Perception, 2009, volume 38, pages 1172 ^ 1182

doi:10.1068/p5943

The scintillating grid illusion: Influence of size, shape,and orientation of the luminance patches
Kun Qian, Yuki Yamada, Takahiro Kawabeô, Kayo Miuraô

Graduate School of Human-Environment Studies (ô Faculty of Human-Environment Studies),
Kyushu University, 6-19-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan;
e-mail: kon@psycho.hes.kyushu-u.ac.jp
Received 7 November 2007, in revised form 17 January 2009; published online 10 July 2009

Abstract. The scintillating grid illusion refers to the illusory perception of black spots on
luminance patches at the intersections of a grey grid on a black background. We examined how
spatial parameters of luminance patches modulated the strength of the illusion. In experiment 1,
we controlled the size and shape of the luminance patches. For the largest-size conditions tested, we
found a significant reduction in the strength of the illusion with squares when compared to circles
or diamonds. In experiment 2, we controlled the orientation of quadrangle patches and confirmed
a significantly larger reduction in the strength of the illusion when the edge orientations ofquadrangle patches were vertical and horizontal (square) than when they were oblique (diamond).
To explore the relationship between orientation processing and scintillating grid illusion, we
controlled, in experiment 3, the global orientation of the display; the strength of the illusion withdiamonds was significantly weaker when it was rotated by 458 than when it was not rotated.
These results indicate that it is not only the difference of edge orientation of luminance patches,
but also the orientation with respect to the grid that determines the strength of the illusion.

1 Introduction
Illusory grey spots are observed at the intersections of a white grid against a black
background (figure 1a). This well-known phenomenon is referred to as the Hermann
grid illusion (Brewster 1844; Hermann 1870). The phenomenon was first explained as asimultaneous contrast between bright and dark areas (Hermann 1870; Hering 1920).
Small eye movements in conjunction with afterimages were proposed as a possible
cause of the illusion (Ehrenstein 1941), but this explanation proved unsatisfactory
because the illusion was even observed at very brief exposure durations (Spillmann1971). The most widely accepted explanation is the retinal-ganglion-cell theory proposing that stronger lateral inhibition at the crossings than elsewhere is the sourceof the illusion (Baumgartner 1960; Wolfe 1984; Spillmann 1994). However, several
inconsistent findings related to the retinal ganglion theory have also been reported.
For example, visual factors which are assumed to enhance lateral inhibition, such as
size variations of stimuli and the addition of diagonal bars, did not effectively influence

(a)

(b)

(c)

Figure 1. (a) Hermann grid illusion; (b) Bergen's illusion; (c) scintillating grid illusion.

Scintillating grid illusion

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the magnitude of the illusion (Lingelbach et al 1985; Spillmann 1994; Schiller andCarvey 2005). On the other hand, visual factors that would not change the putative
differential responses of ganglion cells, such as a 458 rotation of the image, serrationof bar edges, spatial offset of bars, and the change of size ratio of square size tobar width, reduced the illusory effect (Spillmann 1971, 1994; Spillmann and Levine
1971; Levine et al 1980; Lingelbach and Ehrenstein 2002; Schiller and Carvey 2005).
The influences of these visual factors proved the retinal-ganglion-cell theory untenable.
A new theory was proposed positing that S1-type simple cells in the primary visualcortex respond to the grid orientation (Schiller and Carvey 2005). Later, an artificial
neural network, after training for lightness constancy, was explored as a neural modelof the Hermann grid illusion (Bizios et al 2007; Bach 2008). In summary, previous
studies have put forward different hypotheses to explain the mechanism of theHermann grid illusion; however, all these theories assumed that this illusion occurs
in the primary visual cortex (Baumgartner 1960; Schiller et al 1976a, 1976b; Spillman
1994; MacEvoy and Paradiso 2001; Schiller and Carvey 2005).
Stimulus modulations of the Hermann grid illusion produce a novel appearanceof stimuli or scintillation. This scintillating effect was first produced by blurring thedisplay for Hermann-grid illusion (Bergen 1985): scintillating black spots are seen on
the intersections of the blurred grids (Bergen's illusion; figure 1b).
A strong version of the scintillating effect is obtained by adding circular white discs
of high luminance to the intersections of the stimuli of the Hermann grid illusion andby reducing the luminance level of the white bars to grey (figure 1c). This phenomenon
is called the `scintillating grid illusion' (Schrauf et al 1995, 1997). The scintillating grid
illusion is phenomenally different from the Hermann grid illusion in that the illusory
black spots are not constantly perceived, but momentarily scintillate.
Why does the scintillating grid illusion occur? Researchers have examined temporaland spatial properties of this illusion. Regarding temporal properties, Schrauf and colleagues conducted experiments using three different conditions: pursuit eye movements
over a stationary grid, smooth displacements of the grid with a steady gaze, and abrief exposure to a stationary grid. They found it was not the eye movement itself,
but a transient retinal stimulation caused by eye movements or a brief exposure of
the stimuli that was essential for generating the scintillating grid illusion (Schrauf et al2000). They also showed that a high stimulus speed or a very brief exposure (less than
210 ms) reduced the strength of the illusion.
Spatial properties of the scintillating grid illusion have also been investigated.
Schrauf et al (1997) examined the effect of the ratio of grid width to disk diameter on
the strength of the illusion and identified an optimal ratio to elicit a strong illusion.
Schrauf et al (1997) described that, inconsistent with the Hermann grid illusion, thespatial properties of the scintillating grid illusion are not well explained by simple
lateral interactions. Recently, VanRullen and Dong (2003) reported that the distancefrom the attended location to the intersection was a critical parameter determining
the strength of the illusory spots at the intersections, and implied that the spatial
distribution of covert attention affects the strength of the illusion. Yu and Choe (2006)
proposed a neural model that proves the scintillating grid illusion cannot be simply
explained by lateral inhibition. Therefore, it is still unclear what type of spatial interaction in visual processing causes the scintillating grid illusion.
In this study, we explored the spatial mechanism underlying the scintillating grid
illusion by controlling the shape, size, and orientation of the luminance patches at
the grid intersections. Previous studies have examined only the effects of luminanceand the ratio between grid width and disc diameter on the strength of the illusion(Schrauf et al 1997). However, it was unclear whether the size ratio effect could be
extended to other shapes. Therefore, we tested the effects of diamonds and squares in1174

K Qian, Y Yamada, T Kawabe, K Miura

addition to the original circle shape. Although the two new shapes (diamond and square)
have the same side length and interior angles, they are different in terms of their overallorientation. By using three kinds of shapes, we attempted to confirm the role of edge orientation in the illusion. We also controlled the global orientation of the stimulus display,and examined the effect of relative orientation between grids and luminance patcheson the illusion, in addition to the orientation of the luminance patches themselves.
By comparing the strength of the illusion with these stimulus variations, we exploredthe underlying mechanism of the illusion in terms of orientation processing.
2 Experiment 1. Shape and size of luminance patches
2.1 Observers
Five students at Kyushu University served as the observers (two males and threefemales; mean age: 26.4 years). All of them reported normal or corrected-to-normal
visual acuity. They were naive as to the purpose of the experiments.
2.2 Apparatus and stimuli
Stimuli were generated by a computer (Vaio, Sony, Japan) and displayed on a 19-inch
CRT monitor (FlexScan T761; Eizo, Japan). The chin head-rest was used to stabilise
the visual field of the observers. The visual distance was 60 cm. The test stimulus was
an 866 scintillating grid with a visual angle of 11.99 deg615.51 deg. The grey barsof the grid had a luminance of 9.72 cd mÿ2 and a width of 0.33 deg. The distance
between the bars was 1.7 deg. The luminance at the grid intersections was 99.5 cd mÿ2 ,irrespective of shape and size. The black background had a luminance of 2.21 cd mÿ2.
The three shapes (circle, square, or diamond) were presented in five sizes (0.20,
0.26, 0.33, 0.46, or 0.59 deg). The size refers to the side length for the square anddiamond, and the diameter of the circle. 15 stimuli (3 shapes65 sizes) were used in
total (figures 2a and 2b).

(a)

(b)

Figure 2. Stimuli used in experiments 1 and 2. The shape of the luminance patches was(a) diamond (08 quadrangle), (b) square (458 quadrangle), or circle (see figure 1c; only used inexperiment 1). Only parts of these figures are shown.

2.3 Procedure
Prior to the main experiment, observers performed a pilot observation of all thestimuli in order to establish the rating criterion. The observers viewed each stimulus
without a time limit. In the main experiment, at the initial trial the stimulus number

Scintillating grid illusion

1175

was presented for 1 s and followed by the stimulus display. With no time limit imposed,
subjects were asked to rate the strength of the illusion for each stimulus by usinga scale ranging from 1 (weak) to 7 (strong) and marking the rating score on the printed
scale provided. The order of the test stimuli for the rating was identical to that of thepilot observation.
2.4 Results and discussion
Figure 3 illustrates the mean score for illusion strength in experiment 1. A two-way
analysis of variance (ANOVA) revealed significant main effects of shape (F2, 8  8:604,
p 5 0:05) and size (F4, 16  3:931, p 5 0:05) and a significant interaction between
these factors (F8, 32  3:508, p 5 0:01). Tests of simple main effects revealed that theeffect of shape was significant for the larger sizes (0.46 deg: F2, 40  4:853, p 5 0:05;
0.59 deg: F2, 40  14:773, p 5 0:001); the effect of size was significant for the circle(F4, 48  5:334, p 5 0:005) and the square (F4, 48  4:595, p 5 0:005). A posteriori comparison (Ryan's methodöRyan 1960) showed that, when the size was 0.46 deg, thestrength of the illusion generated with circles was significantly greater than that withsquares ( p 5 0:05). When the size was 0.59 deg, the strength of the illusions generated
with circles and diamonds was significantly greater than that with squares ( p 5 0:05).
7

CircleDiamond6

Mean rated strength

Square
5

4

3

2

1
0.20

0.26
0.33
0.46
Size of the luminance patch=deg

0.59

Figure 3. Strength of illusory black spots
in dependence of the shape and size of theluminance patches. Data points represent
the rated strength of the illusion averaged
across observers. Error bars denote 1
SEM (n  5).

The results of experiment 1 suggest that the scintillating grid illusion was weakened
or disappeared when the luminance patches were square in shape. The results indicatedthat the initial increase of the illusion strength with size increments of patches is fairly
independent of their shape. For small sizes there was no significant difference amongshapes. We considered that these findings might have resulted simply from the size
ratio of bar to luminance patch without the contribution of the patch shape. However,the strength of the illusion with the square patches was drastically decreased when thepatch sizes were 0.46 and 0.59 deg, whereas the strength of the illusion with the diamond patches was then only moderately decreased. These results are counterintuitive
because the square and the diamond had the same area, side length, and internalangles. We reasoned that the results were dependent on the edge orientation of luminance patches. Hence, in the next experiment, we examined whether the strength of1176

K Qian, Y Yamada, T Kawabe, K Miurathe illusion was dependent on the rotation of the quadrangle patches from square todiamond, systematically altering the edge orientation of patches from cardinal (horizontal
and vertical) to oblique.
3 Experiment 2. Orientation of the quadrangle
3.1 Observers
Five students at Kyushu University served as observers (two males and three females;mean age: 26.8 years; three of them also participated in experiment 1). All had normal
or corrected-to-normal visual acuity. They were naive as to the purpose of the experiments.
3.2 Apparatus, stimuli, and procedure
The apparatus, stimuli, and procedure for experiment 2 were similar to those used inexperiment 1. We used quadrangle patches with a size of 0.59 deg and one of six different orientations (08, 158, 308, 458, 608, and 758) relative to the grey bars of the grid.
The patch with 08 orientation corresponded to the square, and the patch with 458
orientation corresponded to the diamond. Thus, the former had vertical and horizontal
edges, and the latter had oblique edges. Each stimulus appeared twice in randomisedorder for each observer, and 12 trials were conducted per observer.
3.3 Results and discussion
Figure 4 shows the results of experiment 2. The illusion was most prominent when theorientation of the quadrangle was 458 (diamond), and the illusion strength decreased
as the orientation was reduced to 08 (square). A one-way ANOVA with orientation as afactor revealed a significant main effect (F5, 20  56:432, p 5 0:0001). Multiple comparison tests (Ryan's method) showed that pairs of 08 ^ 308, 08 ^ 458, 08 ^ 608, 08 ^ 758,
158 ^ 308, 158 ^ 458, 158 ^ 608, 308 ^ 458, 308 ^ 758, 458 ^ 758, 608 ^ 758 were significantly
different ( p 5 0:05).
The results of experiment 2 suggest that the edge orientation of the luminance patches
is a critical parameter for the scintillating grid illusion. The strength of the illusion
increased when the edge orientation of the patches became oblique (1) and decreased
when the edge orientation of the patches approached cardinal (vertical and horizontal).
These results imply that orientation of the patch may underlie the scintillating grid
illusion. Results of both experiments 1 and 2 indicate that the scintillating grid illusion(1) In experiments 1 and 2, the strength of the illusion was rated differently even though the stimulus

was the same. For example, the rating of the stimulus with 0.59 deg size diamonds was approximately
4 in experiment 1 but was rated 6 in experiment 2. There are several possibilities to explain thesedifferences. First, the difference of observers between the experiments might explain the different
results. Second, different rating criteria might be established in the pilot experiment of each experiment with different stimulus sets, and this might lead to the different results between experiments.
Specifically, the stimulus set used in experiment 2 did not include the stimulus with circular patches;
the stimulus eliciting the maximum strength of the illusion was the one with diamonds in experiment 2. The difference in stimulus sets might affect the difference of relative strength of the illusion
between experiments, resulting in the rating difference between experiments.
To confirm the first possibility, we extracted the data of three subjects that participated inboth experiments, and checked whether the difference of observers resulted in the inconsistency of
results between experiments. If this had been the case, the data from identical observers should
not have been different from one another. We ran a two-way ANOVA with factors of experiment(1 and 2) and shape (diamond and square). The result revealed a significant interaction between
these two factors (F1, 2  100:000, p 5 0:01). The simple main effect of experiment was significant
when the shape was diamond (F1, 4  48:400, p 5 0:005). In other words, subjects rated different
strengths for the same stimulus with diamond patches in different experiments. So we suggest thatthe difference of observers did not involve the difference of results between experiments in the
diamond-patch condition. It therefore implies that the inconsistent results originate in the second
possibility, namely different rating criteria.

Scintillating grid illusion

1177

7

Mean rated strength

6
5
4
3
2
1
0(90)

15
30
45
60
Orientation of the quadrangle=deg

75

Figure 4. Strength of illusory black spots:
the effect of edge orientation of a quadrangle with respect to the grey bars of
the grid. Data points represent the rated
strength of the illusion averaged acrossobservers. Error bars denote 1 SEM( n  5).

seems to occur when luminance patches with an orientation other than cardinal areplaced at the intersection of the grids.
However, before we reach a firm conclusion we ought to assess the role of orientation interaction between luminance patches and grids in the scintillating grid illusion.
In the stimuli used in experiment 2, rotation of quadrangle patches clearly changed
the relationship between the edge orientation of the patches and grid orientation.
Hereafter, the edge orientation of a luminance patch will be designated as `absoluteorientation' whereas the orientation difference between the grids and the edge ofpatches will be designated as `relative orientation'. Although the results in experiment 2 clearly showed the orientation dependence of the illusion, it was unclear
whether the orientation dependence stemmed from absolute or relative orientations.
To separate the contribution of these two kinds of orientation, we performed thenext experiment.
4 Experiment 3. Absolute orientation, relative orientation, or both orientations
4.1 Observers
Five students at Kyushu University served as observers (four males and one female;mean age: 25.8 years; four of them also participated in the previous experiments).
All participants reported normal or corrected-to-normal visual acuity. They were naive
as to the purpose of the experiments.
4.2 Apparatus, stimuli, and procedure
The apparatus, stimuli, and procedure were the same as those for experiment 1, except
for the following: the test stimulus was an 868 scintillating grid (figure 5) with avisual angle of 15.51 deg615.51 deg. The three shapes (circle, square, or diamond)with a size of 0.59 deg were again employed. In this experiment two kinds of display
orientation were used: upright and rotated. The upright display was the original stimulus used in experiments 1 and 2. In contrast, the rotated display was the original
version of the display rotated by 458. Thus, 6 stimuli (3 shapes62 displays) in total
were used. The order of stimulus presentation was randomised across observers. Wechanged rating scales from 1 ^ 7 to 0 ^ 6, with the value of 0 meaning that no illusory
spots were observed on the luminance patches. In several trials in experiment 2, someobservers reported that no illusion was perceived.

1178

K Qian, Y Yamada, T Kawabe, K Miura

(a)

(b)

(c)

(d)

(e)
(f)
Figure 5. Stimuli used in experiment 3: (a) upright ^ circle; (b) rotated ^ circle; (c) upright ^ diamond;(d) rotated ^ diamond; (e) upright ^ square; (f) rotated ^ square. Note that diamonds become squares
when they are rotated by 458, but they are still labeled as diamonds in accordance with their original
shapes.

4.3 Results and discussion
Figure 6 shows the results of experiment 3. A two-way ANOVA revealed a significant
main effect of shape (F2, 8  139:182, p 5 0:001) and display orientation (F1, 4  45:375,
p 5 0:005) and a significant interaction between these factors (F2, 8  8:432, p 5 0:05).
Tests of simple main effect revealed that the effect of shape was significant for both
displays (upright: F2, 16  71:437, p 5 0:001; rotated: F2, 16  61:065, p 5 0:001). In thefollowing statistical description, we labeled circle as `C', diamond as `D', and square as `S'.

Scintillating grid illusion

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6

Upright
Rotated5

Mean rated strengthp 5 0:001
4

3

2

Figure 6. Strength of illusory black spots
when the entire figures are rotated by 458.
Data points represent the rated strengthof the illusion averaged across observers.
Error bars denote 1 SEM (n  5).

1

0

CircleDiamondSquareA posteriori comparison (Ryan's method) showed that, for the upright display, thethree shape pairs, C ^ D, D ^ S, and C ^ S, were significantly different ( p 5 0:05).
On the other hand, for the rotated display, D ^ S was not significantly different, whereasC ^ D and C ^ S were significantly different ( p 5 0:05).
As observed in experiment 1, in the upright display the illusions were strongest in
the circle condition and weakest in the square condition. In this experiment we found,
for the first time, that this tendency to see illusion with both shapes was preserved
irrespective of the display orientation.
However, in the diamond condition, remarkable changes occurred across display
rotations. The illusion became significantly weaker when the display was rotated; thatis, the shape of the luminance patches changed from diamond to square, whereas in
the square condition the illusion did not become strong when the luminance patches
were changed from squares to diamonds. In both diamond and square conditions of
the rotated display, either the absolute orientation or the relative orientation was 08.
In these situations the illusion was weak.
Therefore, we suggest that not only the orientation of the luminance patches but
also the relative orientation between grids and edges of luminance patches influence
the scintillating grid illusion. Specifically, the illusion was reduced in either of thefollowing two cases: (i) when the edge orientations of patches were vertical and horizontal or (ii) when the edge orientations of patches were parallel and orthogonal
to the grid. In the circular patch condition, no change in the strength of the illusion was observed. We propose that this is because the edge orientation of thecircular patches was neither vertical nor horizontal and because the edge orientationof the patches was neither parallel nor orthogonal. The upright display with the diamond patches elicited a relatively strong illusion. We posit that this is because theedge orientation of the diamond was oblique and diagonal with respect to the grid.
It should be noted that the diamond patches in both the upright and rotated displays
produced equal sampling properties of receptive field in the retina while the strengthof illusion was different for these two displays. These results support the previous suggestion that lateral interaction does not involve the scintillating grid illusion (Schrauf et al
1997; Yu and Choe 2006).

1180

K Qian, Y Yamada, T Kawabe, K Miura

5 General discussion
In this study, we examined whether the size, shape, and orientation of luminancepatches affect the strength of the scintillating grid illusion. In previous studies of thisillusion, only the parameters of white circular disks were investigated. The present
study used luminance patches of circles, diamonds, and squares to examine whether
the scintillating grid illusion was affected by the shape as well as size of the patches.
The illusion in the circle and diamond conditions was stronger than the one in thesquare condition when the patch size was large (experiment 1). The patches withoblique edge orientation caused a stronger illusion than those with vertical and horizontal edge orientation (experiment 2). Furthermore, besides the orientation of theluminance patches per se, the relative orientation between the patches and grids was
also a parameter modulating the strength of the illusion (experiment 3). These results
validate the importance of orientation processing for the scintillating grid illusion.
How can we explain the interaction between the shape and size of luminance patches
in experiment 1? Given that the effect of shape was observed when the size of thepatches was more than 0.46 deg but not when it was below 0.46 deg, we suggest thatwhen patch size is below 0.46 deg, the visual detectors not sensitive to shape/orientation
may be involved in the illusion. As patch size increases, the scale information (spatial

(a)

(c)

(b)

Figure 7. An original Hermann grid illusion (a) incomparison with illusions resulting from shapes
added to luminance patches at the intersections of
the grid: diamonds (b) and squares (c).

Scintillating grid illusion

1181

frequency components) of the patches gradually approaches that of the grids and likely
causes the orientation interaction between the patches and the grids. This interpretation is supported by previous studies showing that orientation integration across scales
is more difficult than the integration within a scale (Dakin and Hess, 1999a, 1999b).
Thus, our results indicate that the scintillating grid illusion is based on spatial integration of orientation information in addition to scale-sensitive processing as shown in
Schrauf et al (1997).
However, clarification is still needed to determine why the cardinal orientation of
the patch inhibited the scintillating grid illusion. As a speculation, we propose thatfigural organisation that is induced by the addition of luminance patches at the intersections alters the strength of the illusion. Figure 7 shows the Hermann grid illusion
with and without luminance patches at the intersections of the grid. In our preliminary
observation, the Hermann grid illusion was reduced when squares were added tothe intersections (figure 7c). Moreover, the addition of squares at the intersections
produced a cross-like shape on the grid. This cross-like shape did not occur when
diamonds were added (figure 7b), and in this case the Hermann grid illusion was toan extent retained. We suggest that figural organisation involving the generation of across-like shape inhibits the orientation interaction across space, resulting in the
reduction of the Hermann grid illusion. In the present study, the spatial interactionof orientation processing was the key mechanism for the scintillating grid illusion.
If the scintillating grid illusion shares a common mechanism with the Hermann grid
illusion, the figural organisation involving the cross-like figure might also induce thereduction of the scintillating grid illusion. Further investigations of this issue are
warranted to clarify the mechanism underlying the scintillating grid illusion as well as
the Hermann grid illusion.
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