitsudo (2016). These results
generally replicated the results obtained at the 1-second presentation duration inExperiment 2 of Qian and Mitsudo (2016). In contrast to presentation durations of
280 and 693 ms, the results obtained at a presentation duration of 40 ms were almost
flat and were relatively closer to the aspect ratio of 1.0 than those of 280 and 693 ms.
This suggested that the observers provided almost a similar response, regardless of thedifferent physical patch shapes. These results indicated that no eggs illusion occurred
when the stimulus was presented for 40 ms, perhaps because the stimulus was almost
invisible. Furthermore, a series of t tests with independent samples were performed tocompare the best-fit values of amplitude, mean, and SD between durations of 280 and
693 ms. The results of t tests revealed a significant difference on amplitude—t(26) ¼ 3.48,
p < .01, Cohen’s d ¼ 1.316—and SD—t(26) ¼ 2.07, p < .05, Cohen’s d ¼ 0.781. The meanvalues were not significantly different—t(26) ¼ 1.07, p ¼ .29, Cohen’s d ¼ 0.404, which isconsistent with the results of multiple comparisons in Experiment 1a.
The significant interaction between grid luminance and presentation duration foundin Experiments 1a and 1b suggested a possible interrelationship between spatial andtemporal properties. To investigate the interaction further, and to thoroughly discussorientation processing, we manipulated spatial configuration and presentation duration in
the following experiments.

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Experiment 2: The Eggs Illusion Produced by Bars
To determine the role of the orientation information provided by the grid and bars, inExperiment 2, we removed either horizontal or vertical bars in the grid configuration of
the eggs pattern. Instead of grid luminance, we employed spatial configuration as an experimental factor. We tested three spatial configurations: horizontal bars only, vertical bars
only, and both horizontal and vertical bars (i.e., the grid used in Experiment 1). We predicted that because orientation information is weakened in the horizontal-bars-only andvertical-bars-only configurations, the eggs illusion would be reduced in these conditions
compared with the grid condition.

Methods
The methods were the same as those in Experiment 1a, except the following.
Observers. Ten observers participated in Experiment 2 (five men and five women; mean
age ¼ 30.3 years; SD ¼ 6.7 years). Three of them also participated in Experiment 1a.
Apparatus and stimuli. For the test stimulus, the luminance value of the grid was 28 cd/m2,
which generated the strongest illusion in Experiment 1a. There were two experimental
variables in Experiment 2: stimulus configuration and presentation duration. The stimulus
configuration varied in three conditions: grid, horizontal, and vertical. In the grid condition,
stimuli were identical to those used in Experiment 1a. In the horizontal condition, the 11
horizontal bars of the original grid and circular patches located on horizontal bars were
presented. Similarly, in the vertical condition, the 11 vertical bars of the original grid andcircular patches were presented. The numbers of bars and circular patches in the horizontal
and vertical conditions were half of those in the grid condition. The presentation duration
varied in eight conditions: 40, 67, 133, 213, 347, 493, 693, and 1,000 ms. Except for 40 ms,
the values of the presentation durations were almost half of those in Experiment 1a, in an
attempt to investigate the time course of the eggs illusion in more detail.
Procedure. In addition to the blank interval, the fixation cross remained on the screen during
the time that the test stimulus was presented. To make the fixation cross salient in the test
stimulus, the color of the fixation cross was changed from white to red. Observers wereasked to view the fixation cross when it was presented, regardless of the presentation of thetest stimulus. For each observer, a total of 120 experimental trials were conducted (3 stimulus configurations  8 presentation durations  5 repetitions).

Results and Discussion
Figure 5 shows the perceived aspect ratios as a function of presentation duration, averaged
over the 10 observers in Experiment 2. We conducted a two-way within-participant
ANOVA on the mean perceived aspect ratios, with factors of stimulus configurationand presentation duration. We found significant main effects of stimulus configuration—
F(2, 18) ¼ 18.691, p < .0001, g2p ¼ .675—and presentation duration—F(7, 63) ¼ 5.049,
p < .001, g2p ¼ .359—and a significant interaction—F(14, 126) ¼ 8.472, p < .0001, g2p ¼ .485.
Tests of simple main effects showed that the effect of presentation duration was significant
for each stimulus configuration—grid: F(7, 189) ¼ 12.68, p < .0001; horizontal: F(7, 189) ¼
3.745, p < .001; vertical: F(7, 189) ¼ 3.287, p < .005. The simple main effect of stimulus
configuration was significant when the presentation duration was equal to or longer than

1206

Perception 48(12)
(a)

(b)

Grid

Vertical

Perceived aspect ratio

1.2

Grid
VerticalHorizontal

1.15

1.1

1.05

1

40 133
67

Horizontal

213 347

493

693

1000

Presentation duration (ms)Figure 5. Stimuli and results for Experiment 2. (a) Schematic illustrations of test stimuli used in the grid,vertical, and horizontal conditions. (b) Results of Experiment 2. Mean perceived aspect ratios, averaged overthe 10 observers, are shown as a function of presentation duration. Error bars denote standard errors ofthe mean.

133 ms—40 ms: F(2, 144) ¼ 0.075, p ¼ .927; 67 ms: F(2, 144) ¼ 1.182, p ¼ .310; 133 ms: F(2,144) ¼ 3.537, p < .05; 213 ms: F(2, 144) ¼ 6.96, p < .005; 347 ms: F(2, 144) ¼ 16.143,
p < .0001; 493 ms: F(2, 144) ¼ 20.464, p < .0001; 693 ms: F(2, 144) ¼ 29.053, p < .0001,
1,000 ms: F(2, 144) ¼ 22.672, p < .0001. Multiple comparisons showed that perceived
aspect ratios were significantly different between the horizontal and grid conditions(p < .0001) and between the vertical and grid conditions (p < .001). There was no significant
difference between the horizontal and vertical conditions (p ¼ .07). Three pairs ofpresentation-duration combinations showed significant differences as follows: 40–133 ms,
40–213 ms, and 40–347 ms (ps < .001). Figure 5(b) shows that the illusion became weaker
when stimuli were presented for more than 347 ms in the horizontal and vertical conditions.
Results of multiple comparisons revealed that for the horizontal condition, the illusion
significantly declined when the stimuli were presented for 1 s compared with stimulus presentations of 133 and 213 ms (ps < .05). A similar decline during the longer presentation was
not significant in the vertical condition (p > .05). In contrast to the case of the grid condition, where the illusion was evident even at longer presentations, the illusory deformation
generated by horizontal bars is likely to be more easily weakened by a prolonged
presentation.
Figure 5(b) suggests that vertical bars might produce a stronger illusion than horizontal
bars across long presentation durations. However, the multiple comparisons between thevertical and horizontal conditions revealed a significant difference between the two, only at apresentation duration of 347 ms (p < .05).
The results of Experiment 2 showed that horizontal or vertical bars could generate theillusory deformation under conditions of short stimulus presentations. A similar tendency of
the reduced illusory effect at longer presentation durations was obtained in the 13-cd/m2
grid condition of Experiment 1a, supporting the idea that the eggs illusion can be generated

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by a brief presentation. The illusory deformation generated by the horizontal or verticalbars was significantly weaker than that generated by a grid (containing both horizontal
and vertical bars) at long presentation durations. However, this might be a result of
the reduction of the number of the stimulus elements in both the horizontal and verticalconditions (i.e., half the number of gray bars and white patches). In Experiment 3, we
controlled orientation information by keeping the number of the stimulus elements as constant as possible.

Experiment 3: Manipulating Bar Orientation
In Experiment 2, the illusory deformation generated by either the horizontal or vertical bars
was found to be significantly weaker than that resulting from the original grid pattern.
However, this reduction might not be associated with the orientation information itself
because the number of the stimulus elements (i.e., patches and bars) in both the horizontal
and vertical conditions was halved compared with that in the grid condition. In Experiment3, we employed new stimulus patterns to manipulate orientation information quantitatively.

Methods
The methods employed in Experiment 1a were used, except the following.
Observers. Fifteen observers (six men and nine women; mean age ¼ 25.1 years; SD ¼
5.7 years), who were recruited from Experiment 1b, participated in Experiment 3.
Stimuli and procedure. The luminance value of the grid was set at 28 cd/m2, as this value
generated the strongest illusion in Experiment 1a. To examine the illusory deformation at
relatively short presentations, we used five levels of presentation duration: 40, 133, 280, 413,
and 693 ms. The stimulus configuration was the other experimental variable, for which thefollowing seven conditions were used: (a) grid, the same as that used in Experiment 1a withboth horizontal and vertical bars; (b) horizontal, circular patches on horizontally oriented
bars with the patch density and bar density virtually identical to those of the grid condition;(c) vertical, the pattern in which the horizontal condition was oriented 90 ; (d) H60, horizontal bars and oblique bars oriented 60 relative to the horizontal bars; (e) H30, horizontal
bars and oblique bars oriented 30 relative to the horizontal bars; (f) V60, vertical bars andoblique bars oriented 60 relative to the vertical bars; (g) V30, vertical bars and oblique bars
oriented 30 relative to the vertical bars (see Figure 6).
With regard to the H60, H30, V60, and V30 conditions, the orientation of the obliquebars (clockwise or counterclockwise) was counterbalanced across trials. Each stimulus waspresented through a circular aperture with a diameter of 12.4 to ensure the consistency ofboth the size and number of the stimulus elements constant across the seven stimulus
configurations.
Each observer completed 140 experimental trials in a randomized order (7 stimulus
configurations  5 presentation durations  4 repetitions).

Results and Discussion
Figure 6 shows the perceived aspect ratios separately for the seven stimulus configurations,averaged over the 15 observers. A two-way within-participant ANOVA was conducted on
the mean perceived aspect ratios, with both the stimulus configuration and presentation
duration as independent variables. We found significant main effects of stimulus1208

Perception 48(12)Figure 6. Schematic illustrations of the seven stimulus configurations and the results of Experiment 3.
Mean perceived aspect ratios, averaged over the 15 observers, are shown separately for the seven stimulus
configurations. The error bars denote the standard errors of the mean. Note: Please refer to the online
version of the article to view the figures in colour.

configuration—F(6, 84) ¼ 7.290, p < .0001, g2p ¼ .342—and presentation duration—F(4,56) ¼ 4.489, p < .005, g2p ¼ .243—and a significant interaction between the two factors—
F(24, 336) ¼ 3.439, p < .0001, g2p ¼ .197. The simple main effects of presentation duration
was significant for the grid, horizontal, and H30 conditions—grid: F(4, 392) ¼ 5.866,
p < .001; horizontal: F(4, 392) ¼ 5.071, p < .001; vertical: F(4, 392) ¼ 1.504, p ¼ .200; H60:
F(4, 392) ¼ 0.935, p ¼ .444; H30: F(4, 392) ¼ 8.083, p < .0001; V60: F(4, 392) ¼ 2.038,
p ¼ .088; V30: F(4, 392) ¼ 1.559, p ¼ .184. The simple main effect of stimulus configuration
was significant when the presentation duration was equal to or longer than 280 ms—40 ms: F(6, 420) ¼ 0.047, p ¼ 1.000; 133 ms: F(6, 420) ¼ 1.282, p ¼ .264; 280 ms: F(6, 420) ¼ 6.099,
p < .0001; 413 ms: F(6, 420) ¼ 10.058, p < .0001; 693 ms: F(6, 420) ¼ 7.974, p < .0001.
As described earlier, the simple main effect of presentation duration was significant inboth the horizontal and H30 conditions, although the same was not found for the vertical or
V30 condition. Considering that these conditions had almost the same configuration except
for the orientation, it was implied that the presentation of the horizontal bars plays animportant role in inducing the eggs illusion. However, multiple comparisons based on
Ryan’s method (Ryan, 1960) showed slightly inconsistent evidence, in that a lack of significant differences was found between the following conditions: horizontal versus vertical,
H60 versus V60, and H30 versus V30 (ps > .05). These results suggest that perceived
deformation is similar between the horizontal and vertical configurations when taking
into account for presentation duration.
Multiple comparisons for the main effect of stimulus configuration with Ryan’s method
revealed a significant difference for pairs of grid-horizontal, grid-vertical, grid-H30,

Qian and Mitsudo

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grid-V30, H30-V60, and H30-H60 (ps < .05). They were as follows: (a) pairs of gridhorizontal, grid-vertical, grid-H30, grid-V30, and H30-V60 at a presentation duration of
280 ms (ps < .05); (b) pairs of grid-horizontal, grid-vertical, grid-H30, grid-V30, H30-V60,
H30-vertical, and H30-H60 at a presentation duration of 413 ms (ps < .05); and (c) pairs ofgrid and all other conditions, and the H30-V60 and H30-H60 pairs, at a presentation duration of 693 ms (ps < .05). These results suggested that the differences between the grid and
H30/V30 conditions and between the grid and horizontal/vertical conditions were moreevident than those between the grid and H60/V60 conditions. These findings provided evidence of a gradual decrease of the illusory effect in the following order: grid (orthogonal),
H60/V60, H30/V30, and horizontal/vertical conditions.
Similar to Experiment 2, Figure 6 suggests that the illusion generated by the verticalcondition might be stronger than that generated by the horizontal condition. However, themultiple comparisons between the horizontal and vertical conditions did not reveal any
significant difference between the two at each presentation duration.
In Experiment 3, we replicated the differential illusory magnitude found between the gridand bar conditions of Experiment 2 and further clarified that the difference resulted fromthe change in orientation information, but not from the density and number of stimulus elements.

General Discussion
This study examined the role of orientation information in the eggs illusion, by manipulating various spatiotemporal stimulus parameters. In Experiment 1a, we replicated Qian and
Mitsudo’s (2016) results, which showed that the eggs illusion was affected by grid luminance, and found a significant effect of presentation duration on this illusion. In Experiment
1b, by using a cancellation method, we found that the illusion occurred when presentation
duration was equal to or longer than 280 ms. In Experiment 2, we clarified the significant
effect of spatial configuration in the eggs illusion and significant interaction between spatialconfiguration and presentation duration. In Experiment 3, we systematically explored theorientation information and demonstrated the significant interaction between orientation
information and presentation duration. Orientation information was demonstrated as animportant factor that influenced the magnitude of the eggs illusion.

Roles of Relative Orientation Information and Local Orientation Information
To explain the results of the three experiments, we introduce two types of orientation
information. We define the orientation signals provided by orthogonally arranged bars as
relative orientation information. Relative orientation information is typically provided by
the grid and does not exist in the horizontal or vertical condition in Experiments 2 and 3,
because all bars in these conditions were parallel to each other. The other type of orientation
information is local orientation information, which refers to the orientation information
around and close to the white patches. Local orientation information exists in all conditions
used in this study.
Although the local orientation information was previously proposed as an importantfactor for the generation of the eggs illusion (Qian & Mitsudo, 2016), the function of relativeorientation information was revealed in this study for the first time. In Experiment 2, longstimulus presentations (347 ms) weakened the illusion when the grid was replaced by either
horizontal or vertical bars. Because Experiment 3 demonstrated that the results were thesame as those of the horizontal and vertical conditions while the numbers of patches and1210

Perception 48(12)bars were controlled, we speculate that a decline in the illusion under the horizontal andvertical conditions of Experiment 2 is because of a lack of relative orientation information.
Considering that the relative orientation is important for the illusion, the illusory deformation would not be reduced by changing the number and density of stimulus elements. Thisidea coincides with the results obtained in all the three experiments in this study: Stimulus
configurations in which sufficient relative orientation information was presented, such as inthose of Experiment 1 and in the grid condition of Experiments 2 and 3, produced a strong
illusory effect when the presentation duration was relatively long. The systematic manipulation of the relative orientation in Experiment 3 provided more conclusive evidence on theimportance of relative orientation information. That is, when changing the relative angle
between horizontal and vertical bars from 90 (orthogonal, i.e., the grid condition) to 60 ,30 , and 0 (parallel to each other, i.e., the horizontal and vertical conditions), we found a
somewhat nonlinear change in the strength of the eggs illusion (Figure 6). Consequently, it
was found that both relative and local orientation information contribute to theeggs illusion.
A reviewer asked us to consider the relation between the eggs illusion and the Helmholtz(1867) irradiation illusion. In the irradiation illusion, a white object on a black backgroundis perceived as larger than a black object on a white background. There are two features in
the irradiation illusion. First, the white and black objects differ in contrast polarity along
their edges. However, in the eggs illusion, each white patch (perceived to be deformed) has
no polarity reversal relative to the gray bar and black background. Therefore, the eggs
illusion seems to differ from the irradiation illusion in terms of contrast polarity. Second,
the two objects in the irradiation pattern differ in luminance contrast. In a later study, vanErning et al. (1988) systematically investigated the effect of edge contrast on perceived sizeand found that an object is perceived larger as the contrast increases. The eggs illusion might
be partly due to the irradiation illusion, because each white patch in the eggs pattern issurrounded by four areas with different luminance values (gray and black). The contrast
between the white patch and black background is higher than that between the white patch
and gray bar. Accordingly, the white patches might be perceived to expand in the direction
orthogonal to the gray bars. If the eggs illusion occurs entirely on the basis of the irradiation
illusion, perceived deformation would be similar between both grid and bar conditions.
However, as demonstrated in Experiments 2 and 3, the illusory deformation was muchlarger in the grid condition than in the bar conditions. A larger magnitude of the eggs
illusion in the grid condition can be well explained by the contribution of the relative orientation information. Therefore, the present data support Qian and Mitsudo’s (2016) viewthat the eggs illusion is distinguished from the Helmholtz irradiation illusion.

Temporal Properties of the Eggs Illusion
By exploring the orientation processing, temporal properties of the eggs illusion have also
been clarified. The results of duration manipulations in the present research revealed two
temporal characteristics of the eggs illusion. Across all the experiments, the illusion occurredunder conditions of brief stimulus presentations (approximately 200–300 ms), steeply
increasing in conditions of very brief duration (approximately 200 ms). Such a steep increase
was observed in all the conditions across the three experiments and was considered as arepresentation of the deformed shape under conditions of brief presentation. In contrast, atlonger presentation durations (approximately 1,000–2,000 ms), the strength of the illusion
remained high, without a significant reduction from the steep increase, for most configurations across the three experiments, except for the horizontal and vertical conditions inQian and Mitsudo

1211

Experiment 2, in which the illusion was significantly weakened at long presentation durations. To explain why the illusory effects generated by horizontal or vertical bars could not
be maintained at longer presentation durations, we noticed the lack of relative orientation in
the horizontal and vertical conditions. The relative orientation information provided byorthogonal bars seems to be indispensable for the eggs illusion under longer presentations.
This is important evidence that the interaction between processing of spatial and temporal
information is effective in modulating the eggs illusion.

Comparing the Eggs Illusion With the Scintillating Grid Illusion
As mentioned in the Introduction section, the eggs illusion and scintillating grid illusion are
influenced by both grid luminance and patch size. In this study, we found three newcommon features shared by the two illusions.
First, the magnitude of the illusions varied as a function of presentation duration in asimilar way. Neither the eggs illusion nor the scintillating grid illusion was evident when thepresentation duration was less than 100 ms; it then increased steeply and became strongest atpresentation durations of around 200 to 300 ms. Schrauf et al. (2000) and the results of the
28-cd/m2 grid condition of Experiment 1 suggest that the illusions occur until the presentation duration was increased up to 1 second. Based on these similarities, we propose thatthe eggs and scintillating grid illusions shared features in the temporal domain.
Second, horizontal or vertical bars placed parallel to each other produced both illusory
effects in some conditions; however, the effect was significantly weaker in the parallel bar
configurations than in the original grid configuration (Qian et al., 2010 and this study).
A reduction in relative orientation information was considered a reason for a decrease in the
scintillating grid illusion with parallel bar configurations (Qian et al., 2010). Nevertheless,distinguishing the local orientation information from the relative one was difficult in the
scintillating grid illusion because both were located at the intersections in the grid. In contrast, we were able to separately assess the two types of information in the eggs illusion, as
the circular patches were not located at the intersection of the grid. The results ofExperiment 3 showed that the decline in the parallel bar conditions resulted from the lackof relative orientation, not from the reduction of the number and density of stimulus elements.
In Experiments 2 and 3, we noted a subtle anisotropic effect with regard to the bar
orientation on the eggs illusion, in which vertical bars tended to produce a stronger deformation than horizontal bars. Interestingly, a similar vertical superiority effect was also
observed in the scintillating grid illusion, since Qian et al. (2010) reported that verticalbars generated a slightly stronger scintillating effect than horizontal bars (their results
were also not statistically significant). Although the exact reason for these anisotropic effects
remains unclear, these data appear to highlight another common feature between the eggs
and scintillating grid illusions.
Third, relative orientation information seems to play a role in both the eggs and scintillating grid illusions. Qian et al. (2012) showed that the magnitude of the scintillating grid
illusion was stable if the relative orientation around an intersection of the grid was
unchanged, even when the relative positions of the intersections were randomly displacedwith respect to each other. As discussed in this section, the magnitude of the eggs illusion
remained constant around long presentation durations (347 ms) as long as the orthogonalbars were presented. Altogether, these results provide further evidence for the similarities
between the eggs illusion and scintillating grid illusion.

1212

Perception 48(12)Future Directions
Further investigation is necessary to resolve several unsettled issues. First, the interaction
between processing of spatial and temporal information on the eggs illusion should be
investigated in detail, with prospects for a possible neurophysiological mechanism of theeggs illusion. Second, the similarities between the eggs illusion and scintillating grid illusion
should be investigated in more detail, to determine the possible common mechanism underlying both illusions. Referring to previous research on the scintillating grid illusion, therelationship between the retinal position (foveal and peripheral) and magnitude of the illusion should be systematically examined in future.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or
publication of this article.

Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or
publication of this article: This research was financially supported in part by the Hirose Research
Grant from the Hirose International Scholarship Foundation, Japan.

ORCID iD
Kun Qian

https://orcid.org/0000-0002-0625-1834

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