Perception, 2010, volume 39, pages 573 ^ 576

doi:10.1068/p6617

LAST BUT NOT LEAST

The jaggy diamonds illusion
Takahiro Kawabe, Kun Qian, Yuki Yamada, Kayo Miura

Kyushu University, 6-19-1, Hakozaki, Higashi-ku, Fukuoka 812 8581, Japan;
e-mail: tkawabe@hes.kyushu-u.ac.jp
Received 13 November 2009, in revised form 4 February 2010

Abstract. We report a new illusion in which the edges of diamonds placed at the intersectionsof grids are perceived to be jaggy (the jaggy diamonds illusion). Interestingly, the illusion disappears when the stimulus is rotated by 458, when the stimuli are observed at a close distance,and on the diamond at which the observers stare. Luminance contrast between diamonds,grids, and background is a strong determinant for this illusion.

Visual illusions induced by intersecting grids (grid illusions) have been reported inthe past. For example, illusory smudges are perceived at the intersection of brightgrids on a dark background (Hermann grid illusion). Scintillating smudges are also
perceived within disks placed at the intersection of grey grids with a dark background(scintillating grid illusion). These anomalous percepts of illusory smudges are affected byluminance and geometrical relationships between the grids, the background, and the disks.
Here we report a new grid illusion: the edges of diamonds placed at the intersectionsof grids are perceived to be jaggy (figure 1a). This illusion was found when we conducted
experiments on the scintillating grid illusion with diamond patches (figure 1b). However,stimulus conditions inducing the illusion of diamonds with jaggy edges are still unclear.
This paper briefly reports two experiments on this finding.
In experiment 1, six observers were presented with an image of the type shown infigure 1a on a 20-inch display at a viewing distance of nearly 70 cm. The stimulus
extended 27.5 cm horizontally and 21.0 cm vertically (a 20616 diamond matrix withcrossing grids). The width of each diamond subtended 0.6 cm and the width of eachgrid was 0.4 cm. The task of the observers was to freely scan the stimulus image anddraw the perceived shape of diamonds with a pen. No time limit was imposed.
The results are shown in figure 1c. Though the perceived shapes of diamonds differed
between the observers, one common feature of patches they drew was the jaggy or starlike edge of the diamonds. Therefore, we call this illusion `the jaggy diamonds illusion'.
Informal observation showed that the jaggy diamonds illusion disappeared when
the stimulus was rotated by  458 (try this with figure 1a), suggesting the dependenceof this illusion on retinal image. These observations also ruled out the possibility
that small image artifacts, such as physical notches along an edge, caused this illusion. Importantly, the illusion could be seen in the peripheral visual field. Moreover,a stronger illusion was reported when the viewing distance was increased and when
the observers scanned the stimulus with eye movements.
Compare figures 1a and 1b. A potential source of the jaggy diamonds illusion seems
to be a luminance contrast between the diamonds and the background, which is the only
difference between figures 1a and 1b. Therefore, in experiment 2, we investigated how
the luminance contrast of the diamonds against the background affected the illusion.
Five observers participated in this experiment. Stimuli were presented on ag-corrected CRT display (RDF193H, Mitsubishi). A Mac Pro (Apple Inc.) controlled
stimulus presentation and data collection. A head-and-chin rest was used to stabilise
the visual field of each observer. The stimulus image in each trial was composed of 868

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(a)

(b)

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dark diamondbright diamond

KY(c)

JY

YK

Rated strengths of the illusion

543210020406080
Background luminance=cd mÿ2100(d)Figure 1. (a) The jaggy diamonds illusion. The observers typically perceive the edge of the diamonds to be jaggy. However, when this image is rotated by 458, the illusion disappears. (b) The
scintillating grid illusion with diamond patches, reported in Qian et al (2009). (c) The results ofexperiment 1: the individual drawings of typically perceived shape of diamonds are shown.
(d) The results of experiment 2: arrows with black and white diamonds indicate luminance values
in dark and bright diamond conditions, respectively. Error bars denote 1 SEM (N  5).

grid diamonds, 868 grid intersections, and background. The side of each diamond
was 1.0 deg long. The width of each grid line was 0.4 deg. The distance between thediamonds was 2.8 deg. Each diamond was placed at a grid intersection. The luminanceof patches was set at either a low (17.0 cd mÿ2 ) or a high (73.8 cd mÿ2 ) level. The luminance of background was randomly selected from nine alternatives (0.0, 11.5, 23.0,34.0, 45.5, 57.0, 68.0, 79.5, or 91.0 cd mÿ2 ). The grid luminance was 45.5 cd mÿ2 (neutralgrey). The task of the observers was to rate the strength of the illusion on a 6-point
scale ranging from 0 (no illusion) to 5 (strongest illusion). Before the experimentalsession, the observers conducted a task similar to that in experiment 1, and all drew
the patch with jaggy edges. No temporal limit was imposed. The rating score in eachtrial was determined by pressing assigned keys. After conclusion of one trial the next trial
was started by pressing the space bar of the keyboard. Each observer performed 72 trials:

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2 (diamond luminance conditions)69 (background luminance conditions)64 (repetitions).
The trial order was randomised across observers.
The results are shown in figure 1d. For each observer, the rated strengths wereaveraged in terms of each experimental condition. These data were submitted to a
two-way ANOVA with diamond luminance and background luminance as factors. The
main effect of diamond luminance was not significant (F1, 4  4:1, p 4 0:1). The main
effect of background luminance was significant (F8, 32  13:3, p 5 0:0001). Importantly,
the interaction between the two factors was significant (F8, 32  62:0, p 5 0:0001).
Tests of simple main effects showed that rated strengths were significantly different
in the two diamond luminance conditions when background luminance was 0.0,11.5, 23.0, 68.0, 79.5, and 91.0 cd mÿ2 ( p 5 0:0001). When the diamonds were dark
(17.0 cd mÿ2), the rated strengths in background conditions with 0.0, 11.5, and 23.0 cd mÿ2luminance were significantly higher than those in background conditions with more than
34.0 cd mÿ2 ( p 5 0:003). On the other hand, when the diamonds were bright (73.8 cd mÿ2 ),the rated strengths in background conditions with 68.0, 79.5, and 91.0 cd mÿ2 luminancewere significantly higher than those in background conditions with less than 57.0 cd m ÿ2
luminance ( p 5 0:0001).
The results showed that the rated strength of the illusion was high when the differencein luminance between the diamonds and the background was small, indicating thatluminance contrast was a strong determinant of the jaggy diamonds illusion. In particular, low luminance contrast between the diamonds and the background strongly elicitedthe illusion.
However, on comparing figures 2a and 2b, in which the contrast between the grids
and the background is greater in the former than the latter with the contrast between
the diamonds and the background fixed, one finds that the illusion is stronger in theformer than the latter figure. This observation suggests that the illusion is also influenced
by the relationship of luminance contrast between the grids and the background.
This study demonstrated that luminance contrast alters perceived shapes of diamonds,
though it is still not clear exactly what kind of mechanism underlies this illusion.
An earlier study has shown that local processing for luminance contrast between thecentral region and background strongly affected perceived size of the central region(van Erning et al 1988). Also, the relationship of contrast polarity between adjacentregions determines the perceived tilt of a line in the Cafë Wall illusion (Kitaoka et al2004). However, none of these previous studies can provide a straightforward explanation
for the jaggy diamonds illusion.
It is interesting to compare the jaggy diamonds illusion with other grid illusions.
Consistent with the jaggy diamonds illusion, the Hermann and scintillating grid illusions are greatly reduced with oblique grids (De Lafuente and Ruiz 2004; Qian et al2009) and with the curved grids (compare figures 2c and 2döGeier et al 2008). The
scintillating grid illusion is also sensitive to the relationship in luminance contrast
between the disks, the grids, and the background (Schrauf et al 1997). Moreover,
one critical aspect of the jaggy diamonds illusion is that jaggy edges of diamonds areperceived to twinkle or scintillate with eye movements or attention shifts, which is aprominent characteristic of the scintillating grid illusion (Schrauf et al 1997; VanRullenand Dong 2003). Hence, the underlying mechanism of the jaggy diamonds illusion ispossibly shared by other grid illusions. The large individual differences of perceived
shapes of diamonds (figure 1c) may be due to this twinkling/scintillation that likely
induces uncertainty about the shape of the diamonds. Still, it is surprising that all ourobservers report jaggy edges of the diamonds.

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(a)

(b)

(c)

(d)

Figure 2. Demonstrations of the modulation of illusion strength by luminance contrast between
grids and background: the illusion is stronger in (a) than in (b). The illusion disappears when gridsin (c) are curved as in (d).
Acknowledgment. We thank an anonymous reviewer for suggesting the important role of luminancecontrast between grids and background in the illusion reported here.
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Geier J, Bernäth L, Hudäk M, Sëra L, 2008 ``Straightness as the main factor of the Hermann gridillusion'' Perception 37 651 ^ 665
Kitaoka A, Pinna B, Brelstaff G, 2004 ``Contrast polarities determine the direction of Cafë Walltilts'' Perception 33 11 ^ 20
Qian K, Yamada Y, Kawabe T, Miura K, 2009 ``The scintillating grid illusion: Influence of size,
shape, and orientation of the luminance patches'' Perception 38 1172 ^ 1182
Schrauf M, Lingelbach B, Wist E R, 1997 ``The scintillating grid illusion'' Vision Research 371033 ^ 1038
VanRullen R, Dong T, 2003 ``Attention and scintillation'' Vision Research 43 2191 ^ 2196

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