ELEKTROTEHNIŠKI VESTNIK 89(3): 81–93, 2022
ORIGINAL SCIENTIFIC PAPER
An augmented reality application for depicting space
using the principles of linear perspective
Katarina Bebar
1
, Bea Tomšiˇ c Amon
1
, Franc Solina
2
1
Faculty of Education, University of Ljubljana, Department of Visual Art Education, Kardeljeva plošˇ cad 16,
1000 Ljubljana, Slovenia
2
Faculty of Computer and Information Science, University of Ljubljana, Veˇ cna pot 113, 1000 Ljubljana,
Slovenia
E-mail: katarina.bebar@gmail.com, bea.tomsic@pef.uni-lj.si, franc.solina@fri.uni-lj.si
Abstract. The linear perspective drawing system is taught in schools with the operational aim of developing
a sense of how to construct the illusion of space, and with the overall aim of developing observation, spatial
imagery and visualisation skills. Despite such aims, it has become clear through teaching practice in the
first years of faculties that students have considerable difficulties when it comes to the visual representation
of the space that surrounds them. Because mobile applications are a contemporary, effective and, above all,
accessible teaching tools for all, we have designed and tested the effectiveness of an innovative didactic tool,
a purpose-developed mobile application for the Android system, based on augmented reality, which acts as an
interface and, through digitisation, draws attention to the nature and the regularities that arise during the transfer
from the real space to the visual space, or to the differences between the experience and the understanding of
the world through interfaces and without them. Since the results of our research have shown that Augmented
reality-based mobile application in linear perspective drawing classes can help solve problems with spatial
image representations and raise awareness of linear perspective concepts, in this paper we present the design
and conditions for its operation.
Keywords: augmented reality, mobile learning, spatial perception, art education, linear perspective, new media
didactics
Prikaz prostora na osnovi linearne perspektive s pomoˇ cjo
obogatene resniˇ cnosti
Sistem risanja linearne perspektive v šolah uˇ cimo z opera-
tivnim ciljem razvijanja obˇ cutka za gradnjo iluzije prostora ter
s splošnim ciljem razvoja sposobnosti opazovanja, prostorske
predstavljivosti in vizualizacije. Kljub tovrstnim ciljem pa se
je skozi pedagoško prakso v prvih letnikih fakultet izkazalo,
da imajo, kadar gre za likovno reprezentacijo prostora, ki jih
obkroža, študenti precejšnje težave. Ker so mobilne aplikacije
sodobno, uˇ cinkovito in predvsem vsem dostopno uˇ cno orodje,
smo zasnovali in preizkusili uˇ cinkovitost inovativnega didak-
tiˇ cnega orodja, namensko razvite mobilne aplikacije za sistem
Android, ki temelji na obogateni resniˇ cnosti in deluje kot
vmesnik ter z digitalizacijo opozarja na naravo in zakonitosti,
ki se pojavljajo pri prehodu iz realnega v vizualni prostor,
oziroma na razlike med izkušnjo in razumevanjem sveta prek
vmesnikov in svetom brez njih. Ker so rezultati naše raziskave
pokazali, da lahko mobilna aplikacija, ki temelji na obogateni
resniˇ cnosti, pri pouku risanja linearne perspektive pomaga pri
reševanju težav s prostorskimi predstavami slik in ozavešˇ canju
o konceptih linearne perspektive, v tem prispevku predstavl-
jamo zasnovo in pogoje za njeno delovanje.
Received 26 April 2022
Accepted 17 May 2022
1 INTRODUCTION
In 1974 Arnheim [1] wrote a statement that transcends
the period from which it comes in both directions,
namely, that the pursuit of surpassing or enhancing
works of art through the application of newer materials
and techniques is entirely consistent with the practice of
contemporary artists and teachers. According to Hock-
ney [2], this very impulse or yearning to push the
boundaries of what is possible in the field of representing
space led to the discovery of a range of optical devices
that were further developed into new media tools and
devices in creation and teaching that are still in use today
and opened up a whole new world to artists and teach-
ers. In line with the European digital and pedagogical
orientation and development, today students are increas-
ingly presented with teaching content using pedagogical
approaches that are very different from the traditional
ones, thus allowing students to have learning experiences
using the new technologies and their content, which
Radu says are more accessible than ever before [3].
Creating high quality didactic tools and environments
that motivate learning about and understanding things
that are not directly accessible to the senses has become

82 BEBAR, TOMŠI
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C AMON, SOLINA
one of the greatest challenges in educational science [4].
1.1 The invention and development of linear per-
spective
The actual invention of a system for drawing linear
perspective was apparently first described in Baghdad in
the 11th century by the mathematician Ibn al Haitham
ali Alhazen, as is known to the Western world. The basis
for the system of drawing according to the principles of
linear perspective apparently came from his studies of
optics [5]. The same historical aspect or origin of linear
perspective is also described by Edgerton [6], who, like
Hockney [2], emphasizes that linear perspective was not
invented in the Renaissance, but rather rediscovered,
when it was attributed to the ancient Greeks rather than
to Arabic science. Belting [5] notes that ancient Greece
knew the concept of perspective but did not have the
scientific apparatus to develop such a system. Ptolemy in
the 2nd century AD already knew perspective but called
it “scenografia.” The geometric method for drawing
linear perspective was also described by Vitruvius as
early as in the 1st century BC.
Throughout history, visual artists have invented many
analog optical devices, such as lenses, concave mirrors,
the camera lucida, and the camera obscura, in an effort
to better understand human perception of space and
in an effort to bring it as close as possible to its
real image in their pictorial representations of space.
Hockney [2] claims that many Western painters, such as
Dürer, Cagnacci, Hals, Rembrandt, Velázquez, Holbein,
etc., had used such optical devices since the early 15th
century. In these theses that Hockney developed with C.
M. Falco, he proposed that the progress in the realistic
representation of the world in Western art since the
Renaissance was mainly due to optical instruments, the
use of which was to give painters a new insight into the
way to view and represent real space according to the
newly discovered principles of linear perspective. In the
21st century, linear perspective is no longer exclusively
the domain of art and mathematics, but a concept that we
use in various conceptual transformations and operate
with in a broader framework; in the fields of visual
arts, computer games, theatre and film scenography, art
history, sociology, etc. [7, 8, 9].
1.2 Use of linear perspective in art education
The Slovenian Curriculum for Art Education [10]
states that “The fundamental task of art education is the
development of a student’s artistic ability or competence,
which results from an understanding of visual (natural,
personal, social, and cultural) space and is expressed
in the active transformation of that space into an art
space”. Gardner [11] understands the artistic ability or
competence as the ability to imagine space and defines
it (along with the ability to perceive the visual world
correctly, to make transformations or modifications of
original perceptions, and to recreate aspects of one’s
visual experiences) as an integral part of spatial intelli-
gence. Gardner [11] adds that “we activate spatial skills
when recognizing objects and scenes and when work-
ing with graphic representations of two-dimensional
or three-dimensional versions of real-world scenes or
other symbols, such as maps, diagrams, or geometric
figures”. In order to effectively perceive and understand
space and the objects within it, we need to develop
spatial skills from an early age, which are, among other
things, “closely related” to representations of three-
dimensional space on a two-dimensional surface [12].
Therefore, Tomšiˇ c
ˇ
Cerkez and Zupanˇ ciˇ c [13] refer to
the development of spatial skills or spatial perception as
“one of the most important goals of arts education”.
This is because, roughly speaking, we understand
learning as a process of acquiring skills and under-
standing, and the consequence of this process is the
ability to perform and/or understand something that we
could not perform or understand before [4]. Therefore,
for the best possible representation of space according
to the principles of linear perspective or of objects
on a two-dimensional surface, it is not enough for
children to be well acquainted with the real features of
space; they must also be able to skilfully coordinate the
different shapes with the features of visual perception
that enable us to see two-dimensional, drawn objects as
three-dimensional ones. The construction of appropri-
ate spatial representations or perspective drawings can
be performed by children only on the condition that
they are well acquainted with the theoretical starting
points and receive high-quality didactic approaches in
the classroom [14]. However, individual differences in
children’s development should also be taken into ac-
count, as they are reflected in “maturation and learning
processes, development of psychomotor skills, cognition
and acquisition of knowledge about the environment, as
well as in their development of skills and the need to
demonstrate knowledge” [15]. This development can be
divided into several phases or periods (e.g.: doodling,
symbolic function, etc.), although it should be empha-
sized that the time of onset and duration of each phase
may vary. The tendency to represent space in a linear
perspective peaks in children around the age of fourteen
[12], because only then are they able to understand and
apply the mathematical knowledge required to correctly
represent space according to the principles of drawing a
linear perspective [16, 11].
1.3 Virtual and augmented reality in education
“The use of diverse and high quality teaching aids
and tools is certainly one of the most important didactic
decisions today in the teacher’s planning of art lessons.
We consider teaching tools to be of a high quality if
they are age appropriate, understandable, clear, have
a suitable format to be shown to all students in the

AUGMENTED REALITY APPLICATION FOR DEPICTING SPACE USING THE PRINCIPLES OF LINEAR PERSPECTIVE 83
class, and are also suitable for display with tools” [17].
In recent years, there has been a strong interest in
the use of new technologies [18, 19] that can bring
virtual information into the learning process or the
real, physical environment of students via smartphones,
webcams, and glasses, allowing them to interact with
a virtual content [3]. In contrast to the early 1990s,
when we could only experience virtuality via a bulky
laptop-connected screen, the latter is now available to
all smartphone owners, whose hardware and software
allow digitally transmitted content to be combined with
virtual information in real time and almost anywhere
within the confines of real space [20, 21]. Education in
which we use portable new media such as cell phones,
tablets, and laptops to teach or disseminate new material
is now referred to as mobile education [22].
Because this is a relatively new phenomenon, the
theoretical basis of mobile education is still in its infancy
[23]. When we talk about virtuality in the classroom, we
are usually talking about learning materials, information,
or experiences that we provide to students through vir-
tual or augmented reality. The main difference between
the two is that virtual reality completely replaces real
space, while augmented reality merely complements it
[24], thus enhancing the user’s sensory and cognitive
reality [25]. Experiences in a virtual environment are
simulated. For this reason, they can be similar to the
real environment or completely different from it [26].
In augmented reality, the concept of experience is dif-
ferent, namely experiences that are directly related to
the real environment and the events that take place in
it. Thus, virtual reality for educational purposes can be
used in cases where we want students to experience
situations that are dangerous or impossible to experience
in the real environment (e.g., presentations and scientific
studies of various cultural and historical objects and/or
events). Augmented reality in the educational process
can be used especially when we use virtual elements
to illustrate phenomena and other things that we would
otherwise not be able to perceive with our senses at a
given moment in the real world. Their use also offers,
among other things, the possibility of manipulating
virtual objects based on the real world. Using interaction
techniques supported by augmented reality technology,
users can change the position, shape, and/or graphical
properties of virtual objects, move around them, and
view them from different angles. Augmented reality,
which has the ability to implement virtual elements
seemingly in the real world, can thus be a medium that
improves the efficiency and attractiveness of learning
and teaching through a unique experience of combin-
ing or simultaneously experiencing the real and virtual
worlds.
Augmented reality allows teachers to convey infor-
mation and students to interact between the real and
virtual worlds in ways they have never known before
[27]. Recent research in the field of using augmented
reality in the teaching process also shows that the latter
successfully addresses different learning styles and in-
creases the motivation of students involved in the class-
room. For example, research by Saltan and Arslan [28]
has shown that augmented reality learning can address
multiple learning styles simultaneously (visual, auditory,
and kinaesthetic), unlike many traditional teaching tools.
The results of Radu’s analysis [3], which included a
study of twenty-six publications comparing the learning
effectiveness of students with and without augmented
reality-based applications, show that the use of aug-
mented reality improves the effectiveness of learning
spatial concepts, comprehension of learning material,
collaboration with peers, and increases motivation. Radu
makes a list of positive and negative effects of aug-
mented reality on students, identifies important aspects
of individual didactic tools or teaching aids when used
in the classroom, and defines their impact on learning
in three stages.
Our hypothesis is that using computer vision tech-
niques to depict the perspective lines and the vanishing
point overlayed on a live video image, captured by a
mobile phone, sensitises the users to correctly interpret
the structure of the observed 3D environment. In this
way they could correctly draw the environment using
the tools of linear perspective. This hypothesis is tested
by comparing two groups of students with the same
task—to draw their observed environment using linear
perspective. It is shown that the students who had the
experience of using the new application perform their
task better and faster.
2 MATERIALS AND METHODS
Children learn about linear perspective in the nineth
grade of primary school, since it is only at this age
that they reach the appropriate artistic maturity or level
of artistic expression that enables them to understand
the schematisation and systematic nature of representing
space according to the principles of linear perspective.
The fact that space is represented on a two-dimensional
surface according to the principles of linear perspective
can be recognised by the fact that the size, shape and
position of objects are determined by a network of
imaginary lines that converge in a single point on the
horizon. This point is called the vanishing point and
the skyline is usually called the horizon which separates
the ground and the sky in the drawing. The horizon is
always at the height of the viewer’s eyes and determines
the height from which we want to show the scene we
are drawing [29].

84 BEBAR, TOMŠI
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C AMON, SOLINA
To correctly depict linear perspective, the following
conditions must be met:
• the eye is at rest,
• the image plane is perpendicular to the ground
plane,
• the distance between the eye and the image plane
and the distance between the eye and the observed
object are constant.
Compliance with the above conditions assures a correct
representation of space on a two-dimensional surface
with a well-defined geometric beginning [30], which
gives the impression of depth or three-dimensionality.
Drawing linear perspective can also be an excellent
tool to determine the level of development of spatial
representation. This is because pedagogical practice in
early college years has shown that students have prob-
lems with visual representation of space, resulting in
unconvincing art products whose spatial representations
do not seem likely—when drawing linear perspective,
they tilt and twist space, often place the horizon too high,
in an unnatural position, they bend lines that should be
straight, etc. To solve the problem of understanding and
representing the space according to the principles of lin-
ear perspective, we have developed a mobile application
for the Android system based on augmented reality. It
draws attention to the differences between experiencing
the world through interfaces and without them, and
enables an easier transition from real (through digital)
to art space. We integrated new media technology, i.e., a
cell phone with an augmented reality-based application,
into the educational process with the specific goal that
users, while observing their visual environment through
the application of perspective infrastructure, to become
aware of their own observation to the extent that their
drawing representations improve in terms of correctly
constructed drawings of the space according to the
principles of linear perspective. The objective goal is to
stimulate the students to raise questions such as why
they see as they see, how they construct an image
according to the requirements of optical realism, and
what lies behind the images.
Our research group has extensive experience in devel-
oping educational applications and applications involv-
ing image processing using computer vision methods
such as a novel user interface for video observation over
the Internet [31], dynamic anamorphosis as a special
computer-generated user interface adapting itself to the
position of the user in the space [32], we studied the
problem of missing eye contact in videoconferencing
and proposing a simple method for improving the eye
contact [33], developed educational applications for
teaching spacial design [34] and worked on user inter-
face design for people with severe learning difficulties
[35]. Therefore, we approached the research problem
described in the hypothesis with confidence that we can
Figure 1. Matrix test, taken from lectures by
ˇ
Crtomir Frelih
(Source: personal archive of Katarina Bebar)
solve it.
2.1 Mobile application for detection of linear per-
spective
The idea for the application comes from and is based
on lectures and research by
ˇ
Crtomir Frelih (Figure 1).
Repeating his experiments with a matrix similar to those
used by teachers when a transparency is placed over
a two-dimensional photograph of real space on which
projection rays are drawn—the transparency is moved
until the rays intersect with the visible edges of the
architecture—shows that already a simple perspective
grid thrown over a photograph helps in understanding
vision mechanisms in the way that the Renaissance re-
discovered with the construction rules of linear perspec-
tive. Using such tools certainly sensitises students to the
question of creating an image according to the rules of
linear perspective allowing for an artistic reconstruction
of visual space.
To use the application in our research, the analog
design of the above learning device is upgraded and
transformed into a new media didactic tool as an ap-
plication for Android mobile phones. Using the data
of the new media enables easy accessibility, mass use,
portability and, last but not least, the possibility to have
its content customized. The mobile application finds and
records elements of linear perspective (vanishing point,
orthogonal lines and horizon) in the space perceived by
the phone camera and displayed in real time on the
phone screen, and keeping them on the screen even when
moving and changing the angle of the camera view, as
shown in examples in Figures 2 and 3. See also the video
demonstration of our application [36].
Applications similar to ours found on the World Wide
Web are primarily aimed at architects and, at first glance,
give an impression that similar applications already
exist on the market (Morpholio trace [37] and Procreate
[38]), but they differ from ours in their principle of

AUGMENTED REALITY APPLICATION FOR DEPICTING SPACE USING THE PRINCIPLES OF LINEAR PERSPECTIVE 85
Figure 2. Demonstration of how our mobile app works by moving the mobile phone from the center position to the right side.
The perspective lines, the vanishing point and the horizon move accordingly. Photo: Katarina Bebar
Figure 3. Demonstration of how our mobile app works by moving the mobile phone from the center position towards the ceiling.
The perspective lines, the vanishing point and the horizon move accordingly. Photo: Katarina Bebar

86 BEBAR, TOMŠI
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operation and interaction with the user. Most appli-
cations that work with perspective grids (matrices) to
visualise perspective elements and/or simplify rendering
according to these rules work on the basis of static
images. This means that the applications record the
perspective elements on a photograph, so they cannot
effectively illustrate the real-time changes that occur
when the camera is moved. Another difference worth
mentioning is that these applications require the user to
determine the vanishing point themselves and align the
lines of the drawn perspective lines with the edges of
the image. This means that users of these applications
must be well acquainted with the laws of drawing linear
perspective.
Our application is developed in the Computer Vision
Laboratory at the Faculty of Computer and Information
Science, University of Ljubljana [39]. It uses computer
vision methods to detect straight edges in the captured
images and combines them into perspective lines to
illustrate the horizon and the vanishing point in real
time, thus sensitising the user to the perception of three-
dimensional space and the role of perspective lines in its
two-dimensional representation [36].
Our main task is to perceive the space in different
conditions and raise awareness of its composition by
automatically detecting edges in an image of the space
captured in real time and recording a matrix over it
with all the key elements of linear perspective. This
means that the user can track changes in proportions
and relationships that occur when the angle between the
image plane and the distance, the distance between the
eye and the image plane, or more specifically, when the
conditions for drawing a linear perspective are changed.
Unlike other applications, our application autonomously
detects/determines and illustrates the vanishing point and
aligns the lines of computer-generated perspective lines
with the edges in the image that follow the movement of
the user or camera in space [36]. The user, thus enabled,
needs no prior knowledge of linear perspective principles
to use it.
2.2 Description of our mobile didactic application
We have developed a mobile phone application that
searches for perspective lines in captured images in real
time, thus further sensitising the user to the perception
of three-dimensional space and the role of perspective
lines in its two-dimensional representation.
The application supports the following functionalities:
• detection of linear perspective elements in an image
captured by a mobile phone camera, depicting
perspective lines, clear lines and horizon;
• extraction of linear perspective elements or per-
spective grids in the captured image;
• changing the proportions and relationships between
the elements of the linear perspective continuously
and dynamically as the device is moved.
The application needs:
• the mobile device to run an Android mobile oper-
ating system and a suitable lighting of the scene or
interior space captured by the camera on the mobile
device.
The application uses the following technologies and
tools:
1) OpenCV software library
• Android version 3.4.2;
• and the following classes in the software
library:
• Mat – a class for working with multidi-
mensional matrices to store the pixels of a
captured image and used as input to various
image processing methods;
• Size – a class to define the size to resize the
source image;
• Point – a class for working with points to store
information about the found point and used to
define distances and quadrants;
• Rect – class for defining and working with
rectangles;
• Vec and Scalar – classes to store vector data,
used for storing data about distances and
colours;
• LineSegmentDetector – a class containing
methods for finding line segments;
and the following functions:
• resize – to resize the image,
• cvtColor – converting the image from one
colour space to another,
• pointPolygonTest – checking that the selected
point is inside the selected polygon,
• line – drawing a line in the image.
For the display on the computer we also used
the CommandLineParser class. It makes it easier
to pass arguments when running the program,
VideoParser and VideoWriter classes which allows
capturing and displaying individual images from
the video. The imshow function is used to display
the processed images.
2) Android mobile operating system
• The Android NDK is used to code part of the
application in native code using programming
languages such as C and C++. The main
part of the application is written in the C++
programming language, as this allowed us
to make it portable, i.e. the application is
run both on a computer and on a mobile
device. The C++ programming language also
implements the OpenCV library.
• The view, user interface and image capture
from the camera are programmed in the Java
programming language enabling calling native
methods when using the Android NDK.

AUGMENTED REALITY APPLICATION FOR DEPICTING SPACE USING THE PRINCIPLES OF LINEAR PERSPECTIVE 87
3) Tools
• Integrated development environments An-
droid Studio are used (to support the devel-
opment of applications, user interfaces, de-
bugging on the device of choice and code
translation) and CLion to support the writing
of C++ code, debugging (using GDB) and
code translation (using CMake and GCC).
2.2.1 Operation of our application
The operation of the application is divided into the
following phases or steps, which consist first of image
processing and mathematical operations to find elements
of the linear perspective and place them in a real-virtual
space.
Figure 4. Captured image of a corridor
Phase I: Camera captures the image of a corridor
(Figure 4).
Figure 5. Conversion of the colour image to greyscale
Phase II: Image preparation for further processing
The image is scaled down to a width of 640 pixels
and a height of 360 pixels (reduction of the original
image size along the x and y axes) to avoid stepped
edges. The colour image is then converted to greyscale.
These are the requirements for the optimal performance
of the Line Segment Detector (LSD) algorithm in the
next phase (Figure 5).
Phase III: LSD (Line Segment Detector) processing
A main tool of computer vision methods is the edge
detection method. It detects distinct changes between
pixels in an image that correlate with changes in the
real space:
• discontinuities in the depth,
• discontinuities in the surface orientation,
• change in the material properties, and
• change in the illumination level, etc.
Ideally, the result of using an edge detector on a
captured image is a set of interconnected curves that
characterize all of the above changes or situations. Using
an edge detection algorithm in an image significantly
reduces the amount of data to be processed, thereby
filtering out information that is considered less relevant,
while still preserving the important structural features of
the image. The edges extracted in this way are separated
into two groups: angle-dependent edges and non-angle-
dependent edges. The independent edges usually reflect
properties inherent to three-dimensional objects (such as
texture and surface shape), while the angle-dependent
edges, which can move or change with changes in the
angle of view, usually reflect the geometry of the scene.
One of the many algorithms for detecting or finding
edges is the LSD algorithm. It is used in the development
of our application, mainly because of its fast computa-
tion capability (which means a good performance of the
application or fast responsiveness to changes in the real
space image in real time). The LSD algorithm is a set of
different mathematical methods whose common goal is
to identify points in a digital image where the brightness
of the image changes significantly, or points where
there is a brightness discontinuity [40]. These points are
usually organised in a set of curved line segments called
edges. To understand how the LSD algorithm works, the
concepts of the contour, gradient and edge are important.
The gradient represents the change when the grey level
of an image changes from dark to light or vice versa.
When gradient changes are fast, so are the transitions
between grey levels in the image—especially when they
occur over a short distance, these changes are observed
as contours or edges in an image (Figure 6).
Figure 6 shows the brightness discontinuity or edge
segment in the image (left) and a zoom of the edge
segment showing the gradient or transition between dark
and light grey (right). The LSD algorithm computes
gradients and thus edges using matrices or masks that
assign each pixel one of the 256 greyscale values,
where a value of 0 represents black and a value of
255 represents white. Sudden changes in the intensity
of the greys in a certain area of the image, together
with changes in the intensity of the pixels, i.e. the pixels
to which the algorithm assigns the highest values, imply
line segments or edges. The result of the LSD algorithm
is a set of disconnected lines in the form of a curve,

88 BEBAR, TOMŠI
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Figure 6. Changes of the grey level at an edge in an image
indicating a potential edge in the captured image.
Phase IV: Filtering the edge lines
In the first part of this phase, the algorithm first
arranges the found edges (Figure 7) into quadrants
centered on the calculated centers (if these are not yet
calculated, the image centers are used, as we expect the
user to initially point the phone towards the center), and
then arranges them according to the quadrants and their
slopes. This is done by looking at all the edges returned
by the LSD algorithm and filtering them by quadrant. In
the odd quadrants, it selects and keeps the edges with
a slope between 0.2 and 1.2 radians (11.4
◦ and 68.7
◦ ),
and in the even quadrants it selects and keeps the edges
with a slope between -0.2 and -1.2 radians (-11.4
◦ and -
68.7
◦ ). Edges not in accordance with the specified slope
are discarded. This gives a refined set of edges which
contribute to the estimate of the position of the vanishing
point (Figure 8).
Figure 7. Original edge segments
Combining shorter edge segments into longer seg-
ments
Incomplete image data and/or incomplete edge detec-
tion algorithm results can lead to two types of deficien-
cies: either a break in the curves (curves can be a set
of unconnected points after applying the edge detection
algorithms or spatial deviations from the ideal line,
circle or ellipse. Our method detects and corrects such
deficiencies. It works by combining the disconnected
Figure 8. Filtered edge segments
line segments of the detected edges in the transformed
space with algorithms to form the so-called object can-
didates or longer distances, which are important for the
determination of the vanishing point.
In our application, the algorithm does this in the
following steps:
1) It arranges the edge segments according to their
size from the longest to the shortest.
2) Around each selected edge segment, it makes a
polygon that is extended to the center of the image
in one direction and to the edge of the image in
the other.
3) The shorter edges contained in the polygon are
used to increase the length of the longer edges.
Figure 9. Two short edge segments (within the white polygon),
will be joined into a single edge segment.
Phase V: Estimation of the vanishing point using the
RANSAC algorithm
Lines or edges perceived as parallel in real space
are usually seen as converging in two-dimensional pho-
tographs. If these edges are extended, they intersect at
least at one point in the plane. This point is called
the intersection point in mathematical terminology and
the point of view or vanishing point in art theoretical
language.
In order to be able to determine the position of the
centroid in real time on a dynamic image of a real space,
the application first had to detect the edges in the image.

AUGMENTED REALITY APPLICATION FOR DEPICTING SPACE USING THE PRINCIPLES OF LINEAR PERSPECTIVE 89
Figure 10. Two short edge segments are joined into a single
edge segment.
This is done by the edge detector. The colour image
is converted into a greyscale image, from which the
algorithm calculates the position of the edges based on
the pixel greyscale intensity. The result of the processing
at this point is a set of shorter distances which are filtered
and merged into several longer distances.
The application estimates the position of the vanishing
point in the following six steps:
1) A two-dimensional graph in a transformed space
is created where, for each edge segment, a point
is entered in the graph with the slope on one axis
and the offset of the line on which the selected
edge segment lies on the other axis.
2) Given the length of the selected line, the points in
the transformed space are further weighted. This
means that longer distances have more power in
determining the distance from which the origin
is obtained—in our case, this looks like entering
the selected distance several times in the graph,
depending on its length.
3) The RANSAC algorithm is then used to fit the
lines to the points in the transformed space.
RANSAC (Random Sample Consensus) is an
algorithm whose primary function is to find a
mathematical model in a set of collected data [41].
The algorithm works by selecting the smallest
possible number of random samples from all the
data, analysing them and defining a mathematical
model that represents the entire data set. Finally, it
checks its goodness of fit or how well the mathe-
matical model describes the given data set. It does
this by calculating for each sample an estimate
of the deviation from the resulting mathematical
model. As the algorithm is based on chance, it
does not guarantee the discovery of the correct
result, so it is necessary to define the maximum
number of trials within its scope. This ensures
that if the algorithm is unable to define a suitable
mathematical model from the selected samples,
image processing is abandoned.
Figure 11. Example of how RANSAC performs. The task is
to find the line which is best supported by data points.
4) The resulting lines lying on the collinear points
are then mapped back to the points in the original
image space.
5) The resulting points represent an estimate of the
current vanishing point (for the current image).
6) To avoid jerky movements, the average of the
positions of the centers from ten previous images
are averaged for the current vanishing point.
Phase VI: Determination and plotting the perspective
lines
To determine the perspective lines, all the lines ob-
tained in Phase IV shall be filtered as perspective lines
if they intersect in the vanishing point or are less
than 15 pixels from the vanishing point. Finally, the
elements obtained in this way (the vanishing point and
the perspective lines) are scaled back to the size of the
original captured image and drawn over it (Figure 12).
Figure 12. Perspective lines and the vanishing point in the
captured image
3 PRACTICAL EVALUATION OF OUR
MOBILE APPLICATION
The sample of the study, which was conducted as a quan-
titative study and also included a qualitative analysis of
the results consisted of 150 students of art education
and architecture. Due to the nature of the study, the
sample was conditioned by courses or subjects that cover

90 BEBAR, TOMŠI
ˇ
C AMON, SOLINA
the basics of perspective drawing of spaces and are
basically conducted in the first years of study at the
two faculties. The study was a single-factor, non-random
pedagogical experiment with two comparison groups
(experimental and control) and modalities. Both groups
initially benefited from the traditional implementation
of the teaching and learning process using traditional
didactic tools and resources such as photographs and
other images. Then the experimental group started to use
the mobile app as a tool to solve an art task (Figure 14),
while the control group solved the art task without the
mobile app (Figure 13). As part of the evaluation, they
made a drawing that focused on spatial keys, taking into
account the conditions for drawing a linear perspective
with a 90-degree slope of the project plane. The students
were asked to draw within the parameters of a real
closed space or corridor, the artistic expression took
three school hours. The students in the experimental
group (EG) received a link to the application by email
on the day of the evaluation. At the beginning they
downloaded the application on their phone and began
using it according to the instructions.
The students were asked to observe changes in various
proportions and relationships occuring when the angle
between the image plane and the distance and/or the
distance between the eye and the image plane changes.
In this way, they took different positions, i.e. spatial
views, and observed changes in the construction of the
perspective drawing in real time on the screen. They
were not allowed to use the application while drawing as
they might take a screenshot in a certain spatial view and
perform the drawing or the art task by simply copying it.
Based on the pedagogical evaluation, differences were
determined in the quality of artistic representation of
the real space according to the principles of drawing a
linear perspective between the experimental (EG) and
the control group (CG); we were interested to know
• whether the students perceived and became aware
of the problems that arose when transferring from
the real space to the art space more quickly and
consequently solved them more efficiently than
without the application;
• how the mobile application affects the perception
and understanding of the differences between real
and artistic space;
• and how it affects the learning process, students’
motivation and the implementation of art tasks.
The results of the evaluation show that the EG students
solved the art tasks significantly better and faster than
the CG students, as shown in Figs. 13 and 14.
The first drawing (Figure 13) is made by a CG
student who was not familiar with the application. In
his drawing there are irregularities such as: a tilted
and inverted space, multiple vanishing points and hori-
zons, deformation of lines (orthogonal lines ) and their
curvature, similar to the fisheye effect of the camera,
which is what we call the effect of a circular lens that
creates a distorted, curved image of the object due to
the wide angle. The aesthetics of the student’s drawing
also indicates that the drawing was made quickly, the
use of spatial keys is present (reducing the size of
differentiation of details) but indistinct (e.g. low intensity
of lines and shading). The result is a work of art that is
not convincing enough.
Figure 14 presents a drawing made by an EG student
who was familiar with our application. In his draw-
ing there is only one horizon with a properly defined
vanishing point and proper framing. The perspective
drawing looks more complete and is also better laid
out in terms of composition. The spatial keys are used
more intensively, e.g. through a correct differentiation
of details and light intensity. The drawing is more
expressive, the lines are well drawn and express the
student’s personal style.
The use of the application significantly affects the
differences in the student’s motivation to complete the
art task. A comparison of the results of the CG and EG
students shows that 92.2 % of the EG students were
motivated to solve the art task, compared to 58.5 % of
the CG students. The use of the presented augmented
reality-based mobile application proves to be an effective
tool to draw the space according to the principles of
linear perspective and it raises awareness of the back-
ground and methods of constructing spatial drawings,
and it qualifies itself as a tool that helps teachers and
students to achieve their goal, provided that teachers are
well prepared for their task.
Like any other didactic tool that we use in the class-
room, the application has positive and negative features.
Among the most positive are the high motivational effect
and its simple use, since the mobile phone is a device
with which almost every teacher and student is familiar.
Other important features of the application are also its
capacity for simultaneous drawing of the orthogonal
lines, viewpoint and horizon in real time on the image
of real space.

AUGMENTED REALITY APPLICATION FOR DEPICTING SPACE USING THE PRINCIPLES OF LINEAR PERSPECTIVE 91
Figure 13. Drawing by a CG student with hand-drawn perspective lines. The perspective lines do not intersect in a single
vanishing point and the horizon is not defined uniquely.
Figure 14. Drawing by an EG student. The perspective lines intersect as expected in a single vanishing point.

92 BEBAR, TOMŠI
ˇ
C AMON, SOLINA
4 CONCLUSIONS
When using our application for depicting the space
according to the priciples of linear perspective good
lighting and a suitable space are very important. To
use the application the concepts or contents should be
known on presentation and visualisation of the spatial
keys to create an illusion of depth such as differentiation
of details, light intensity and textures. The application is
meant to be only used as a supplement to other teaching
and learning activities. Attention should be paid to a
proper teaching and learning process and the interaction
between teacher and student. It is important when and
in what way the application is included in the teaching
process. Using our application can provide a good basis
for developing short debates and simultaneously raise
questions on the topic, all of which takes time to con-
sider or participate in preparing particular lessons. The
focus of our further research will be on drawing complex
spatial formations using the principles of drawing with
linear perspective.
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Katarina Bebar received her Professor Diploma in Art Education in
2009 and her Ph.D. degree in 2021 from the University of Ljubljana,
Slovenia, Faculty of Education, Department of Fine Art Education. Her
interests are focused in didactics, pedagogy, digitization, virtualization
and advanced technologies. Her fields of activity are the transfer
of new contents through new media into the creative, cultural and
economic sector. In 2011–2012 she worked as an Assistant of Art
Education at the University of Ljubljana. She then joined the economy
sector where she worked in the aerospace industry. From 2018–2019
she was a Researcher in the field of Education at the Faculty of
Computer and Information Science, University of Ljubljana, and at
the end of 2019 she joined the Cabinet of the Slovenian Minister of
Culture. Currently, she is with the Slovenian Association of Fine Arts
Societies.
Bea Tomšiˇ c Amon is an associate professor of Didactics of Art
Education at the Department of Art Education at the Faculty of
Education, University of Ljubljana. In 1987 she graduated as an
architect from the Faculty of Architecture and Urbanism in Buenos
Aires, Argentina. In 1993 she graduated from the Academy of Fine
Arts, University in Ljubljana, and then received her M.Sc. degree
in Sociology of Culture from the Faculty of Arts in Ljubljana and
her Ph.D. degree on Experiential Learning and Spatial Design from
the Faculty of Education, Ljubljana. Her areas of interest are visual
art education, pedagogy of architecture, spatial perception, theory of
architecture, geometry and art, and interdisciplinary education.
Franc Solina is a full professor of computer science at the University
of Ljubljana, Faculty of Computer and Information Science, Slovenia.
He received his Ph.D. degree in computer and information science
from the University of Pennsylvania in the USA. His research interests
include 3D modelling from images and the use of computer vision in
human–computer interaction, heritage science, and in art installations.
He is a Fellow member of IAPR, a Life Senior member of IEEE, a
member of ICOMOS, Slovenian Association of Fine Arts Societies,
Slovenian Academy of Engineering and a regular member of the
European Academy of Sciences and Arts in Salzburg.