Educational Information
We continue the section of our
journal devoted to publications concerning various aspects of education in the
area of computer graphics and geometry.
V.Pilyugin
Experiments with
the Eyesight Frequency Model on the Perception
of the Architectural Environment
Mihail Shargorodsky,
Technical University of Moldova, Kishinev,
Republic of Moldova,
Abstracts: The author
describes the model of visual perception used in the educational process for
students studying architecture. The model is used for objective estimation of
architectural forms on criteria of lightness-massiveness, symmetry-asymmetry,
contrast-nuance, etc. This model is based on the modern neurophysiological data
and is meant for studying regularities of the visual perception of
architectural environment by man. The results of the experiments are presented,
in which the images are estimated according to the criteria of
lightness-massiveness and fitness-exposure of an object in the environment.
Key words: Fourier analysis,
model, visual, lightness factor, exposure factor.
At
the heart of the proposed model lies the eyesight frequency theory [4],
according to which in the visual analyzer of the higher animals and people the
image projected on the retina 
undergoes Fourier analysis:
|
|
(1) |
where 
are the two-dimensional periodic
trigonometrical functions. On the analysis of the dynamic images 
we
suppose that factors Сi are the functions of time.
|
|
(2) |
The eyesight frequency theory sets a
deep analogy between the perception of information by ear and by eye (it has
been known for a long time that the auditory system of man makes Fourier
analysis of sounds).
On the basis of expressions 1 and 2 the monocular model of
the visual apparatus has been created, the main units of which are the three
three-dimensional Fourier-analyzers (red, green and blue). The original static or dynamic images are either generated on the computer or
obtained by digitization of the real objects shots. Fourier analyzers develop
the corresponding color components of images into Fourier series which are the
functions of two coordinates 
and time
or the
frame number 
.
The model has been exposed to some
experiments on the image analysis on the following criteria:
lightness–massiveness, static–dynamic character, symmetry–asymmetry,
fitness–exposure of a form in the environment, etc. The results of some of
these experiments are given below.
It has become clear that the
estimates of the model as well as those of man depend on the perspective an
architectural form is perceived, its lighting, its coloring, trajectory the
observer is moving along with respect to the form, its environment, etc.
To estimate quantitatively a static
image on criterion of “lightness-massiveness” the “lightness factor” was proposed estimating the quantity of the
high frequencies in the spectrum of this image [2, 4]. The “lightness factor” for dynamic images is
determined as the time average 
or the
frames average 
[3]:
|
|
(3) |
.In Figure 1
there are given static images of three architectural forms and corresponding
factors 
.
According to the model estimate form (A) is approximately 5.5 times lighter
visually than form (C).
|
|
|
|
A) |
B) |
C) |
|
Fig. 1.
Image estimates generated on the computer on criterion “lightness
- massiveness” |
||
Another example shows the
application of the model for the analysis of the photographs of real objects.
In Figure 2 (B) you can see the wooden Trinity church in Larga village (built
in 1897). The folk’s craftsmen
interpreted inventively the standard design of this church at the basis of
which there are forms of the Russian church.
In Figure 2(A) there is shown St.
Nicholas church in Belti city constructed by the Moldavian boyard George Panait
in 1791-1795 according to the plan of the Roman Catholic church (the author of
the design is the Austrian architect Weisman).
In the model’s opinion the image in
Figure 2(B) is approximately 1.2 times lighter than the image in Figure 2(A).
A)
KL=0,095 B) KL=0,110
Fig. 2 Estimate of the digitized
photographs on criterion
“lightness-massiveness”
The environment creates the
background against which an architectural form is perceived. To determine
quantitatively the exposure of the form in the environment we introduce factor 
which estimates the distinction of object and
environment spectrums [5]. “The exposure factor” has the following
characteristics [6, 7]: if form 
better
fits the environment than form 
, then 
.
А)
B)
C)
D)
Fig. 3. Visual estimate of the
objects on criterion “fitness-exposure”
During the experiment on the
computer there were generated visual series, which were perceived by an
observer moving along the same street ending with different architectural
forms. Each of the visual series included 100 frames.
In Figure 3 for each of the four
ending forms there are given 3 frames with numbers 
and the corresponding “exposure factors”. “The
exposure factors” were determined by the formula:
.
In Figure 3, as appears, visual
series (A) has the most exposure (the exposure factor is 21.21). And the object
fits the environment best of all in visual series (D) (the exposure factor is
5.51, approximately 4 times less than in case (A)).
In Figure 4 there are given results
of the experiment on the exposure factor calculation for the building of the
Fig.4. Estimate of the building of
the
References
[1] M. Sargorodchi, Modelul percepţiei vizuale // Spiritualitatea. Stiinta. Tehnica. –Universitatea Tehnica din Moldova, Chisinau, 2004. ISBN 9975-9820-3-4.
[2] M. Sargorodchi, Modelul percepеtiei vizuale a mediului arhitrctural // Culegere de materiale stiintifice
ale colaboratorilor Facultatii Urbanism si Arhitectura. –Universitatea Tehnica din Moldova, Chisinau, 2002. ISBN 9975-9638-9-7.
[3] M. Shargorodsky The
model of visual recognizing of architectural form // Abstracts of the
International Conference “Information Technologies 2002”. –
[4] В.Д.Глезер и др. Зрительное опознание и его нейрофизиологические механизмы.– Ленинград: Наука, 1975. с. 272.
[5] М.Т.Шаргородский, Б.Н. Бендерский Применение двумерного Фурье-преобразования для оценки восприятия проектируемых архитектурных объектов в существующей городской среде //Аcta Academica 1999. - Evrica, Chişinău, 1999. ISBN 9975-941-58-3. P.238-241.
[6] М.Т. Шаргородский Математические модели зрительного восприятия архитектурной среды // Материалы международной научно-практической конференции «Математическое моделирование в образовании, науке и производстве», Тирасполь, 2001. С. 232-234.
[7] М.Т. Шаргородский
Модель восприятия архитектурной среды // Probleme actuale ale urbanismului
si amenajarii teritoriului.
Conferinta tehnico-stiintifica
internationala. Vol. 1. – Universitatea Tehnica din Moldova, Chisinau, 2004. ISBN 9975-70-448-4. P.85-90.
[8] М.Т. Шаргородский Модель визуального
восприятия в архитектуре // Probleme actuale ale urbanismului si amenajarii
teritoriului. Conferinta
tehnico-stiintifica jubiliara. Vol. 1.- Universitatea
Tehnica din