QR Codes on Curved Media Facades
Two Approaches for Inverse Distortion based on Raytracing and Image Warping
Morin Ostkamp, Sven Luzar and Gernot Bauer
Software Engineering Lab, M
¨
unster University of Applied Sciences, Soester Straße 13, 48155 M
¨
unster, Germany
Keywords:
QR Code, Media Facade, Curved Surface, Raytracing, Image Warping.
Abstract:
Media facades and other public displays are a common sight in our everyday life. They can be found at various
places, such as shopping malls or traffic hubs, e.g., the Times Square in New York City or Shibuya Crossing
in Tokyo. Thanks to advances in technology, media facades are not bound to plane, rectangular shapes. Thus,
many media facades are curved to increase their visual appearance or to better harmonize with the building
behind. One example of such a curved media facade is the “Medienfassade” in the city of M
¨
unster. The shown
content, however, is visually distorted due to the facade’s concave shape. That visual distortion may cause
problems for certain types of content, i.e., QR codes, that may thus not be scanned with mobile apps. Since
QR codes became popular in recent years, it appears desirable to display these codes on curved media facades,
too. Thus, we propose two preprocessing approaches to compensate for the visual distortions of the curved
media facade. An in-situ evaluation showed that both approaches can be used to “rectify” the distorted QR
codes and let them be scanned successfully.
1 INTRODUCTION
Nowadays, displays are not restricted to plane, rect-
angular shapes anymore. Thanks to recent technolog-
ical advances, e.g., OLED, almost all possible forms
and sizes can be realized. On the one hand, this may
be an advantage for product designers, as they are less
bound to technical restraints. On the other hand, how-
ever, this gain in flexibility may cause problems for
content designers, as their displayed content may be
visually distorted. These visual distortions may not
cause problems for most content types. Certain types
of content, however, may be affected negatively, i.e.,
QR codes. Though the specifications of QR codes
allow to print them on curved surfaces, most non-
industrial scanners, especially smart phones, struggle
to scan them. The QR code in Figure 4 (d), for ex-
ample, cannot be scanned by “ZBar” on an iPhone
4. An example for a curved display is the “Medien-
fassade” in the city of M
¨
unster, which is shown in
Figure 1. This media facade has a size of 13.20 m
(width) by 13.90 m (height). It is embedded in the
front side of a building, 8.70 m above the ground. To
better harmonize with the building’s architecture and
due to restrictions of the city’s government, the me-
dia facade’s surface is concave and set back into the
building’s body. This causes a noticeable visual dis-
tortion, that can be observed in Figure 1. The actual
display surface is made of a semi-transparent grid of
LEDs with a resolution of 192 x 212 pixels. As QR
codes became a popular marketing means on flyers,
posters, and billboards in recent years, there was a
rising need to show QR codes on the Medienfassade
as well. Due to the curved surface, however, usual
QR codes, cf. Figure 4 (a), could not be scanned with
most smart phone apps, cf. Figure 4 (d). Since there
are many more examples of curved media facades and
other types of public displays all over the world, e.g.,
the Times Square in New York City or Shibuya Cross-
ing in Tokyo, we believe that the compensation for
visual distortions of QR codes is a significant and im-
portant contribution to the community. Thus, we ana-
lyzed how to counter the visual distortions of the Me-
dienfassade by following two approaches: (i) raytrac-
ing (in the sense of, mathematically speaking, projec-
tive geometry) and (ii) image warping. The remain-
der of this paper is structured as follows: First, we
position our research within related work. Then, we
present two approaches to let QR codes be scanned
successfully on curved surfaces. Next, we present re-
sults of an in-situ evaluation of both approaches. We
discuss the findings in the following section and con-
clude the paper with a summary of our contributions
and an outlook on subsequent work.
424
Ostkamp M., Luzar S. and Bauer G..
QR Codes on Curved Media Facades - Two Approaches for Inverse Distortion based on Raytracing and Image Warping.
DOI: 10.5220/0004655904240429
In Proceedings of the 9th International Conference on Computer Graphics Theory and Applications (GRAPP-2014), pages 424-429
ISBN: 978-989-758-002-4
Copyright
c
 2014 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: The Medienfassade showing a rectangular grid.
Due to the facade’s curved surface, the grid appears visually
distorted, i.e., horizontal lines are bent.
2 RELATED WORK
The work presented in this paper touches upon several
research areas. First, we provide an overview of the
most important characteristics of QR codes. Then, we
present two particular approaches to image process-
ing: The first one is based on raytracing and thus uses
a 3D model of the scene shown in the image. The
second approach uses 2D image warping techniques
instead.
2.1 QR Codes
During the last years, QR codes became popular due
to their robust design, high data capacity, and adapt-
ability. A common use case is to print QR codes fea-
turing URLs on flyers, posters, or billboards. Denso
Wave developed the two-dimensional bar codes in
1994. The specifications are available as an ISO norm
(Denso, 2000) and also in parts online (Denso, 2013).
QR codes consist of black and white areas, so called
modules. There are different “versions”, according to
the the number of modules, i.e., the size of the QR
code. Figure 4 (a) shows a version 1 QR code con-
taining the word “Test”, before applying any transfor-
mation described in Section 3. There needs to be an
empty area, called “quiet zone”, around the code. The
size of the quiet zone should be four times as big as a
module. If the quiet zone is too small, scanners may
fail to scan the code. QR codes can be printed with
any color on any background, as long as the contrast
between the foreground and the background is kept
high. QR codes support four error correction levels:
low, medium (used in this paper), quartile, and high.
The first one allows 7% of the code to be damaged,
while the latter allows to scan codes that are more than
30% damaged. Therefore the contained data is spread
redundantly within the code. Furthermore, QR codes
are robust against certain (linear or affine) transfor-
mations, e.g., rotation or skew. Thus, users can scan
codes printed on billboards from almost any position,
for example. Though other (non-linear) distortions
are also covered by the specifications (Denso, 2013),
they may still cause problems, at least for smart phone
scanners. Codes printed on coffee mugs, for example,
can usually not be scanned with a mobile app. In or-
der to restore the support for smart phones, QR codes
can be preprocessed as proposed by this paper.
2.2 Raytracing
Raytracing is a well-established concept in computer
vision and graphics (Glassner, 1989). Back in 1968,
Appel sparked the development of the raytracing the-
ory in his publication on “Some techniques for shad-
ing machine renderings of solids” (Appel, 1968). The
basic idea is to trace the path of a ray of light in a
virtual scene. Whenever the ray hits an object, the
physical effects that can be observed in reality, e.g.,
refraction, are simulated on a two-dimensional im-
age plane. In subsequent years, the presented algo-
rithms were further evolved and became widely used
to generate scene renderings in computer games, for
example. Though there may be different raytracing
manifestations or implementations, they are all based
on mathematical 3D models of the scene that is to be
rendered. The creation of such models can be diffi-
cult and time-consuming because the reality’s details
have to be re-created in the virtual space. In this pa-
per, however, the architectural blue prints of the Me-
dienfassade were available and could thus be used to
create a suitable 3D raytracing model.
2.3 Image Warping
Image warping is an image manipulation technique
that maps points of a source image to specific points
in a destination image. One particular application is
image morphing, which has been used as a special ef-
fect in movies, for example, since it can be used to
QRCodesonCurvedMediaFacades-TwoApproachesforInverseDistortionbasedonRaytracingandImageWarping
425

create smooth transitions between different shapes of
a character or an object. Besides that, image warp-
ing is also widely discussed in scientific scenarios.
Wohlberg (Wolberg, 1996) and Lin and Huang (Lin
and Huang, 1999), for example, propose face or facial
expression morphing as a means for authentication,
speech animation, or natural human computer inter-
faces. Zhang and Tan (Zhang and Tan, 2002), Liang et
al. (Liang et al., 2005), and Meng et al. (Meng et al.,
2012) present different approaches for straightening
warped text lines in scanned documents. This may
help to increase the overall readability for humans as
well as the accuracy of machine based optical char-
acter recognition (OCR). The undistorted projection
of images onto a curved display is also a prevalent
use case. Chuang et al. present an approach based
on an approximation scheme that can be realized as
a hardware component with reasonable performance
(Chuang et al., 2010). In contrast to the approach pre-
sented in this paper, their system requires an exhaus-
tive specification of environmental parameters, such
as the dimensions of the object, which the image is
projected on. Their approach is comparable to the one
presented in Section 3.1 in this paper. Harville et al.
(Harville et al., 2006) and Raskar et al. (Raskar et al.,
2005) present self-configuring projector systems that
can be used to build large displays on non-planar sur-
faces. Both systems use cameras to automatically cal-
ibrate the projected images and apply image warping
in such a way that the final image appears with a min-
imum local distortion for the viewer. Except for the
suggested application scenario, both approaches are
comparable to the one presented in Section 3.2 in this
paper.
As the review of previous publications reveals, the
theoretical basis for the work in this paper has been
laid out by the related work cited above. The present
paper applies these findings to a specific use case or
application scenario and evaluates the feasibility as
well as the results.
(x − l)
2
+ (y − m)
2
= r
2
(1)
x = x
1
+ (x
2
− x
1
) ∗t = x
1
+ i ∗ t
y = y
1
+ (y
2
− y
1
) ∗ t = y
1
+ j ∗t
z = z
1
+ (z
2
− z
1
) ∗ t = z
1
+ k ∗t
(2)
(x
1
+ i ∗ t − l)
2
+ (y
1
+ j ∗t − m)
2
= r
2
(3)
t
2
(i
2
+ j
2
) + t(2ix
1
− 2li + 2 jy
1
− 2m j)
+ (x
2
1
− 2lx
1
+ l
2
+ y
2
1
− 2my
1
+ m
2
− r
2
) = 0
(4)
p = (2ix
1
− 2li + 2 jy
1
− 2m j)/(i
2
+ j
2
)
q = (x
2
1
− 2lx
1
+ l
2
+ y
2
1
− 2my
1
+ m
2
− r
2
)/(i
2
+ j
2
)
t
1,2
= −p/2 ±
p
p/2 − q
(5)
3 APPROACH
We premised our research on two fundamentally sep-
arate approaches: (i) raytracing and (ii) image warp-
ing, as described in more detail below. The raytracing
approach is based on a theoretical 3D model and may
thus not take all real influences, such as camera lens
distortions, into consideration. The image warping
approach, however, is based on empirical data. We
were curious about the outcomes of a comparison of
these two opposed approaches.
3.1 Raytracing
Since the Medienfassade has been embedded in a
building constructed in 2008, the architectural blue
prints were still available. This information could
thus be used to create a corresponding 3D model. As
a result, the Medienfassade was modeled as a cuboid
of 13.20 m width and 13.90 m height, 8.70 m above
ground. The cuboid is intersected by a cylinder with
a diameter of 21.57 m and an infinite height. The
distance between both centers of the cuboid and the
cylinder is 22.37 m. The estimated position of the
viewer’s eye is in 34.00 m in front of the facade and
in a height of 1.80 m (supposed the average viewer
is about that tall). In the remainder of this paper we
are going to refer to this position as the “sweet spot”,
since the viewing experience will be optimal from
there. Further, the presented approach assumes that
the source image, that is undistorted and has not been
preprocessed, is held parallel in 0.01 m distance to the
viewer’s eye. The source image’s resolution is twice
as high as the resolution of the target, i.e., the media
facade, to avoid interpolation issues, that may appear
as black spots in the preprocessed image.
The presented approach is based on a minimalis-
tic raytracing implementation. The scene has been
modeled as a linked list of the following objects:
the world’s origin, the viewer’s eye (the camera), the
source image, the cylinder, and the media facade. The
further implementation is based on the following no-
tion. Let the facade’s cylinder be defined as in (1),
with l and m as the center and r as the radius. A
ray, that originates in the viewer’s eye, intersects the
source image, and finally hits the media facade is de-
fined as in (2), with x
1
,y
1
,z
1
as its origin and x
2
,y
2
,z
2
as a second point on the ray specifying the ray’s di-
rection. Now, plug (1) in (2) which in turn provides
(3). Solving this equation for t provides two solutions.
One of them can be ignored (t < 0), which provides
the result in (4) and (5) (p and q are parts of the p-q-
formula to solve the quadratic equation). Plugging (5)
back into (2) provides x,y and z coordinates for each
GRAPP2014-InternationalConferenceonComputerGraphicsTheoryandApplications
426

Figure 2: The curved media facade showing a QR Code that
has been preprocessed using the raytracing approach.
pixel of the source image on the media facade. Figure
4 (b) shows what the preprocessed image looks like,
while Figure 2 displays the visual experience from the
sweet spot.
3.2 Image Warping
In order to empirically reproduce the distortion
caused by the Medienfassade, we displayed a regu-
lar grid on the media facade, see Figure 1. The dis-
torted image of the grid was photographed from the
sweet spot. This photograph was used as a calibra-
tion image. After cutting and resizing the calibration
image in a standard image processing software, it had
the same dimensions as the undistorted regular grid.
That allowed us to identify the 24 intersection points
~u
i
(i=1,. . . ,24) of the grid’s lines with their correspon-
dences ~v
i
in the calibration image. We then used the
correspondence between ~u
i
and ~v
i
to find a transfor-
mation T , that matches any point in the undistorted
original image to the corresponding point in the dis-
torted image on the media facade, cf. Equation (6).
Note that T has also to fulfill the 24 boundary condi-
tions.
~v
i
= T (~u
i
).
(6)
For our purposes, it is sufficient to assume that the
~v
i
in (6) depend on the~u
i
up to third order in the com-
ponents of the ~u
i
. In order to find a suitable T we
thus have to adjust a set β = (β
1
,.. ., β
20
) of 20 fit-
ting parameters. Equation (6) also takes the form (7),
with a remark that ~u
i
= (u
x,i
,u
y,i
). This matrix equa-
tion, that is linear in β, can be solved easily, providing
the desired transformation T (Whitaker, 2009). Note
that the transformation T , that represents the distor-
tion applied to an image when displayed on the me-
dia facade, is invertible. That is, if the media facade
displays the inversly distorted image T
−1
(QR) of an
Figure 3: The curved media facade showing a QR Code that
has been preprocessed using image warping.
original QR code QR, the viewers – and any QR code
scanner – will perceive T (T
−1
(QR)) = QR, i.e., the
original undistorted QR code, as desired. Figure 4 (c)
shows what the preprocessed image looks like, while
Figure 3 displays the visual experience from the sweet
spot.
3.3 Implementation
To allow for a comprehensive and fast evaluation of
the two approaches presented in Sections 3.1 and 3.2,
we designed a web front end to generate the individ-
ual QR codes. This web front end allows users to
enter any string, e.g., texts or numbers, that the pre-
processed QR code shall contain. Furthermore, the
desired preprocessing method, foreground and back-
ground color, as well as the error correction level can
be selected. As soon as the user changes any param-
eter, e.g., the text, the preprocessing is triggered. The
result is directly shown in the web front end and can
be saved to a local file as well. Since this work is sup-
posed to illustrate the general feasibility of showing
QR codes on curved media facades, the implementa-
tion is done in a simple, not necessarily most efficient
way: The raytracing approach is implemented in PHP,
as this programming language integrates well with the
web front end. The image warping, however, is done
in Java, since there is a well-tested implementation
of polynomial image warping available in the “Warp-
Polynomial” class of the “javax.media.jai” package.
The only apparent difference between both ap-
proaches is the time it takes to preprocess an image.
Figure 4: QR codes samples. (a) Original; (b) Raytracing;
(c) Image Warping; (d) Simulated perception of an original
QR code on the Medienfassade that cannot be scanned.
QRCodesonCurvedMediaFacades-TwoApproachesforInverseDistortionbasedonRaytracingandImageWarping
427

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u
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3
x,1
u
2
x,1
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1
y,1
u
1
x,1
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0 0 0 0 0 0 0 0 0 0
1 u
x,2
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y,2
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x,2
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x,2
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2
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x,2
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0 0 0 0 0 0 0 0 0 0 1 u
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2
x,2
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u
2
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x,24
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u
2
y,24
u
3
x,24
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2
x,24
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1
y,24
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1
x,24
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2
y,24
u
3
y,24

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β
1
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β
10
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11
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β
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=
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v
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x,2
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(7)
The PHP raytracing takes up to 8 seconds on a recent
web server, while the image warping only takes 2 sec-
onds on the same machine. This difference, however,
is probably due to the varying performance of the em-
ployed programming languages and the naive imple-
mentation only. Once the images of the QR codes had
been preprocessed, the results were saved as bitmap
files. Finally, the video editors, who are in charge of
the media facade’s content, used these bitmap files to
include the preprocessed QR codes in the daily fea-
ture show.
4 EVALUATION
The Medienfassade is located in a spot of M
¨
unster
that is highly frequented by passersby, cars, and
trains. Thus, preliminary tests prior to public ex-
posure are highly advisable. To verify the prepro-
cessed QR codes in a first step, we used a 3D Blender
(www.blender.org) model that is based on the same
architectural data as presented in Section 3.1. Once
the simulation’s results seemed reasonable, the same
QR codes were tested in-situ. In total, there were
three test sessions: (i) a first test with the preprocessed
QR codes validated by the Blender simulation; (ii) a
subsequent test with refined QR codes based on the
findings of the first test; (iii) a final test with opti-
mized QR codes in the afternoon and at night. Dif-
ferent times of the day were chosen since the media
facade is exposed to varying lighting due to differ-
ent weather conditions. The different conditions may
have an impact on the contrast and saturation of the
shown content, compare Figures 1 and 2. An iPhone
4 and a Samsung Galaxy S3 were used to test whether
a QR code could be scanned from the sweet spot.
The third test session showed, that all prepro-
cessed QR codes could be scanned from the sweet
spot using either the raytracing or the image warp-
ing approach. The width of the sweet spot was about
3.00-4.00 m, while the QR codes had a physical size
of approximately 7.50 m on the media facade, cf. Fig-
ures 2 and 3. Within the perimeter of the sweet spot,
QR codes could be scanned reliably, while most tries
failed outside. To verify that the QR codes could
be scanned due to the actual preprocessing steps pre-
sented above, the system was counterchecked with an
ordinary QR code of the same size and content, cf.
Figure 4 (a). As expected, the distorted QR code, cf.
Figure 4 (d), could not be scanned from any position
with none of the testing devices.
The tests also showed that QR codes, which do
not use prime colors, i.e., red, green, and blue, for the
foreground as well as the background color, cannot be
scanned. In contrast to this large impact of the cho-
sen colors, the lighting conditions, i.e., day vs. night,
as well as defective LEDs did not have a noticeable
influence.
5 DISCUSSION
As the in-situ evaluation revealed, both presented pre-
processing approaches – the theoretical as well as the
empirical – are viable means to display QR codes on
curved media facades so that they can be scanned with
smart phones.
Both approaches, however, are limited to a pre-
defined sweet spot. Once the viewer leaves this
sweet spot, the visual distortions of the curved sur-
face are not completely compensated anymore so that
the QR code cannot be scanned. This shortcoming,
however, could be mitigated using the raytracing ap-
proach: Preprocessed QR codes could be generated
on the fly for any sweet spot, thanks to the detailed 3D
model, if the implementation’s performance could be
improved. Even then, however, the shown QR code
could still be scanned from only one sweet spot at a
time. To alleviate this, cameras could be used to lo-
cate the largest group of viewers, causing the system
to generate QR codes for that particular viewing posi-
tion.
Though the raytracing’s flexibility is advanta-
geous on the one side, the need for a 3D model ren-
ders this approach less general and more complex on
the other side. To remedy this, depth scanners etc.
GRAPP2014-InternationalConferenceonComputerGraphicsTheoryandApplications
428

could be used to derive sufficient models more easily.
However, defining the correspondences for the image
warping approach can be done easily using standard
image processing software and may thus be the more
feasible approach for real scenarios.
With regards to the relatively low resolution of
the media facade at hand, the mandatory “quiet zone”
takes up a significant amount of display real estate. In
turn, that display area becomes unavailable, though
it could be used more efficiently, e.g., to display a
larger QR code. This loss of display space could be
countered by reducing the error correction level to a
minimum. However, this is only a feasible step, if
the overall quality of the shown QR code is reason-
ably high, e.g., there are no defective pixels. Which
version of a QR code is available for specific media
facades in general depends on the facade’s resolution
and other characteristics, such as the physical size of
a pixel.
Though the specifications allow QR codes to be
printed in many color combinations (as long as the
contrast between the foreground and the background
is high enough), there appears to be a constraint when
displaying QR codes on an LED media facade. Ap-
parently, the media facade blends colors using pulse
width modulation (PWM) if the color is not a “true”
red, green, or blue. To display a 75% red, for exam-
ple, the media facade turns on the red LEDs for 75%
of a cycle and turns them off for 25% of the time.
These fast changes are not perceptible for the human
eye, but become visible in a picture taken by a camera.
These fluctuations apparently influence the scanning
process of QR codes heavily.
6 CONCLUSION
In this paper, we presented two approaches to pre-
process images of QR codes in such a way that the
codes can be scanned successfully on the surface of a
curved media facade. Though there are some limita-
tions to both approaches, they proved to work well in
the given application scenario.
The contribution of this paper is relevant since
QR codes become increasingly important in numer-
ous use cases, e.g., pedestrian indoor and outdoor
navigation, advertising, or mobile internet access –
many more lie undiscovered. At the same, the number
of media facades and other types of digital signage is
rising (Schaeffler, 2008).
To further elaborate this research area, we would
like to focus on the following aspects: The raytrac-
ing performance could be improved by porting the
approach to a more powerful programming language,
e.g., C or C++, and make use of dedicated hardware,
such as the GPU on recent graphics cards. Moreover,
it would be desirable to increase the perimeter of the
sweet spot or to avoid such a designated viewing loca-
tion in the first place. We would also like to further in-
vestigate the maximal and minimal sizes of QR codes
with regards to the media facade’s resolution and the
users’ viewing position.
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