a Pion publication
i-Perception (2011) volume 2, pages 69– 76
ISSN 2041-6695 perceptionweb.com/i-perception
Applying the Helmholtz illusion to fashion: horizontal stripes
won’t make you look fatter
Department of Psychology, University of York, York, YO10 5DD UK; e-mail: email@example.com
Department of Psychology, University of York, York, YO10 5DD UK; e-mail: firstname.lastname@example.org
Received 25 August 2010, in revised form 18 February 2011; published online 4 April 2011
Abstract. A square composed of horizontal lines appears taller and narrower than an identical
square made up of vertical lines. Reporting this illusion, Hermann von Helmholtz noted that such
illusions, in which ﬁlled space seems to be larger than unﬁlled space, were common in everyday life,
adding the observation that ladies’ frocks with horizontal stripes make the ﬁgure look taller. As this
assertion runs counter to modern popular belief, we have investigated whether vertical or horizontal
stripes on clothing should make the wearer appear taller or fatter. We ﬁnd that a rectangle of vertical
stripes needs to be extended by 7.1% vertically to match the height of a square of horizontal stripes
and that a rectangle of horizontal stripes must be made 4.5% wider than a square of vertical stripes to
match its perceived width. This illusion holds when the horizontal or vertical lines are on the dress of a
line drawing of a woman. We have examined the claim that these effects apply only for 2-dimensional
ﬁgures in an experiment with 3-D cylinders and ﬁnd no support for the notion that horizontal lines
would be ‘fattening’ on clothes. Signiﬁcantly, the illusion persists when the horizontal or vertical lines
are on pictures of a real half-body mannequin viewed stereoscopically. All the evidence supports
Helmholtz’s original assertion.
Keywords: size perception, Helmholtz illusion, fashion.
Helmholtz (1867) reported that a square composed of horizontal lines appears to be too tall,
and one composed of vertical lines appears too wide (ﬁgure 1-left). Helmholtz notes: “There
are numerous illustrations of the same effect in everyday life. An empty room looks smaller
than one that is furnished; and a wall covered with a paper pattern looks larger than one
painted uniformly in one colour. Ladies’ frocks with cross stripes on them make the ﬁgure
look taller” (page 193). This last observation is particularly interesting, as it is commonly
assumed by people concerned with fashion that horizontal stripes on clothing makes the
wearer look fatter rather than taller.
Left: The Helmholtz Illusion. The square of horizontal lines appears to be taller and narrower
than the identical square of vertical lines. Right: The Oppel–Kundt Illusion. The line B lies equidistant
between A and C but appears displaced towards A, indicating that the ﬁlled extent B–C appears larger
than the unﬁlled extent A–B.
70 P Thompson, K Mikellidou,
The Helmholtz square illusion is one of a family of illusions of ﬁlled extent, of which
the Oppel–Kundt illusion is the best known (Robinson 1972;ﬁgure 1-right). A spatial extent
broken by a regular series of ‘tick’ marks appears longer than an unbroken line of the same
length. There has been some research on the Oppel–Kundt illusion, but our understanding
of the effect is still very limited. No convincing explanation of the illusion has emerged,
and most suggestions from differential eye-movements to constancy mechanisms can be
dismissed. What we have learned is that the illusion is greatest when the tick marks are more
numerous and positioned in a regular fashion (Robinson 1972) and when the stimuli are
smaller rather than larger (Obonai 1954; Long and Murtagh 1984).
The Helmholtz illusion has beneﬁted from even less research, and it too is poorly
understood. That the square of horizontal lines in ﬁgure 1 should look too tall might be
explained by the vertical–horizontal illusion (Künnapas 1955), but this illusion should be
equally applicable to the two squares. The fact that they look different is clearly a result of
a different effect, the expansion of ﬁlled extent as seen in the Oppel–Kundt illusion. The
general idea, that ﬁlled extent increases perceived size, is widespread; Coren and Girgus
(1978) report this is common in the clothing industry “when a tailor or salesman suggests
some particular striped pattern to make you look taller, shorter, fatter, or thinner in direct
application of the Oppel–Kundt effect” (pages 45–46). However, they give no evidence that
tailors or salesmen advise the wearing of horizontal stripes to make one slimmer and taller
or the wearing of vertical stripes to make one look wider. Indeed, modern fashion advice
seems almost universal in the opposite direction (eg, Feldon 2000, page 33).
It has been claimed (Taya and Miura 2007) that the 2-D Helmholtz illusion does not hold
for 3-D forms, such as the human ﬁgure. They propose that vertical lines on clothing produce
two competing effects, a widening by virtue of the Helmholtz illusion and a narrowing as a
result of the 3-D cues given by the vertical lines. It is the latter effect that proves stronger, and
hence vertically striped clothes have a slimming effect.
In the experiments described here we compare the Helmholtz illusion both in its usual
format with squares of vertical and horizontal lines (experiment 1) and in the context of
clothing on a human form (experiment 2). Further we examine the effects of vertical and
horizontal stripes on real 3-D cylinders to test Taya and Miura’s supposition (experiment
3). Finally, we examine the effects of vertical and horizontal stripes on pictures of half-body
mannequins viewed stereoscopically (experiment 4).
2 Experiment 1
In our ﬁrst experiment we measured the size of the Helmholtz illusion by the method of
constant stimuli, with observers comparing the apparent width and height of near-square
patterns of horizontal and vertical stripes. We also investigated the effect of ‘duty cycle’—that
is, the fraction of each cycle that is white (thus a duty cycle of 0.9 will have a narrow dark bar
that occupies 10% of each cycle of the pattern).
2.1 Methods and results
Two conditions were interleaved; in one a standard square set of vertical stripes (5 deg. of
visual angle on each side) was compared with one of ﬁve comparator stimuli composing a
near-square of horizontal stripes of various widths, from slightly narrower to slightly wider
than the vertical standard. The deviations from the standard width were
and 40.6 minutes of arc. At the start of each trial a ﬁxation stimulus of 300 ms (either a
short vertical or horizontal line) indicated to the observer whether a judgement of the
height or the width of the stimuli was required on that trial. The ﬁrst of the stimuli to be
compared (randomly the standard or one of the comparator stimuli) was then presented
for 750 ms, followed by a 450 ms chequered pattern mask. The second stimulus followed for
Applying the Helmholtz illusion to fashion 71
750 ms followed by the mask as before. The observer then responded as to which of the two
stimuli appeared wider or taller. Each of eight naïve observers (ﬁve female) undertook 1000
trials; twenty pairs of stimuli each presented ten times for ﬁve duty cycles from 0.1 to 0.9.
Psychometric functions gave the point of subjective equality (PSE) where the vertical and
horizontal patterns appeared of equal width. The second condition presented a square of
horizontal stripes with a range of near-square vertical comparitors. All other details were
identical to the ﬁrst condition except that observers reported which of the two patterns
appeared taller. This yielded the point of subjective equality where vertical and horizontal
patterns appeared of equal height.
Results of Experiment 1. The blue squares indicate how much taller vertical stripes must be
to match the height of horizontal stripes. The red circles indicate how much wider horizontal stripes
must be to match the width of vertical stripes. Error bars indicate 95% conﬁdence intervals.
The results (ﬁgure 2) show that a pattern of vertical stripes is perceived to be of equal
height with a pattern of horizontal stripes when it is between 4.1 and 10.1% taller, depending
on duty cycle. That is, when both patterns are the same height, the horizontals are perceived
as being taller.
A pattern of horizontal stripes is perceived to be of equal width as a pattern of vertical
stripes when it is between 1.3 and 6.5% wider, depending on the duty cycle. That is, when
both patterns are the same width, the verticals are perceived as being wider. Note that the
effect is consistently greater when the height of the horizontal lines is being judged rather
than when the width of the vertical lines is being judged. These results conﬁrm and quantify
the Helmholtz square illusion and show that the duty cycle of the patterns used is important;
narrow black lines on a white background produce a larger effect than broad black lines.
3 Experiment 2
Experiment 1’s conﬁrmation that vertical stripes make a pattern look wider than a pattern
of horizontal stripes is at odds with the popular belief that the wearing of horizontal stripes
makes the human ﬁgure look wider and that vertical stripes are slimming. Experiment 2
examined this aspect of the Helmholtz illusion, investigating the relative slimming effect of
horizontal lines on clothes worn by a human ﬁgure (ﬁgure 3). This is an equivalent task to
investigating the effect on height of horizontal stripes (which was Helmholtz’s original claim),
72 P Thompson, K Mikellidou,
but the principle is the same, and in terms of fashion there appears to be more interest in
one’s perceived width than one’s perceived height.
Examples of the human ﬁgures used in experiment 2. Here the outlines of the two women
are identical, but the vertically striped pattern makes the hips appear broader.
3.1 Methods and results
Twelve naïve observers judged which of two ﬁgures—one clad in horizontal stripes, the other
in vertical stripes—appeared wider in the hips (ﬁgure 3). The manipulation of the ﬁgure
width affected only the width around the hips; there was no change in the upper body, head,
arms, or lower leg regions. The grating pattern on the dress was now 15.5 cycles/deg., with a
duty cycle of 0.75. For each trial a standard ﬁgure clad in vertical stripes was compared with
one of nine horizontally clad ﬁgures: four narrower in the hips, four broader in the hips, and
one identical to the vertically clad standard. The standard width was 25.8 mins arc with four
narrower and four wider stimuli in steps of 0.5 mins arc. Only estimates of hip width were
made; there were no measures of perceived height.
Again, as in experiment 1, psychometric functions were ﬁtted to the data and the PSE
calculated. In agreement with experiment 1 it was found that the horizontal stripes-clad
woman needed to be 5.8% broader in the hips to be perceived as identical to the woman
in vertical stripes. A paired sample t-test revealed a signiﬁcant difference between the
mean PSEs (
d f =
0.05). This suggests a relative slimming effect of horizontal
compared with vertical stripes.
4 Experiment 3
Clearly the line drawings used in experiment 2 do not fully represent the 3-dimensional
form of a human ﬁgure. Furthermore, it has been shown by Taya and Miura (2007) that
in 2-D pictures of vertical cylinders the addition of shading and vertical stripes designed
to increase the perceived 3-dimensionality of the cylinders serves to make the cylinders
appear narrower. If vertical stripes were to convey more effectively depth information about
a vertically oriented cylinder, then this effect might lead to the human body (essentially a
vertical cylinder in most cases) appearing narrower when clad in vertical stripes despite the
competing broadening effect of the Helmholtz illusion.
Applying the Helmholtz illusion to fashion 73
However, this proposal is at odds with ﬁndings by Li and Zaidi (2000) that the perception
of 3-D shape from 2-D texture cues is most accurate when the orientation of the pattern lies
parallel to the maximum curvature of the surface. That is, for a vertically oriented cylinder it is
horizontal, not vertical, stripes that would give us the most depth information. In the human
form the maximum curvature is along the horizontal axis (in most parts of the body, for most
people), and thus horizontal lines, and not vertical ones, should give the most information
about 3-D shape and hence give rise to perceived narrowing. Thus Li and Zaidi’s results cast
doubt on Taya and Miura’s reconciliation of the Helmholtz illusion with prevailing fashion
To resolve this issue, we examined the effects of horizontal and vertical stripes on the
perceived width of real 3-D vertically oriented cylinders.
4.1 Methods and results
Ten participants matched (by adjusting the separation of two 1-degree long vertical lines
on a computer screen) the perceived width of 20-cm-high cylinders covered with uniform
grey (luminance 10 cd/m
) and vertical or horizontal gratings (high contrast rectangular
wave grating, duty cycle 0.75.). The viewing distance was 57 cm. Cylinders of 2.5, 4.0, 6.5, 8.0,
and 11.5 degrees in diameter were investigated. Each cylinder was presented ﬁve times (in
randomised order) and the mean perceived diameter calculated. The spatial frequency of
the vertical stripes on each cylinder was such as to ensure that there were sixteen cycles per
circumference; thus approximately eight cycles were visible on each cylinder. Horizontal and
vertical stripes had the same spatial frequency.
Results of Experiment 3. Perceived diameters of horizontally striped cylinders (red squares)
and vertically striped cylinders (blue circles) expressed relative to perceived width of uniform grey
cylinders. Error bars indicate 95% conﬁdence intervals.
The results (ﬁgure 4) show that the perceived width of cylinders with horizontal stripes is
close to veridical but that observers systematically overestimated the diameter of vertically
striped cylinders in most conditions. There is no evidence of a slimming effect of the vertical
lines. Again, this result is in agreement with Helmholtz’s observations—that a ﬁlled extent
looks bigger than an unﬁlled extent. We also ﬁnd that the effect disappears with the largest
cylinders; this result is in accord with the ﬁndings of Obonai (1954) and Long and Murtagh
(1984), who found that the Oppel–Kundt illusion diminished with larger stimuli.
74 P Thompson, K Mikellidou,
5 Experiment 4
Finally, we decided to address directly the debate on the Helmholtz’s illusion regarding
striped garments. The aim of this experiment was to observe what happens to the illusion
when 3-D ﬁgures of real mannequins dressed in strapless t-shirts with either black horizontal
or vertical stripes were used as stimuli.
We decided that a half-body model mannequin was suitably realistic to use as a stimulus
because, according to Cornelissen et al (2009), people judge body size by focusing their
gaze on the stomach, with the ‘scanning’ area consisting of only the upper part of the body
(shoulders to pelvis). Therefore participants were asked to compare the width of two 3-D
ﬁgures (ie, four ‘fused’ 2-D images) and indicate the wider one. An example stimulus is
illustrated in ﬁgure 5 below.
Examples of the Figures Used in Experiment 4. Here the outlines of the two mannequins are
identical, but the vertically striped pattern makes the ﬁgure appear broader.
5.1 Methods and results
On each trial a standard ﬁgure clad in vertical stripes was compared with one of a set of nine
horizontally clad ﬁgures: four narrower, four broader, and one identical to the vertically clad
standard. An example is shown is ﬁgure 6. The standard width was 40.5 mins arc and the
height was 98.2 mins arc, with four narrower and four wider stimuli in steps of 0.5 mins arc.
Only estimates of width were made; there were no measures of perceived height. Again, as in
experiment 1 and experiment 3, psychometric functions were ﬁtted to the data and the PSE
Pictures of the mannequin in two different positions 40.0 cm away from each other were
taken so that participants would be able to view the two pairs of pictures simultaneously
as if there were two model mannequins one next to the other. The digital camera was 115
cm away from the model mannequin and the left image was taken at a distance of 6.30 cm
[representing the average pupillary distance (Dodgson 2004)] away from the right image.
A mirror stereoscope was set up 56.0 cm away from a computer screen, and participants
were asked to view the images from a speciﬁc eye position determined by a pair of goggles.
The four mirrors were calibrated to allow fusion of the four 2-D images into two 3-D images.
When the four 2-D images were combined, the illusion of depth was created. The four 2-D
ﬁgures appeared simultaneously for 3000 ms followed by a white screen awaiting response.
Eight observers able to fuse a sample stimulus took part in the experiment. The duty cycle
of the striped t-shirts was 0.50, and the ﬁgures’ width was manipulated using Corel Draw
Graphics Suite (Version 13). The experiment was set up using SUPERLAB, and forced-choice
responses were recorded. The screen’s resolution was 1280 x 1024 pixels, and the frame rate
was 76 Hz.
Applying the Helmholtz illusion to fashion 75
In agreement with experiment 1 and experiment 3, it was found that the mannequin
in horizontal stripes needed to be 10.7% broader to be perceived as identical to the one in
vertical stripes. A paired sample t-test revealed a signiﬁcant difference between the mean
d f =
0.05), thus supporting the Helmholtz’s illusion. This suggests a
relative slimming effect of horizontal compared with vertical stripes.
We have conducted 4 experiments to investigate the generality of the Helmholtz square
illusion to pictures of the human form and real 3-D cylinders. The results show that in all
cases space covered with vertical stripes appears wider than a similar space covered with
horizontal stripes. In experiment 3, where we included a neutral grey condition, it appears
that horizontal stripes do not signiﬁcantly affect the perceived width of a pattern, and we
would suggest that neither do vertical patterns affect perceived height.
In experiment 3 we can see that the illusion persists on real cylinders, contradicting
the suggestion of Taya and Miura (2007) that perhaps vertical stripes increase the 3-
dimensionality of ﬁgures and hence make them appear narrower. However, this effect seems
to disappear for larger cylinders. This ﬁnding agrees with Long and Murtagh (1984), who
reported that the Oppel–Kundt illusion was much more prominent with small stimuli.
Experiment 4 was our most direct attempt to resolve the debate on the application of
Helmholtz’s illusion to fashion. By using 3-D images of a mannequin, we have dealt with
the limitations of experiments 2 and 3, where the stimuli were not as realistic. Findings
from experiment 4 have shown that vertical stripes made the mannequin look 10.7% wider
than the mannequin in horizontal stripes, and this effect was found to be signiﬁcant. We
did not make use of real women as models because doing so would bring with it many
methodological problems, one of them being the inability to manipulate the stimuli.
One ﬁnal observation, made in a personal communication by Wolfgang Metzler to
Zanforlin (1967), may convince the reader: when asked to make a vertical pile of coins
so that its height is equal to the coins’ diameter, a subject will typically make the pile about
30% too low. This illusion is a compound of two effects—the Helmholtz illusion and the
vertical–horizontal illusion. The horizontal orientation of the coins will make the pile appear
taller than it really is because of the Helmholtz illusion, and the vertical–horizontal illusion,
in which a vertical line appears to look longer than an identical horizontal one will reinforce
this overestimation of the vertical. Hence, in judging the height of the coins equal to its width,
observers make the pile too short. However, if this task is repeated with the coins turned 90
deg., the Helmholtz illusion and the vertical–horizontal illusion are placed in opposition to
each other, and the size of the effect is markedly reduced, though not abolished, suggesting
that the Helmholtz illusion is larger than the vertical–horizontal illusion.
The Helmholtz Square and Oppel–Kundt illusions show a consistent and large overestimation
of ﬁlled space such that horizontal lines serve to make a space appear taller, and vertical
lines serve to make a space look wider. This effect persists when used on pictures of clothing,
on cylinders of diameter less than about 6 deg., and on pictures of half-body mannequins
viewed stereoscopically. These results indicate that more research is needed to identify the
underlying mechanisms of this effect and that there is no evidence to support the widely
held beliefs that horizontal stripes make the human form appear wider and that vertical
strips have a slimming effect. All the evidence here points in the opposite direction.
Acknowledgements. We acknowledge the help of Hannah Smith with experiment 1 and Nicoletta
Psyllidou for help with experiment 2 and experiment 4.
76 P Thompson, K Mikellidou,
Coren S, Girgus J S, 1978, Seeing is deceiving: the psychology of visual illusions (Oxford: Lawrence
Cornelissen P L, Hancock P J B, Kiviniemic V, George H R, Tovée M J, 2009 “Patterns of eye move-
ments when male and female observers judge female attractiveness, body fat and waist-to-hip
ratio” Evolution and Human Behavior 30 417 –428 doi:10.1016/j.evolhumbehav.2009.04.003 J
Dodgson N A, 2004 “Variation and extrema of human interpupillary distance” 5291 36–46
Feldon L, 2000, Does This Make Me Look Fat? (New York: Villard) J
Helmholtz H v, 1867/1962, Treatise on Physiological Optics, volume 3 (New York: Dover, 1962);
English translation by J P C Southall for the Optical Society of America (1925) from the 3rd
German edition of Handbuch der physiologischen Optik (ﬁrst published in 1867, Leipzig: Voss) J
Künnapas,T M, 1955 “An analysis of the ‘vertical-horizontal illusion”’ Journal of Experimental Psy-
chology 49 134 – 140 doi:10.1037/h0045229 J
Li A, Zaidi Q, 2000 “Perception of three-dimensional shape from texture is based on patterns of
oriented energy” Vision Research 40 217– 242 doi:10.1016/S0042-6989(99)00169-8 J
Long G M, Murtagh M P, 1984 “Task and size effects in the Oppel-Kundt and irradiation illusions”
The Journal of General Psychology 111 229–240 doi:10.1080/00221309.1984.9921112 J
Obonai T, 1954 “Induction effects in the estimates of extent” Journal of Experimental Psychology 47
57–60 doi:10.1037/h0057223 J
Robinson J O, 1972, The Psychology of Visual Illusion (London: Hutchinson University Library) J
Taya S, Miura K, 2007 “Shrinkage in the apparent size of cylindrical objects” Perception 36 3–16
Zanforlin M, 1967 “Some observations on Gregory's theory of perceptual illusions” The Quarterly
Journal of Experimental Psychology 19 193–197 doi:10.1080/14640746708400092 J
received his degree in Psychology from the University of Reading and
his PhD from the University of Cambridge under the supervision of Oliver Braddick. He was
awarded a Harkness fellowship, which took him to Jack Nachmias’s lab at the University of
Pennsylvania. He returned to the UK to the University of York, where he still works. In 1990
he was an NRC Senior Research Associate with Beau Watson’s Vision group at NASA’s
Ames Research Center. He is a Royal Society—British Association Millennium Fellow and a
HEFCE National Teaching Fellow. He has created the solar system (www.solar.york.ac.uk)
and viperlib—a resource of images for vision scientists (www.viperlib.com). For more
information visit www-users.york.ac.uk/∼pt2.
originally from Cyprus, received her degree in Psychology at the
University of York, UK. Then, she was awarded with a departmental scholarship to do an
MSc in Cognitive Neuroscience, and in 2009 she received a three-year education grant
from the A G Leventis Foundation to continue her studies with a PhD in Psychology at the
University of York. Currently, her research focus is on illusions of ﬁlled extent, and she is
carrying out both psychophysics and neuroimaging experiments to determine under which
conditions they become most prominent, as well as their origin in the human visual system.
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