=Paper=
{{Paper
|id=Vol-2590/paper30
|storemode=property
|title=Applying Numerical Optimization to Arrangement of Elements in Spatial Interface for Historical Moscow Center Virtual Reconstruction
|pdfUrl=https://ceur-ws.org/Vol-2590/paper30.pdf
|volume=Vol-2590
|authors=Leonid Borodkin,Stepan Lemak,Margarita Belousova,Anna Kruchinina,Maxim Mironenko,Victor Chertopolokhov,Sergey Chernov
|dblpUrl=https://dblp.org/rec/conf/micsecs/BorodkinLBKMCC19
}}
==Applying Numerical Optimization to Arrangement of Elements in Spatial Interface for Historical Moscow Center Virtual Reconstruction==
https://ceur-ws.org/Vol-2590/paper30.pdf
Applying Numerical Optimization to
Arrangement of Elements in Spatial Interface for
Historical Moscow Center Virtual
Reconstruction∗
Leonid Borodkin1[0000−0003−0422−1938] , borodkin@hist.msu.ru, Stepan
Lemak1[0000−0002−2242−6956] , lemaks2004@mail.ru, Margarita
Belousova1[0000−0003−3535−5752] , mb@vrmsu.ru, Anna
Kruchinina1[0000−0001−9720−8163] , a.kruch@moids.ru, Maxim
Mironenko1[0000−0003−4779−0989] , mm@vrmsu.ru, Viktor
Chertopolokhov1[0000−0001−5945−6000] , psvr@vrmsu.ru, and Sergey
Chernov2[0000−0003−0627−1146] , chernovsz@mail.ru
1
Lomonosov Moscow State University, Moscow, Russian Federation, info@vrmsu.ru
2
Institute for Archaeology, Russian Academy of Sciences, Moscow, Russian
Federation
Abstract. The article describes a novel approach to representing vir-
tual reconstruction of historical cities cultural heritage. As example, the
reconstruction of buildings of the historical city center in Moscow was
carried out using preserved plans, drawings of buildings, texts and other
information. We want to provide users with an opportunity to see the
historical territories restored in virtual reality. Everyone should be able
to study historical sources for every object, compare them with the result
of the virtual reconstruction, see the process of area transformation over
time. The usage of virtual reality spatial interface for displaying infor-
mation about historical objects is proposed. Interface elements should be
placed next to interactive objects (such as historical buildings and their
parts, landscape sectors, control buttons).
The task of optimizing the automated arrangement of interface elements
in the space of virtual reconstruction was considered. Restriction sets
for the layout of interface elements have been introduced. Restrictions
were obtained from physiological characteristics of human arms and ocu-
lomotor apparatus. The tasks of determining the restrictions, the prin-
ciples that reduce the probability of placing interface elements outside
the restrictions was considered. A hand planar movement hypothesis was
proved, it allows us to reduce the dimension of the studied system.
Keywords: Virtual reality · Historical reconstruction · Interface · Op-
timization · GIS · Restrictions · Eye tracking · Arm Movement.
Copyright c 2019 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0).
∗
Supported by Lomonosov Moscow State University and by the Russian Foundation
for Basic Research grant 18-00-01684 (K) (18-00-01590 and 18-00-01641)
2 L. Borodkin et al.
1 Introduction
The problem of documentation and verification of virtual historical reconstruc-
tions became relevant in the early 21st century [1].
For a long time, the problem of historical sources publishing that were used in
virtual reconstructions was not in the spotlight [2]. Source publication resembled
a simple database [3]. This format is good for publishing sources as a separate
study, and is almost unlimited in content. Thus a double result is obtained from
the project: reconstruction and sources are published as independent results.
Sometimes projects are not generally accompanied by sources.
In the last years more and more scientific projects published their reconstruc-
tion in the form of images and video source [4]. There are only a few exceptions
that not only describe sources, but also publish them [5]. Such projects tradi-
tionally use renderers such as Vray, Redshift, Arnold, Keyshot, Lumion. As the
result we have videos and rendered images or video without any interaction with
sources.
With the development of technology real-time reconstructions have appeared
as a lot of reconstructed objects published at Sketchfab platform [6]. Our pre-
vious projects included source uploading on a website [7]. The sources were
published on the special pages [8]. These sources work like additional part for
interactive reconstruction of Strastnoy monastery. Developing ways of represent-
ing historical sources, we decided to use virtual reality (VR). The experiment
was intended to be conducted at two monastery complexes, Strastnoy and Chu-
dov ones. All models were implemented in virtual environment. A part of this
solution is a verification module for historical reconstruction of cultural heritage
in VR [9]. It was the first step in real-time interface presentation in VR. For all
monasteries we developed a 2D sources verification module (Fig. 1).
Fig. 1. Example of the verification module.
Title Suppressed Due to Excessive Length 3
This allowed us to bring the presentation of historical sources to a new level. But
we also faced with some limitations. For example, each building reconstructed
according to different amounts of sources. In some cases there were 2–3 images,
in other more than 10.
During the reconstruction of the Chudov Monastery, an additional task was
the integration of sources into decorative elements and interiors, which changed
several times during the period of the monastery’s existence while maintaining
the basic forms of objects. This once again complicated the structure of source
presentation and made it difficult for a user to interact with an interface.
The next step in improving the interactive capabilities of the user to assess
the information potential of the sources used, to verify 3D models is to immerse
the user in a virtual environment. Integration of reconstruction sources into VR
requires new algorithms for creating a three-dimensional 3D interface. When de-
veloping such interfaces, it is necessary to take into account a large number of
parameters of human movement in virtual environment, which will be discussed
below. An additional condition for us was the historical landscape, the recon-
struction of which is one of the main objectives of our project. 3D models of
historical buildings are placed on the landscape, in compliance with the scale of
objects and features of the relief. This allows the user, moving in a reconstructed
historical urban space, to expand interaction with both 3D models and sources
used for building those models.
Fig. 2. Example of a landscape reconstruction of Moscow Belyi Gorod area.
Historical part of our actual research project is aimed at the virtual reconstruc-
tion of Moscow historical center (Belyi Gorod) landscape and historical buildings
located on its territory. To reconstruct the landscape of Belyi Gorod and domi-
nant historical buildings in 16th – 18th cc. we used archaeological and geological
measurements of the Belyi Gorod relief, preserved plans and drawings of his-
torical buildings, old photos, textual sources and other historical materials. The
results include both sources and reconstructed objects data.
4 L. Borodkin et al.
2 Numerical optimization of the interface element layout
2.1 The task of the interface layout numerical optimization
Each object of the virtual reconstruction is provided with reference information
and with interactive elements that allow to open the Menu, to change the object
state or to get access to a historical source. The task is to locate information
interface elements and interactive interface elements. Despite some differences
between information and interactive elements, this article suggests a general
approach to the search of the proper position for both types of elements.
To determine the location of interface elements on a computer screen, the
Fitts law [10] and its various extensions are often used. This law describes an
empirically determined relationship between the duration of motion to the target
in the plane, the distance to the target and its size. It works well for planar
interfaces, but virtual reality leads us to a three-dimensional problem.
A user interacts with a 3D interface using his eyes and his own body mo-
tion. The simplest way — user places his hand in a specific point in a virtual
space. Obviously, elements should be placed inside a limited area where it will be
convenient for a user to interact with them. They shouldn’t overlap with other
objects of the virtual scene and with each other. Here, we describe ideas how
to define a priority zone for the interface elements location, taking into account
existing restrictions.
Interface elements should be considered as closed sets, further they will be
represented by a center point. Let there be a dynamic system that describes the
movement of an eye or hand: ẋ = f (t, x, v), where v ∈ V is a perturbation vector.
Perturbations may be inaccuracies in determining parameters of the hand, the
position of the target interface element, and so on.
We assume that the movement goes from an initial state to an interface
element or from one element to another. In the latter case we take the the first
element position as initial conditions, and the position of the other as terminal.
We define the perturbation vector. Then the problem of optimizing the positions
of interface elements can be posed.
We enumerate all the elements of the interface and define the probabilities of
the transition from the i–th to the j–th element as the coefficients kxi xj of the
weight of each transition from xi –position to xj –position. The probabilities are
defined according to the information or functionality attached to the interface
element.
As was said before, elements should not overlap and intersect with other
objects in the scene, which imposes restrictions on the set of feasible system
solutions. At the same time, it should be possible for a user to reach all of the
interface elements, both information (by eyesight) and interactive (by eyesight
and hand). All these restrictions can be defined as Υ , a set of the interface
element position restrictions, x ∈ Υ .
As a result, if perturbation vector v is given, we have the problem of minimiz-
ing the weighed sum for N interface elements by placing them in the restriction
Title Suppressed Due to Excessive Length 5
set Υ :
X
JN = kxi xj J(xi , xj , v) → min , i = 1, 2, . . . N, j = 1, 2, . . . N, (1)
xm ∈Υ
i,j
where J(xi , xj , v) is an optimal movement time from the i-th to the j-th element
or more complex functional, for example, energy expended for the transition. It
can be determined from a model or from an experiment.
The optimal positions of interface elements affected by perturbations can be
found using game theory. Let the lengths of the joints, masses, etc. be disturbed.
The relative position of the interface elements will be our control.
We can get the antagonistic game Γ : the player in charge of controls min-
imizes the functional, the player in charge of perturbations maximizes it. The
lower estimate of the quality of the interface is the following value:
X
min max kxi xj J(xi , xj , v). (2)
xm ∈Υ v∈V
i,j
This formulation of the problem allows us to optimize the layout of the interface
elements, taking into account ”hard” restriction set Υ for the users hands and
eye movements. But in a real situation, some locations of objects lies on the Υ
set boundaries. Although they remain reachable, can cause discomfort for a user
when looking at them or when trying to reach them. It is required to find a set
of comfortable arrangement of interface elements. Let us call this set Ξ ”soft”
restrictions. We can define a penalty factor sm (ρ(xm , Ξ)) when placing elements
outside this set, where ρ is a distance between an interface element xm and the
set Ξ. If xm ∈ Ξ, then sm = 1.
Taking into account the penalty factor, the problem (2) could be formulated
as follows: X
min max kxi xj si sj J(xi , xj , v) (3)
xm ∈Υ v∈V
i,j
To solve this problem, dynamic programming methods [11] are applied. Using
them we could automatically optimize interface element placement for every
object of the historical reconstruction.
The purpose of this article is to define ”soft” restrictions such as human
hand movement restrictions and visual restrictions due to possible intersensoral
conflict.
We also summarize results of the eye and arm movements analysis. From eye
movements we find the criteria for ”soft” restrictions on elements placement and
size. For arm we describe a hypothesis of planar movement which allows us to
reduce the dimension of the problem for goal-directed hand movement from one
interface element to another.
2.2 Arm motion analysis
Human arm mobility Let us describe the restrictions imposed on the optimal
positions set of interface elements that arise due to the limited reach of a persons
6 L. Borodkin et al.
arm. We define the reachability set of the end arm effector, i.e. the set of all
permissible positions of the hand. For this, we need parameters and possible
rotations of each link in the arm.
Many possible arm positions are constructed and they describe the set of
constraints for interactive interface elements. We used a book [12] describes in
detail the results of the parameter measurements of the human body parts.
More than 200 men and women from the space crew and NASA employees were
invited as subjects. These personnel are in good health, fully adult in physical
development, and an average age of 40 years. Body masses were measured as
well as masses of body parts (neck, head, shoulder, forearm, hand, etc.), their
lengths and centers of mass positions, inertia moments, volumes, changes in the
centers of mass in various poses, permissible movements for parts of human
bodies. Reachability sets were found for various segments.
From [12] the average values of the parameters of the right hand for men
were taken and used for calculations: l1 , l2 are the lengths of the shoulder and
forearm. According to [12] l1 = 0.366 m., l2 = 0.305 m.
To build the reachability set for the hand joints, we used data from [12]. The ta-
ble 1 below shows the limits of feasible rotation angles for different axes for most
male subjects. To simplify the problem, we suppose that a human arm rotates
only around its longitudinal axis. This statement will not affect the reachability
set, therefore it will be built only for the shoulder and forearm.
Table 1. Various joints rotation feasible angles (NASA, [12]).
Boundary angles values
Description of rotation
deg. rad.
Horizontal abduction (Fig. 3, 4) 188,7 3,292
Shoulder lateral rotation (Fig. 3, 5A) 96,7 1,686
Shoulder medial rotation (Fig. 3, 5B) 126,6 2,208
Shoulder flexion (Fig. 3, 6A) 210,9 3,679
Shoulder extension (Fig. 3, 6B) 83,3 1,453
Elbow flexion (Fig. 3, 7) 159,0 2,773
In Fig. 3 we can see the measured angles and angles of reference. All figures have
angles which are marked by letters A and B. Not all of these angles are indicated
in Table 1, for example, the angle B of elbow flexion/extension is indicated for
the horizontal direction, since the sum of the angles A and B is 180◦ . Also, the
sum of the angles A and B for flexion and extension of the forearm is 180◦ .
When we change the angle of the shoulder, the feasible angles of rotation of
the forearm also change. This statenemt was also described in [12]. Fig. 4 is
an example of a reachability set presented for a forearm with the restrictions
specified in the Table 1.
Reachability sets for the whole arm are obtained by combining reachability sets
for the forearm for all valid shoulder locations. We use the human arm parameters
values from [12] as average data. A tracking system of a virtual reality device
Title Suppressed Due to Excessive Length 7
Fig. 3. Rotation of human arm: shoulder and forearm (NASA, [12]).
Fig. 4. Reachability set for a forearm.
allows us to specify it for every user. It helps us to determine ”soft” restriction set
Ξ for interactive interface element placement, but we do not take into account
user’s comfort when moving hands to extreme positions.
Plane motion hypothesis According to the problem (3), the definition of
the functional J and the penalty factors sm (describing user’s discomfort during
interaction with elements that are not in the set Ξ) could lead us to very different
interface element placing.
One of the ways to define J and sm is an energy criteria, when we consider the
equations of motion for hand and calculate energy consumption for the transfer
from one interface element to another (especially for extreme positions). The
spatial problem of moving an arm from one position to another is complex and
has an infinite number of solutions even if a wrist trajectory is pre-defined.
That is why a planar problem was considered. We determined some situations
when the spatial movement of an arm can be considered planar. A hypothesis
test was carried out: the movement of the hand will be planar if there is a plane
in which the hand lies at the initial and final moments. This statement was
proved experimentally.
The experiment involved 17 right-handed students (4 females, 13 males).
They were asked to hit the target as quickly and accurately as possible with a
pointer (Fig. 5), located on the board in front of them. Targets (goals) are square
holes in the plane with the sides of 3, 4, 5, 6 cm. The order of achieving the goals
8 L. Borodkin et al.
is predetermined. The initial position of the arm, from which the movement
started, was also set and marked. A mark for the palm was put on the pointer;
during the experiment it was not allowed to change the position of the pointer
in the hand. After each movement, the subject’s arm returned to its original
position and remained there for 3–5 seconds. To record the experimental data,
markers of the video analysis system were fixed on the shoulder, forearm of the
human right hand and pointer, to track their positions in space. We recorded
the coordinates and orientation of the specified markers and time.
Fig. 5. Target and pointer with the object of the video analysis system.
Fig. 6. The pointer’s trajectories compressed along the axis of motion and rotation Oy.
The trajectories are rotated around the axis Oz and shifted to match the end points.
The data obtained were interpreted using the MathWorks MATLAB software.
For the trajectories of each marker, the approximate planes to which they be-
long were constructed, the average trajectory deviations from the corresponding
planes. Then we calculated the values of standard deviation for the previous
deviations. The angles between the planes of the motion of the tracking system
markers were also found.
Tables 2 and 3 show the average values of the obtained values for all move-
ments.
Title Suppressed Due to Excessive Length 9
Table 2. Deviations of the trajectories of markers from the plane of motion.
Average (mm): Standard deviation (mm):
Shoulder 1,89 1,85
Forearm 1,89 1,84
Pointer 5,6 4,84
Table 3. Angles between the planes of motion of markers.
Average (deg.) Standard deviation (mm):
Shoulder–forearm 0,4710 0,4575
Forearm–pointer 1,0633 0,4901
Fig. 7. Average value distribution for the trajectory deviation from the plane of the
pointer movement.
Fig. 7 shows the average values of the distribution calculated for the trajectory
deviation from the plane of pointer movement. The average deviations from the
plane of movement and their standard deviations were 2–3 times greater for
targets not lying in the plane of the initial arm position. The average range of
motion (the distance between the start and end points of the trajectories) is
about 400 mm. It is two orders of magnitude greater than deviations from the
plane. The angles between the planes of marker motion are small (see Table 3).
So the movement trajectories can be considered planar. This allows us to
use planar models of arm motion dynamics [13] to describe transitions between
interface elements.
2.3 Eye motion analysis
The eye motions are quite complex. The motion from point to point is only one of
tasks solved in this field by human nerves system. How we see, the convergence
angle is changing during saccade, but this is not the only situation when it’s
happen. When we examined the interface element our eyes are permanently
moving. Eye motion control mechanisms provide clear vision [14]. Any human
movement requires such resources as energy, ions. There are a lot of adaptation
mechanisms in human organism, but sometimes our organism use to spend more
10 L. Borodkin et al.
resources to solve really important problem. Such task is a visual perception of
the world.
Following Filin our eye make two or more small saccades per second when
gaze is stable [14]. That small saccades are bit different in amplitude and latency.
We suppose that investigation such movements could be criteria as an index of
comfortable vision. It could help us to find the ”soft” restrictions set Ξ for
informational interface elements and to define the penalty factor.
Eye movement analysis in daily life conditions is not simple problem. There
are a lot of disturbance because of person head rotations, walking, breathing, eye
tracking system displacement. The first high accuracy eye tracking systems were
huge, hard fixed, and persons head fixed hardly too. In such conditions there
are a lot of research on the functioning of the visual system were produced.
Now it is necessary to shift at technics we have in new conditions when eye
tracking system is placed as glasses, there are some disturbances and we need
real time information. The probabilistic moments of eye tracker signals can be
a characteristic of eye movement strategy.
Probability moments in eye movement analysis In ideal world we can
identify saccade parameters and interpreted eye movement as physiological an-
swer on presented to person situation. Usually we have a number of artefacts
in eye tracking data. I this situation we offer to use the probability moments to
class the visual surround.
In the work [15] were shown there is a comfortable distance for examine the
object. We prolong their investigation for object in virtual reality. In virtual
reality we have a conflict between accommodation and convergence because a
distance to the screen is fixed.
We make an experiment using Panoramic virtual reality system, Arrington
research eye tracker and the accompanying software. The process of the exper-
iment is as follows. After a participant puts on stereo glasses and assumes a
comfortable sitting pose, a calibration is performed using built-in tools. After
confirming successful calibration, the main testing application is launched.
Participant is then shown yellow spheres on a black background spawning
in front of him at distances from 0.4 to 6 meters in random order. Angular
sphere size was constant value and equals 0.7 degree. Each sphere is displayed
for 60 seconds, then it changes color giving the participant a cue for blinking
several times. This behaviour triggers changing distance to a sphere. After the
last sphere is shown, only black background is shown and we let the participant
to take a rest. Then we change the participant’s distance to the screen from 0.4
to 6 meters in random order six times.
At the end we let the participant to remove the stereo glasses and finish his
participation. A total of 12 persons took part in this study. All of them gave
informed consent to participate.
Usually three component of eye position is registered and analysed. We con-
sider the angle between visual axis of the eyes. For this quantity we analysed
probability second moment [16]. Values are presented in the Table 4.
Title Suppressed Due to Excessive Length 11
Table 4. The STD mean value in radians [16].
Sphere distance
Screen dist.
0.4 m 0.68 m 1.18 m 2.03 m 3.49 m 6 m
0.4 m 0.0224 0.0188 0.0075 0.0197 0.0081 0.0078
0.68 m 0.0163 0.0160 0.0064 0.0093 0.0070 0.0084
1.18 m 0.0116 0.0086 0.0058 0.0081 0.0108 0.0135
2.03 m 0.0292 0.0093 0.0127 0.0116 0.0062 0.0080
3.49 0.0212 0.0107 0.0078 0.0098 0.0067 0.0130
6m 0.0163 0.0093 0.0085 0.0106 0.0074 0.0098
We find that probability second moments correlated with degree of mismatch
in real and imagine distance. In most comfortable situation the dispersion value
from eye position were lowest.
In a comfortable situation, a person has saccades in one direction and vergent.
In a mismatch situation as sensory conflict the proportion of vergent saccades
is increasing. This phenomena we see in our investigations. In study [15] oculo-
gram probability moments had not significant divisions. But in 3D case we see
significant divisions correlated with mismatch between real and virtual distance.
This way we can make a criteria for ”soft” interface restrictions Ξ: the time
when the convergence angle STD is high need to be minimal. According to the
STD changing, we can define the penalty factor sm (ρ(xm , Ξ)).
3 Conclusions
The article describes a novel approach to the interface design for virtual histor-
ical reconstruction. The problem of optimizing the location of spatial interface
elements is stated. The solutions of some related problems are given.
Human arm parameter analysis gives us the restriction set for the interactive
elements. The hypothesis of targeted hand movement planarity is confirmed.
According to the eye motion analysis, informational interface elements with
which long interaction is supposed need to be placed a meter or more away. The
time of interaction with close placed object must be minimized. The next stage
is to apply frequency analysis which allows us to slightly change the interface
in real time. During the interaction with the interface, cutoff frequency for each
user can be specified and virtual environment adapts to it.
This study allows us to create a convenient virtual reality interface giving
information about reconstructed objects.
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