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Our perception of an object's size arises from the integration of multiple sources of visual information including retinal size, perceived distance and its size relative to other objects in the visual field. This constructive process is revealed through a number of classic size illusions such as the Delboeuf Illusion, the Ebbinghaus Illusion and others illustrating size constancy. Here we present a novel variant of the Delbouef and Ebbinghaus size illusions that we have named the Binding Ring Illusion. The illusion is such that the perceived size of a circular array of elements is underestimated when superimposed by a circular contour - a binding ring - and overestimated when the binding ring slightly exceeds the overall size of the array. Here we characterize the stimulus conditions that lead to the illusion, and the perceptual principles that underlie it. Our findings indicate that the perceived size of an array is susceptible to the assimilation of an explicitly defined superimposed contour. Our results also indicate that the assimilation process takes place at a relatively high level in the visual processing stream, after different spatial frequencies have been integrated and global shape has been constructed. We hypothesize that the Binding Ring Illusion arises due to the fact that the size of an array of elements is not explicitly defined and therefore can be influenced (through a process of assimilation) by the presence of a superimposed object that does have an explicit size.
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, Dartmouth College USAMing Meng
, University of BelgradeDejan Todorović
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RESEARCH ARTICLE
The Binding Ring Illusion: assimilation affects the
perceived size of a circular array [v2; ref status: indexed,
http://f1000r.es/12q]
J Daniel McCarthy, Colin Kupitz, Gideon P Caplovitz
Department of Psychology, University of Nevada Reno, Reno, NV, 89557, USA
Abstract
Our perception of an object’s size arises from the integration of multiple
sources of visual information including retinal size, perceived distance and its
size relative to other objects in the visual field. This constructive process is
revealed through a number of classic size illusions such as the Delboeuf
Illusion, the Ebbinghaus Illusion and others illustrating size constancy. Here we
present a novel variant of the Delbouef and Ebbinghaus size illusions that we
have named the Binding Ring Illusion. The illusion is such that the perceived
size of a circular array of elements is underestimated when superimposed by a
circular contour – a binding ring – and overestimated when the binding ring
slightly exceeds the overall size of the array. Here we characterize the stimulus
conditions that lead to the illusion, and the perceptual principles that underlie it.
Our findings indicate that the perceived size of an array is susceptible to the
assimilation of an explicitly defined superimposed contour. Our results also
indicate that the assimilation process takes place at a relatively high level in the
visual processing stream, after different spatial frequencies have been
integrated and global shape has been constructed. We hypothesize that the
Binding Ring Illusion arises due to the fact that the size of an array of elements
is not explicitly defined and therefore can be influenced (through a process of
assimilation) by the presence of a superimposed object that does have an
explicit size.
Gideon P Caplovitz ( )Corresponding author: gcaplovitz@unr.edu
McCarthy JD, Kupitz C, Caplovitz GP (2013) The Binding Ring Illusion: assimilation affects the perceived size of aHow to cite this article:
circular array [v2; ref status: indexed, ] 2013, :58 (doi: 10.12688/f1000research.2-58.v2)http://f1000r.es/12q F1000Research 2
© 2013 McCarthy JD et al. This is an open access article distributed under the terms of the ,Copyright: Creative Commons Attribution Licence
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Data associated with the
article are available under the terms of the (CC0 1.0 Public domain dedication).Creative Commons Zero "No rights reserved" data waiver
Institutional Development Award (IDeA) from the National Institute of General Medical Sciences of the National Institutes ofGrant information:
Health under grant number 1P20GM103650-01 and a grant from the National Eye Institute of the National Institutes of Health: 1R15EY022775.
The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: No competing interests were disclosed.
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F1000Research 2013, 2:58 Last updated: 23 JAN 2014
Introduction
Correctly perceiving the size of objects is essential to successfully
interact with the world around us. Due to the fact that we sense
the 3D visual world through an analysis of 2D retinal images, the
process of size perception is intrinsically ambiguous. As a result, the
perception of an object’s size arises from the integration of multiple
sources of visual information including the size of its retinal image,
its perceived distance1, and its size relative to other objects in the
visual scene2,3. These constructive processes are revealed through
a number of classic size illusions such as the Ebbinghaus Illusion4
(Figure 1A), the Delboeuf Illusion5,6 (Figure 1B), the Müller-Lyer
Illusion7 (Figure 1C) and several others that illustrate how mecha-
nisms that underlie size constancy sometimes lead to illusory ercepts
resulting from a discrepancy between retinal and perceived size. In
each of these illusions, the perceived size of an explicitly defined
object is influenced by the context in which it is presented. Most rel-
evant to the current paper are the Delboeuf and Ebbinghaus illusions
that demonstrate that the size of an inner circle is overestimated or
underestimated depending on the surrounding context in which it
is presented. Though several explanations have been proposed for
these illusions, recent research demonstrates that the effect is largely
determined by the relative size of the inducer(s), their distance from
the target2, and in the case of the Ebbinghaus Illusion, the complete-
ness of the surrounding array of elements8. Taken together, the bal-
ance of these factors determines the magnitude of the illusion and
whether the inner circle is overestimated or underestimated.
Here we address the question of how we perceive the size of an
implicitly defined object–an array of elements–by introducing a
novel variant of the Ebbinghaus illusion that we have named the
Binding Ring Illusion. We describe the illusion and investigate the
underlying mechanisms that lead to misperceived size. A basic
stimulus that elicits perception of the Binding Ring Illusion is com-
posed of a circular array of small circles onto which a larger circle is
superimposed as shown in Figure 2A. The superimposed circle leads
to an underestimation of the perceived radius of the circular array
relative to an equally sized array without the binding ring (Figure 2B).
To our knowledge, previous research on the Ebbinghaus Illusion
has focused on the effect the surrounding elements have on the
explicitly defined circle. Here we consider the possibility of mutual
influence in that the inner circle may also lead to misperceived size
of the surrounding array. In the following experiments, we investi-
gate the magnitude of this illusory decrease in size and attempt to
study the components of the stimulus that are responsible for the
observed effect.
In experiment 1, we demonstrate that the effect of the binding ring
can be quantified. In experiment 2 we demonstrate that the illusion
arises due to assimilation toward the binding ring9,10. In experiment 3,
we investigated the effect of spatial frequency. Finally, in experiments
Figure 1. Notable size illusions: A) Ebbinghaus illusion, B) Delboeuf
illusion, C) Müller-Lyer illusion.
Changes from Version 1
In this revised article we address several of the issues raised by
the reviewers. We have corrected the references in order to more
accurately reflect the historical record. We have included a brief
discussion of recent findings suggesting a significant role for the
early visual cortex including V1 in representing the perceived size
of an object. We have included a broader discussion of other size
illusions.
See referee reports
Figure 2. The Binding Ring Illusion. Which array of circles looks
bigger? A) The test stimulus used in experiment 1 or B) The reference
stimulus used in experiment 1.
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F1000Research 2013, 2:58 Last updated: 23 JAN 2014
4a and 4b we investigated the roles of local configural features in
producing the illusion.
General methods
Participants
Five observers (3 men, 2 women; age range: 18–25; mean age = 20.2)
participated in experiment 1, ten observers participated in experi-
ment 2 (4 men, 6 women; age range: 19–28; mean age = 22.4),
twelve observers participated in experiment 3 (6 men, 6 women; age
range: 18–27; M = 21.75) and five observers participated in experi-
ment 4 (3 men, 2 women; age range: 18–25; M = 20.6). All partici-
pants were naïve to the aims of the experiments, reported normal or
corrected-to-normal vision and received course credit for their par-
ticipation. Prior to participating, each observer provided informed
consent according to the guidelines of the Department of Psychology
and the IRB of the University of Nevada, Reno.
Apparatus and display
Stimuli were presented on a Dell Trinitron P991 monitor (19 inches,
1024 × 768) with an 85 Hz refresh rate. The stimulus computer was
a 2.4 GHz Mac Mini with an NVIDIA GeForce 320M graphics
processor (256MB of DDR3 SDRAM). Stimuli were created
and presented with the Psychophysics Toolbox11 for MATLAB
(Mathworks Inc., Natick, MA). In experiments 1, 2 and 4, the
stimuli were white (120 cd/m2) presented on a black (0.06 cd/m2)
background. In experiment 3, the stimuli were either low- or high-
pass filtered and presented on a grey background (20.5 cd/m2).
Luminance values were measured with a Photo Research PR655
spectroradiometer. Participants placed their head on a chin rest and
viewed the stimuli binocularly from a distance of 57cm.
Experiment 1
The goal of experiment 1 was to establish a ‘standard’ configuration
and quantify the magnitude of the illusion in order to serve as a
baseline for further testing. Specifically, we sought to measure the
perceived reduction in size of an array superimposed with a binding
ring compared to an unbound array of equal size.
Stimuli and procedures
The basic paradigm is illustrated in Figure 3. On a given trial,
participants were presented with a small central fixation point (0.35°)
for 500ms, followed by the additional simultaneous presentation
of two circular arrays (a reference and a test) for 500ms at which
point the stimuli were removed from the screen and replaced by a
random noise mask displayed for 500ms to discourage afterimages.
Participants indicated by pressing one of two buttons (two-
alternative forced choice), which of the two stimuli had appeared
larger. Each array consisted of 12 small equally spaced circles with
radii of 0.05° visual angle. On every trial, the reference array had
a fixed radius of 3° visual angle (from the center of the array to
the center of any circular element). Using the method of constant
stimuli12, we investigated the perceived size of each of two test arrays
compared to the reference array. The test array either had a binding
ring superimposed or did not (the lack of a binding ring served as
a control condition). In non-control conditions the binding ring had
a radius selected to match the radius of the test circular array that
was measured from the center of the array to the center of one of
the smaller component circles. Because the control array did not
have a superimposed binding ring it was identical to the reference
array in all ways except its trial-by-trial size. As such, it was used to
determine A) how accurately observers were able to perform the task
(discriminate the sizes of the arrays) and B) to serve as a point of
comparison for determining the size of the illusory effect. On each
trial, the radius of the test array was selected from the following list:
2.5°, 2.6°, 2.8°, 2.9°, 3.0°, 3.1°, 3.3°, 3.4° and 3.5°.
On each trial, the centers of the two arrays were randomly positioned
within a circular radius of 1.16° of visual angle centered 6.75° along
the horizontal axis to the left or right of the central fixation point.
This positional-jitter was used to prevent observers from basing
their judgments on horizontal matching or distance comparisons
with the edges of the monitor. Participants were instructed to main-
tain fixation on the center of the screen throughout the experiment.
The sides on which the two arrays were presented were randomly
determined on each trial. In total there were 18 trial types: nine test
radii for both the test and control array types. Trials were pseudo-
randomly ordered such that 20 of each trial type were presented
in random order for a total of 360 trials. Prior to the experiment,
participants were trained on 20 trials of the largest and smallest test
array sizes that were not included in the analyses.
Results
For each array size, we computed the percentage of times the test
or control array was perceived to be larger than the reference. Thus,
for the test (bound) and control (unbound) arrays, nine values (one
for each radius) were calculated. Because the 2AFC task has two
categorical responses, the following sigmoidal-shaped binomial-
logit function was then fit to the corresponding data for each of the
two test arrays using the MATLAB (glmfit() command)13:
fx e
e
bxb
bxb
()=+
+
+
100
1
12
12
×
The points of subjective equality (PSE) were determined for each
subject by interpolating the 50% chance level from the function fit to
the data (x = b1
/ b2
). The PSE indicates the size the test array needs
to be in order to be perceived as equal in size to the reference. The
resulting curves plotted for the mean responses across participants
are shown in Figure 4. The clear and steep-sloped sigmoidal shaped
psychometric curve derived from the control condition in which
neither the reference nor control array have a binding ring confirm
that participants were able to perform the task and accurately
report their perceptions. Specifically, participants were at chance
performance when the two arrays were indeed the same size. The
rightward shift of the other psychometric curve, derived from the
test (binding ring) condition, demonstrates that the size of the array
was underestimated when the binding ring was present. The inset
of Figure 4 illustrates the mean points of subjective equality across
subjects for the test and control arrays.
A paired t-test between the PSEs of the test and control arrays
revealed that the addition of the binding ring significantly (t(4) = 7.71,
p < 0.01) reduced the perceived size of the test array. The mean dif-
ference of the PSEs between the test and control arrays was ~0.18°
Page 3 of 15
F1000Research 2013, 2:58 Last updated: 23 JAN 2014
Figure 3. Schematic diagram of a trial in experiment 1. A fixation point appeared for 500ms followed by the presentation of the reference
and test array for 500ms at which point the stimuli were removed from the screen and replaced by a noise mask for another 500ms to prevent
the formation of afterimages. The screen then remained blank until participants indicated which array appeared larger via a key press.
Figure 4. Results of experiment 1. Psychometric curves indicate the mean fit of the data averaged across all participants. The inset of the
figure illustrates the mean points of subjective equality (PSEs) for the test and reference stimuli. The black curve indicates that participants
were accurately judging the radius of an unbound array. The grey curve shows that the array radius must increase by ~0.18° to be perceived
as being the same size as an unbound array. Thick curves with error bars indicate the mean response across participants for each array
radius. Thin curves indicate the function fitted to the data. Error bars represent standard error of the mean PSE computed across subject.
500ms
500ms
Stimulus
500ms
Noise Mask
Response
2.5 2.625 2.75 2.875 3 3.125 3.25 3.375 3.5
0
10
20
30
40
50
60
70
80
90
100
% Test Perceived Larger
Test Size Radius (ref = 3) ºvisual angle
p < 0.05
Control Binding Ring
2.5
3
3.5
PSE
Test Size (ref = 3) ºvisual angle
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F1000Research 2013, 2:58 Last updated: 23 JAN 2014
of visual angle or 6% of the overall radius of the array. Thus, an
array superimposed with a binding ring of radius 3.18° was per-
ceived as having the same size as a no-binding ring array with a
radius of 3°. This is comparable in magnitude to underestimation
effects observed in the classic Ebbinghaus and Delbeouf Illusions14,15.
Experiment 1: Proportion of participants perceiving test
arrays as being larger than reference arrays
1 Data File
http://dx.doi.org/10.6084/m9.figshare.157057
Experiment 2
Having quantified the magnitude of the illusion in experiment 1, we
explored possible mechanisms contributing to the underestimation of
perceived size. Size illusions such as the Delboeuf and Ebbinghaus
illusions have been explained on the basis of size assimilation
(when the size of the element of interest is biased toward the ref-
erence component) and contrast (when the size of the element
of interest is biased away from the reference component)9,10,16,17.
Because the size of an array is not explicitly defined, it remains
unclear whether the illusion arises due to assimilation or contrast
with the binding ring. In order to determine if the illusion is medi-
ated by assimilation or contrast we investigated the effect of chang-
ing the size of the binding ring (bottom of Figure 5). If assimilation
is responsible for the effect, we would predict that the magnitude of
the illusion should increase as the binding ring gets smaller. Alter-
natively, if the illusion arises due to contrast, the magnitude of the
illusion should increase as the binding ring gets larger.
Stimuli and procedures
The basic stimuli were the same as those used in experiment 1;
however, due to the larger number of configurations tested, we used
staircase procedures18 rather than the method of constant stimuli.
The individual trials within the staircases again consisted of a
reference and test array simultaneously presented for 500ms. As in
the previous experiment, the reference array had a fixed radius of
3°; however, unlike the previous experiment, the reference contained
a binding ring and the test array did not. This was done so as to
be able to compare the magnitude of the illusion for a fixed size
array across binding-ring sizes. Separate staircases were run for
five distinct reference conditions defined by the size of the binding
ring with radii chosen from the following list: 2°, 2.67°, 3°, 3.33° and
4° (see Figure 5). Because the radius of each circular element was
0.5°, the binding ring did not physically overlap with the circular
array in two of the five conditions and was either entirely inside
(2°) or outside (4°) the array. Four staircases were run for each trial
type–two in which the initial test or control array was larger than
the reference array (descending) and two in which it was initially
smaller (ascending). The starting radius for the test or control array
was randomly selected to be 0.5° to 1° larger or smaller than the
radius of the reference array. On each trial, participants completed
a 2AFC task indicating which stimulus had appeared larger.
According to standard staircase procedures, the size of the test array
was adjusted by a step size ranging randomly on each iteration
from 2 to 5 pixels (0.07° to 0.18°) in the direction opposite of the
participant’s response. The staircase finished when four reversals
were recorded. In total, each participant completed 20 staircases
presented in pseudorandom order.
Figure 5. Stimuli and results of experiment 2. The radius of the binding rings from left to right: 2°, 2.67°, 3°, 3.33° and 4°; circular array
radius was consistently 3°. The graph illustrates the PSEs for each stimulus type: lines and asterisks below the bars indicate significant
(p < 0.05) differences, based on post-hoc paired t-tests, between the three overlapping binding ring conditions. Superimposed asterisks
indicate significant changes in perceived size induced by the presence of the binding ring compared to an array without a binding ring
(observed for all five conditions). A positive shift on the ordinate axis indicates that the array must increase in size to be perceived as having
the same radius as the reference and vice versa. Error bars indicate standard error of the mean.
−1º −.33º +.33º +1º
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
BR Shift (Radius)
BR − Test ºvisual angle (radius)
*
*
**
*
*
*
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F1000Research 2013, 2:58 Last updated: 23 JAN 2014
Results
The mean of the four reversal points was calculated for each
staircase and the PSE for each reference condition was obtained
by averaging these results across the corresponding four staircases.
Although we used a different experimental paradigm than in
experiment 1, the size of the measured effect when the binding
ring had a radius of 3.0° (same as in experiment 1) is comparable
to that observed in experiment 1 (0.16° vs. 0.18°). The results
illustrated on the top of Figure 5 indicate:
A) The size of the binding ring had a significant influence on the
perceived size of the array (main effect of binding ring size-repeated
measures ANOVA: F(4, 36) = 31.22, p < 0.001).
B) In each of the five conditions, the perceived size of the array was
significantly influenced by the presence of the binding ring (one
sample two-tailed, t-tests vs. zero: all p < 0.05 uncorrected).
C) The binding ring array was perceived as being smaller than an
array without a binding ring in each of the four conditions in which
the radius of the binding ring was less than the radius of the exterior
portion of the array.
D) In the condition where the binding ring completely encompassed
the array, the perceived size of the array was larger than when no
binding ring was present. This is the reverse effect of the other four
conditions.
E) The magnitude of the effect is greatest when the binding ring is
superimposed on the array. A follow-up planned comparison of the
three overlapping conditions with the two non-overlapping condi-
tions revealed that the magnitude of the effect is significantly larger
when the binding ring intersects the array compared to when it does
not intersect the array (F(1, 9) = 50.87, p < 0.001).
F) A second repeated measures ANOVA examining just the three
superimposed conditions revealed that the size of the binding ring
(within this range) significantly influences the magnitude of the
illusion (F(2, 18) = 3.84, p < 0.05). As can be seen in Figure 5, the
magnitude of the illusion increases as the size of the binding ring is
reduced for the three superimposed conditions. However, once the
binding ring becomes too small, such that it no longer overlaps the
array, the magnitude of the illusion is greatly decreased. That said,
even in this innermost binding ring condition, the perceived size
of the array is underestimated. It is noteworthy that this particu-
lar stimulus condition is quite similar to that typically used in the
Ebbinghaus Illusion (see right side of Figure 1A). Here we demonstrate
that there are in fact two illusory effects revealed in the Ebbinghaus
Illusion, one operating on the inner circle (making it appear larger)
and one operating on the outer array (making it appear smaller).
Taken together, these observed effects are consistent with the
assimilation hypothesis and inconsistent with the contrast hypoth-
esis. Furthermore, these results appear to indicate that the outer
edge of the circular array is serving as a boundary for the assimila-
tion. When the radius of the binding ring exceeds this boundary,
the assimilation bias is to increase the perceived size of the array.
Similarly, if the radius of the binding ring is within this boundary,
the assimilation bias is to decrease the perceived size of the array.
Experiment 2: reversal choices
1 Data File
http://dx.doi.org/10.6084/m9.figshare.157058
Experiment 3
In this and the following experiment, we attempt to identify specif-
ic stimulus factors that may influence the Binding Ring Illusion. It
is suggested that some visual illusions, including the Müller-Lyer19
and Oppel-Kundt20,21 or filled area illusion22, are mediated by dif-
ferential processing of low- and high-spatial frequency informa-
tion2327. Specifically, differential effects can be obtained resulting
in changes to the magnitude of the illusions depending on spatial
frequency filtering. Here, we investigated the effect of spatial fre-
quency filtering on the magnitude of the Binding Ring Illusion
(Figure 6A).
Stimuli and procedures
The stimuli and procedures used in experiment 3 were analogous
to those used in experiment 1 except that the stimuli were either
high- or low-pass filtered. The high-pass cutoff was set at (2 cpd)
and the low-pass cutoff was (0.5 cpd). Stimuli were presented on
a gray (20.5 cd/m2) background. In each case, similarly filtered
stimuli were compared to each other (i.e. a high spatial frequency
(HSF) reference was compared to a HSF test or control). In total
there were 36 trial types: nine test radii (same as in experiment 1)
for the test and control array types (with and without binding ring)
in both HSF and low spatial frequency (LSF) conditions. Trials were
pseudorandomly ordered so that 20 of each trial type were presented
for a total of 720 trials.
Results
After fitting the curves using the same procedures described above,
we conducted a 2 (binding ring vs. control) × 2 (HSF vs. LSF)
repeated measures ANOVA on the derived PSE for each of the four
conditions. This analysis revealed a main effect of the binding ring
on perceived size (F(1, 11) = 27.05, p < 0.01), a main effect of
spatial frequency on perceived size (F(1, 11) = 12.30, p < 0.01)
and a significant interaction between the binding ring and spatial
frequency (F(1, 11) = 5.57, p < 0.05). As can be seen in Figure 6B,
for both low- and high-pass stimuli, the array containing the
binding ring was perceived to be smaller than when no binding ring
is present. As reflected in the significant interaction, this effect is
greater when the stimuli are low- as compared to high-pass filtered.
Although the illusion was observed in both the LSF and HSF
configurations, the size of the effect observed for the LSF condition
(~0.3°) is substantially larger than that observed in the previous
experiments that range from 0.16° to 0.18°. In contrast, when
the stimuli were high-pass filtered, the resultant ~0.2° reduction
in perceived size is comparable to that observed in the previous
experiments.
Experiment 3: percieved size of test and reference arrays at high
and low spatial frequency
1 Data File
http://dx.doi.org/10.6084/m9.figshare.157059
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F1000Research 2013, 2:58 Last updated: 23 JAN 2014
samples t-test between the PSEs of the test and control arrays
revealed no significant difference in perceived size (t(4) = 2.05, ns).
Results 4b
The data shown in Figure 7D were analyzed using the same curve
fitting method described in the previous experiments. A paired t-test
between the PSEs of the test and control arrays again revealed no
significant difference in perceived size (t(4) = 1.93, ns).
The Binding Ring Illusion was not observed in either of the partial
binding ring configurations tested here. As such, we can conclude
that processing of the preserved local features does not underlie
the illusion. Alternatively, these results suggest that mechanisms
within a higher, more global stage of processing may underlie the
illusion.
Experiment 4: perceived size of test and reference arrays with
lines only present either within the interior of the elements or
connecting the elements
1 Data File
http://dx.doi.org/10.6084/m9.figshare.157060
General discussion
In this manuscript we introduced a new size illusion that we call
the Binding Ring Illusion. The Binding Ring Illusion is a variant
of the Delboeuf and Ebbinghaus Illusions and demonstrates that
Experiment 4a
Lastly we investigated the role of the local configural features of the
stimulus. A number of visual illusions can be attributed to the pro-
cesses of local configural features3,8,28. In these two closely related
experiments, we investigated the impact of presenting only parts of
the binding ring on the presence or magnitude of the Binding Ring
Illusion. In doing so we address the question of whether the Binding
Ring Illusion is mediated by the processing of specific local fea-
tures, or perhaps on the basis of more global representations of the
objects present in the image.
In the first part of this experiment, the binding ring only connected the
array of elements so that it was not visible in the interiors (Figure 7A).
In the second part of the experiment, the binding ring was present
solely within the interiors of the array elements (Figure 7B) leaving
them unconnected from each other.
Stimuli and procedures
The stimuli and procedures used in experiments 4a and 4b were
identical to those used in experiment 1 except that in the test condition,
the binding ring only connected the array of elements as if viewing a
chain of pearls (experiment 4a) or the binding ring was only visible in
the interiors of the array elements (experiment 4b).
Results 4a
The data shown in Figure 7C were analyzed using the same curve
fitting method described in the results of experiment 1. A paired
Figure 6. Spatial frequency manipulations. A) Low- (top left) and high-pass (top right) versions of the binding ring stimuli. B) Results of
experiment 3. The points of subjective equality (PSE) of both high (HSF) and low spatial frequency (LSF) conditions are plotted for both the
control and binding ring conditions. Error bars represent standard error of the mean. Asterisks indicate significance at p < 0.05.
A)
LSF HSF
2.5
2.75
3
3.25
3.5
Test Size (ref = 3) ºvis ang
PSE
Control
Binding Ring
*
*
*
*
p < .05
B)
Page 7 of 15
F1000Research 2013, 2:58 Last updated: 23 JAN 2014
the perceived size of an array is subject to effects of assimilation.
Specifically, the perceived size of a circular array of elements is
underestimated when a ‘binding ring’ is superimposed on the array.
The purpose of the above experiments was to demonstrate that the
illusion can be quantified, to investigate possible explanations for
its occurrence and to begin to characterize the stimulus factors that
lead to misperceived size.
A number of observations can be made based on the results of these
experiments. Firstly, the Binding Ring Illusion can indeed be quanti-
fied. Using both methods of constant stimuli and adaptive staircases
we were able to measure significant differences in the perceived size
of an array as a function of the presence and size of a binding ring.
Secondly, the size of the binding ring significantly influences the
magnitude of the illusion (experiment 2). Specifically, in order to
produce the greatest effect, the binding ring has to superimpose the
array and furthermore, as the size of the superimposed ring decreases,
the magnitude of the illusion increases. These findings are consistent
with existing assimilation theories of similar size illusions such as the
Delboeuf and Ebbinghaus illusions9,10,15,17. In addition, the perceived
size of the array was slightly increased only when the binding ring
was large enough to completely encompass the array. This suggests
that the outer radius of the array serves as the reference point for the
assimilation process. It has been argued that assimilation is largely
influenced by the perceived unification of the components as a single
object17,29. This is consistent with our results such that the strongest
assimilation effects occurred when the circle was superimposed on
the array and could be easily perceived as a unified figure. In these
conditions we observe a significantly larger magnitude of size illu-
sion than when the binding ring was not superimposed on the array.
The Delboeuf and Ebbinghaus Illusions both demonstrate that
the perceived size of an interior object can be influenced by the
presence of a surrounding stimulus. The Binding Ring Illusion,
on the other hand, provides a complimentary observation that the
perceived size of a surrounding stimulus can be influenced by the
presence of an interior stimulus. Indeed, the smallest binding ring
condition in experiment 2 is an identical configuration to that com-
monly used to demonstrate the Ebbinghaus illusion.
Secondly, the magnitude of the illusion is greater when the stimuli are
low- compared to high-pass filtered (experiment 3). However, in both
cases the magnitude of the illusion is comparable if not greater than
that observed with full spectrum stimuli. As such, we can conclude
that: either processes within distinct spatial frequency channels can
independently lead to the illusion, or the illusion is mediated by
mechanisms at a later stage of processing that follows the integra-
tion of high- and low-spatial frequencies. In the latter case, one
may conjecture that the initial LSF bias is attenuated once spatial
frequency information has been integrated in object recognition
areas such as those located in the inferotemporal cortex (IT)30. This
stands in contrast to several recent findings using functional and
structural MRI that have implicated visual areas as early as V1 as
playing a key role in the representation of perceived size3133. Given
the classical receptive field properties of V1 neurons, it is likely that
these observations arise due to feedback to V1 from higher visual
areas, that in the case of the Binding Ring Illusion may contain
integrated representations of spatial frequency. This is in line with
recent research on the Müller-Lyer Illusion using dynamic causal
modelling34. It was demonstrated that illusion strength could be
predicted by modulating bilateral connections between the lateral
Figure 7. Configurally altered binding ring stimuli. A) The test stimulus used in experiment 4a. B) The test stimulus used in experiment
4b. C) The results of experiment 4a. D) The results of experiment 4b. There was no significant difference (n.s.) in perceived size between the
control and binding ring tests in either condition.
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F1000Research 2013, 2:58 Last updated: 23 JAN 2014
occipital cortex (LOC) and right superior parietal cortex (SPC). The
model suggests that LOC is involved in size scaling to generate size
invariant object representations that are further processed in SPC
and relayed back to V1 to generate conscious illusory percepts.
One hypothesis for why the illusion is greater in the LSF condi-
tion is that due to blur, the individual array elements in the LSF
condition are perceptually larger than the HSF and full-spectrum
conditions. Because the elements appear larger, the perceived dis-
tance between the outer radius of the array and the binding ring is
increased. The results of experiment 2 suggest that this may lead to
an increased assimilation effect. Alternatively, the blurring of the
image increases the thickness of the binding ring and it could be
the case that this increases its effect on the perceived size of the
array. Further research will be necessary to fully determine why the
blurred stimulus increased the magnitude of the illusion.
Thirdly, the illusion does not manifest when only the local con-
figural features of the binding ring are present. This was true even
when the binding ring only connects the array elements (experi-
ment 4a). This result is intriguing because past work has demon-
strated that elements that are perceptually grouped into a common
object will be perceived to be closer together than those that are
not. Specifically, if a series of dots are arranged to form a dot-
ted contour, the distance between any two adjacent dots will be
perceived as being shorter than the distance between any one of
them and another equally-distanced dot that does not lie along
the contour35. One possible extension of this observation is that
an object formed out of the grouping of individual elements may
appear smaller on the basis of the elements appearing closer
together. Based on this assumption we thought it possible that the
partial binding ring of experiment 4a may serve as an additional
cue that the individual elements belong to a common object and
therefore lead to it appearing smaller. The configuration of experi-
ment 4a explicitly links the elements of the array; however, this
does not lead to the illusory reduction in perceived size. This may be
explained by the observed effects of the Oppel-Kundt Illusion20,21 that
demonstrates that the distance between two points is overestimated
when it is filled with a number of tick marks compared to two
equally spaced points of an undivided extent; however, as the den-
sity of these divisions increases, the effect diminishes36. Therefore,
connecting the interior elements should lead to a more veridical
perception as observed here. As such, it is unlikely that the Binding
Ring Illusion arises due to a misperception of the perceived dis-
tance between array elements.
Conclusion
Although we readily perceive a circular array of elements as a circle,
there are many possible alternate perceptions that could be formed.
For example, the circles could be grouped into pairs symmetrical
about the vertical axis, or perceived as ellipses arranged in an ellipti-
cal array that is receding in depth. That we perceive such a stimu-
lus as a circle reflects the constructive processes that are embodied
in the functional and structural architecture of the visual system.
Importantly, the circle that we perceive does not explicitly exist
in the retinal image and must therefore be constructed. As such,
the size of the circle that we perceive must be itself constructed as
well. The Binding Ring Illusion demonstrates that this construc-
tive process includes the assimilation of other co-occurring stimuli,
particularly those that spatially overlap the array.
Author contributions
Dan McCarthy contributed to the theoretical foundation, experi-
mental design, data analysis and writing of the manuscript Colin
Kupitz contributed to the experimental design, implementation,
data collection, data analysis and writing of the manuscript Gideon
Caplovitz contributed to the theoretical foundation, experimental
design and writing of the manuscript.
Competing interests
No competing interests were disclosed.
Grant information
Institutional Development Award (IDeA) from the National
Institute of General Medical Sciences of the National Institutes of
Health under grant number 1P20GM103650-01 and a grant from
the National Eye Institute of the National Institutes of Health:
1R15EY022775.
The funders had no role in study design, data collection and analysis,
decision to publish, or preparation of the manuscript.
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Current Referee Status:
Referee Responses for Version 2
Dejan Todorović
Laboratory of Experimental Psychology, Department of Psychology, University of Belgrade, Belgrade,
Serbia
Approved: 23 January 2014
23 January 2014Referee Report:
The authors have taken into account my comments in the revised text. I have no further comments.
I have read this submission. I believe that I have an appropriate level of expertise to confirm that
it is of an acceptable scientific standard.
No competing interests were disclosed.Competing Interests:
Ming Meng
Department of Psychological Brain Sciences, Dartmouth College, Hanover, NH, USA
Approved: 21 January 2014
21 January 2014Referee Report:
I have read this submission. I believe that I have an appropriate level of expertise to confirm that
it is of an acceptable scientific standard.
No competing interests were disclosed.Competing Interests:
Simone Gori
Developmental and Cognitive Neuroscience Lab, Department of General Psychology, University of
Padua, Padua, Italy
Approved: 20 January 2014
20 January 2014Referee Report:
I approve this version, I think this paper was already interesting in its first version and I believe the Authors
did improve it even further in this new version.
I have read this submission. I believe that I have an appropriate level of expertise to confirm that
it is of an acceptable scientific standard.
Page 11 of 15
F1000Research 2013, 2:58 Last updated: 23 JAN 2014
F1000Research
No competing interests were disclosed.Competing Interests:
Referee Responses for Version 1
Simone Gori
Developmental and Cognitive Neuroscience Lab, Department of General Psychology, University of
Padua, Padua, Italy
Approved: 03 April 2013
03 April 2013Referee Report:
The presented manuscript is very interesting and well written. The experiments are very well conducted
and it is a pleasure to read. The authors introduce a new size illusion and they investigate it using a very
good methodology, providing clear results. I have some suggestions that in my opinion could improve the
manuscript even more, but my general opinion is extremely positive.
Please see my suggestions below:
1. The introduction is really short, and it doesn't cover the topic of size illusion properly. Several other
interesting examples of size illusions should be cited and discussed to provide a better understanding of
the topic. Firstly, I would suggest discussing the literature on the illusions that are cited by the authors
which are very similar to the one that they introduced here. For example, several interesting papers have
been produced on The Ebbinghaus Illusion (which should maybe be called the Ebbinghaus-Titchener
illusion, referring also to the 1902 Titchener book that made it popular) that maybe should be discussed
(just few examples, without pretending to be complete at all: Roberts . 2005; Nemati, 2009; Doherty et al
, 2010; Schwarzkopf and Rees, 2013). The same can be said for the related Delboeuf illusion, whichet al.
is suggested to be caused by the same brain mechanisms by Roberts . (2005). A few examples ofet al
recent works that may be worth checking are: Zanuttini and Daneyko (2010); Jaeger and Long (2007).
Moreover, other interesting size illusions could be mentioned in the introduction, for example: The
Muller-Lyer Illusion (Zeman . 2013; Plewan . 2012; Proulx and Green, 2011), the Oppel-Kundtet al et al
Illusion (Wackermann, 2012a,b; Savazzi ., 2012) and the related filled area illusion (Giora and Gori,et al
2011); the Breathing Light Illusion (Gori and Stubbs, 2006; Anstis . 2007; Gori . 2010), StarTreket al et al
Illusion (Qian and Petrov, 2012), Accordion Grating Illusion (Gori ., 2011; 2013; Yazdanbakhsh andet al
Gori, 2011) and the Fat Face Illusion (Thompson and Wilson, 2012; Sun . 2012), to name just a few.et al
2. Moreover, it would be nice if the authors could explain in more detail why studying this new illusion is
relevant. In other words I would like to know which characteristics separate this new configuration from
the ones already known.
3. In the introduction of Experiment 3, it should be noted that the filled area illusion (Giora and Gori, 2010)
is influenced by spatial frequency and a similar procedure to the one used in this study was employed. As
both are size illusions, it would be interesting to discuss the similarities between the two.
4. When the authors state that several illusions are based on local configuration features, as well as citing
the 1860’s work, they should also cite some new literature to provide more up to date references.
5. In the discussion, the difference between perceiving a difference and perceiving a group (Gori and
Page 12 of 15
F1000Research 2013, 2:58 Last updated: 23 JAN 2014
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5. In the discussion, the difference between perceiving a difference and perceiving a group (Gori and
Spillmann, 2010) could be interesting to discuss in relation to the last experiment.
6. The link with the Oppel-Kundt Illusion could be discussed in more detail, for example, by also referring
to the work done by Wackermann.
7. In the discussion, some references to the potential brain mechanisms involved would be the icing on
the cake in my opinion. Visual illusions are open windows on how the brain works and they are interesting
tools to investigate it in a non-invasive manner. It would be nice to read about the hypothetical brain
mechanisms underlying specific illusions.
References
Anstis S, Gori S, Wehrhahn C. . . 2007; (5):791-4.Afterimages and the breathing light illusion Perception 36
Doherty MJ, Campbell NM, Tsuji H, Phillips WA. The Ebbinghaus illusion deceives adults but not young
. . 2010 Sep 1; (5):714-21.children Dev Sci 13
Giora E, Gori S. . .The perceptual expansion of a filled area depends on textural characteristics Vision Res
2010 Nov 23; (23):2466-75.50
Gori S, Giora E, Agostini T. Measuring the Breathing Light Illusion by means of induced simultaneous
. . 2010; (1):5-12.contrast Perception 39
Gori S, Spillmann L. Detection vs. grouping thresholds for elements differing in spacing, size and
. . 2010 Jun 11;luminance. An alternative approach towards the psychophysics of Gestalten Vision Res 50
(12):1194-202.
Gori S, Stubbs DA. A new set of illusions--the dynamic luminance-gradient illusion and the breathing light
. . 2006; (11):1573-7.illusion Perception 35
Gori, S., Giora, E., Yazdanbakhsh, A. and Mingolla, E. (2011) ‘A new motion illusion based on competition
’, , : 1082-1092.between two kinds of motion processing units: The Accordion Grating Neural Networks 24
Gori, S., Giora, E., Yazdanbakhsh, A. and Mingolla, E. (2013) ‘The novelty of the “Accordion Grating
”’, , 2013 Mar; :52.Illusion Neural Networks 39
Jaeger T, Long S. Effects of contour proximity and lightness on Delboeuf illusions created by
. . 2007 Aug; (1):253-60.circumscribed letters Percept Mot Skills 105
Nemati F. Size and direction of distortion in geometric-optical illusions: conciliation between the
. . 2009; (11):1585-1600.Müller-Lyer and Titchener configurations Perception 38
Plewan T, Weidner R, Eickhoff SB, Fink GR. Ventral and dorsal stream interactions during the perception
. .of the Müller-Lyer illusion: evidence derived from fMRI and dynamic causal modeling J Cogn Neurosci
2012 Oct; (10):2015-29.24
Proulx MJ, Green M. Does apparent size capture attention in visual search? Evidence from the
. . 2011 Nov 23; (13).Muller-Lyer illusion J Vis 11
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F1000Research
Qian J, Petrov Y. . 2012 Feb 16; (2):15. StarTrek illusion--general object constancy phenomenon? J Vis 12
Roberts B, Harris MG, Yates TA. (2005). "The roles of inducer size and distance in the Ebbinghaus
". . (7): 847–56.illusion (Titchener circles). Perception 34
Savazzi S, Emanuele B, Scalf P, Beck D. Reaction times and perceptual adjustments are sensitive to the
. . 2012 Apr; (1):119-28.illusory distortion of space Exp Brain Res 218
Schwarzkopf DS, Rees G. Subjective Size Perception Depends on Central Visual Cortical Magnification
. . 2013; (3):e60550.in Human V1 PLoS One 8
Sun YH, Ge L, Quinn PC, Wang Z, Xiao NG, Pascalis O, Tanaka J, Lee K. . A new "fat face" illusion
. 2012; (1):117-20.Perception 41
Thompson P, Wilson J. . 2012; (10):765-74. Why do most faces look thinner upside down? Iperception 3
Titchener, E.B. (1902). Experimental psychology: A manual of laboratory practice. New York, NY:
MacMillan & Co., Ltd.
Wackermann J. . Determinants of filled/empty optical illusion: Influence of luminance contrast and polarity
. 2012; (4):412-20.Acta Neurobiol Exp (Wars) 72
Wackermann J. . Determinants of filled/empty optical illusion: differential effects of patterning Acta
. 2012; (1):89-94.Neurobiol Exp (Wars) 72
Yazdanbakhsh A, Gori S. Mathematical analysis of the accordion grating illusion: a differential geometry
. Neural Netw. 2011;24(10):1093-101.approach to introduce the 3D aperture problem
Zanuttini L, Daneyko O. . . 2010 Dec;Illusory lightness in the Delboeuf figure Percept Mot Skills 111
(3):799-804.
Zeman A, Obst O, Brooks KR, Rich AN. The müller-lyer illusion in a computational model of biological
. . 2013; (2):e56126.object recognition PLoS One 8
I have read this submission. I believe that I have an appropriate level of expertise to confirm that
it is of an acceptable scientific standard.
No competing interests were disclosed.Competing Interests:
Dejan Todorović
Laboratory of Experimental Psychology, Department of Psychology, University of Belgrade, Belgrade,
Serbia
Approved: 21 March 2013
21 March 2013Referee Report:
This paper is a study of a size perception illusion related to the Ebbinghaus illusion and the Delboeuf
illusion. The study includes quantification of the basic phenomenon and some relevant parameters. It is
well designed and executed, and contributes to our knowledge of this class of illusions. Size illusions of
this class have been known for a long time and are still lacking a generally accepted explanation, but have
Page 14 of 15
F1000Research 2013, 2:58 Last updated: 23 JAN 2014
F1000Research
well designed and executed, and contributes to our knowledge of this class of illusions. Size illusions of
this class have been known for a long time and are still lacking a generally accepted explanation, but have
not been studied much in recent years.
My only substantial criticism concerns the authors’ suggestion that the effect they studied is based on a
high-level mechanism, late in the processing stream. I don’t find that they have offered enough evidence
for such a conclusion. Note that recent research on the Ebbinghaus illusion (Schwarzkopf 2010, et al
), not cited by the authors, indicated that the strength of the illusion, (1), 28-30Nature Neuroscience 14
correlates with the size of V1, suggesting contributions to the illusion fairly early in the visual stream.
As a minor comment, it is commendable that the authors have cited the early research on size illusions,
but some of the references, although often cited in that form in the recent literature, are in fact incorrect.
For example, Oppel did not publish about the the illusion named after him in 1854/55 but in 1860/61, and
in that paper he did not report about the dependence of the illusion on the number of tickmarks. For more
details, see . Also, Ebbinghaus didWackermann J. & Kastner K. (2010), , Acta Neurobiol Exp : 423–43470
not publish the illusion named after him in the reference cited in the paper, and in fact seems to have
never published it. For details, see Burton, G. (2001), , , 228-244.History of Psychology 4
I have read this submission. I believe that I have an appropriate level of expertise to confirm that
it is of an acceptable scientific standard.
No competing interests were disclosed.Competing Interests:
Ming Meng
Department of Psychological Brain Sciences, Dartmouth College, Hanover, NH, USA
Approved: 18 March 2013
18 March 2013Referee Report:
The current paper presents a novel variant of visual size illusion that is named the Binding Ring Illusion by
the authors. The illusory effect is quite strong as one could easily experience the illusion him/herself by
looking at figure 2. The authors further tested several stimulus conditions to investigate why the Binding
Ring Illusion occurs. Their results suggest that size assimilation at a relatively high level in the visual
processing stream may underlie the illusion. I think this is a clearly written paper, the results are clear-cut,
and the conclusion of this paper is well supported by the results.
I have read this submission. I believe that I have an appropriate level of expertise to confirm that
it is of an acceptable scientific standard.
No competing interests were disclosed.Competing Interests:
Page 15 of 15
F1000Research 2013, 2:58 Last updated: 23 JAN 2014
... Due to the contradictory results of various methods to quantify the illusion effect, and due to the large number of Ebbinghaus figure configurations tested in this study, the widely studied and applied two-up, onedown staircase procedure was chosen, which is a two alternative forced choice method (2AFC). Several previous studies also applied the staircase procedure to study different features of the Ebbinghaus figure (Roberts et al., 2005; Im and Chong, 2009; McCarthy et al., 2013). Another version of the 2AFC method to study perception is the method of constant stimuli, in which a fixed number of combinations of (Ebbinghaus) figures are shown a certain number of times in a random order. ...
... he horizontal shift of this psychometric function (i.e., a cumulative probability distribution) and the X 50 value (also called the Point of Subjective Equality) then specify the illusion effect. A big area of uncertainty might be linked to a shallow slope of the psychometric function, and the PT should be equal to the point of subjective equality. McCarthy et al. (2013) have performed 4 experiments with using both the staircase procedure (experiment 2) and the method of constant stimuli (experiments 1, 3, and 4) showing that both methods result in similar points of subjective equality. Considering the long history of staircase procedures in the field of psychophysics (García-Pérez, 1998), and the magni ...
Article
Full-text available
Over the last 20 years, visual illusions, like the Ebbinghaus figure, have become widespread to investigate functional segregation of the visual system. This segregation reveals itself, so it is claimed, in the insensitivity of movement to optical illusions. This claim, however, faces contradictory results (and interpretations) in the literature. These contradictions may be due to methodological weaknesses in, and differences across studies, some of which may hide a lack of perceptual illusion effects. Indeed, despite the long history of research with the Ebbinghaus figure, standardized configurations to predict the illusion effect are missing. Here, we present a complete geometrical description of the Ebbinghaus figure with three target sizes compatible with Fitts’ task. Each trial consisted of a stimulus and an isolated probe. The probe was controlled by the participant’s response through a staircase procedure. The participant was asked whether the probe or target appeared bigger. The factors target size, context size, target-context distance, and a control condition resulted in a 3×3×3+3 factorial design. The results indicate that the illusion magnitude, the perceptual distinctiveness, and the response time depend on the context size, distance, and especially, target size. In 33% of the factor combinations there was no illusion effect. The illusion magnitude ranged from zero to (exceptionally) ten percent of the target size. The small (or absent) illusion effects on perception and its possible influence on motor tasks might have been overlooked or misinterpreted in previous studies. Our results provide a basis for the application of the Ebbinghaus figure in psychophysical and motor control studies.
... It would be reasonable to expect that judgments of the size of the array would be based on this contour. However, the Binding Ring illusion demonstrates that the outermost portion of a circular array of individual elements is perceived as smaller when superimposed with a continuous contour that intersects the centroids of individual elements (McCarthy, Kupitz, & Caplovitz, 2013). Providing a continuously defined contour thus appears to increase the influence of the centroid on size judgments of individually grouped elements, highlighting its importance in size perception. ...
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... All the visual illusions employed in the Happé (1996) study are clearly characterized by global information that produces illusory percepts. The Ebbinghaus illusion (Titchener, 1901; Ebbinghaus, 1902, see Table 1for details) produced a large number of papers (e.g., Weintraub, 1979; McCarthy et al., 2013), showing how relevant this pattern is in vision sciences. The Ponzo illusion (Ponzo, 1911), also produced a large amount of literature (e.g., Fisher, 1968; Parks, 2013). ...
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... For example, classical size-contrast and size-assimilation illusions such as the Ebbinghaus illusion (Burton, 2001; Thiéry, 1896) or the Delboeuf illusion (Delboeuf, 1892) demonstrate that the size of a surrounding context can influence the perceived size of a central object (Figure 1). More recently described illusions, such as the ''binding ring illusion'' (McCarthy, Kupitz, & Caplovitz, 2013), the ''StarTrek illusion'' (Qian & Petrov, 2012), the ''shrinking building illusion'' (Fukuda & Seno, 2011), and the ''breathing light illusion'' (Anstis, Gori, & Wehrhahn, 2007; Gori, Giora, & Agostini, 2010; Gori & Stubbs, 2006), further demonstrate that the perceived size of an object is influenced by the context in which it is viewed. Together, these illusions have provided insights into our understanding of how we perceive the size of an object. ...
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"Some geometrical figures appear to be distorted in such fashion that figural elements attract each other… . Some geometrical figures appear to expand as a whole… . Some geometrical illusions in direction, straightness or size are hardly attributed to the displacement or the change of location of the points which constitute the illusional figures… . Illusions in angle or direction generally are greater in the oblique orientation than in the vertical or horizontal direction. The vertical length is overestimated more than the horizontal length. There are intimate kinships between the geometrical illusions and the figural after-effects." (83 ref.) (PsycINFO Database Record (c) 2012 APA, all rights reserved)