=Paper=
{{Paper
|id=Vol-1710/paper17
|storemode=property
|title=The Results of Sulfur Print Image Classification of Section Images
|pdfUrl=https://ceur-ws.org/Vol-1710/paper17.pdf
|volume=Vol-1710
|authors=Oxana S. Logunova,Ivan A. Posokhov,Anatoliy Y. Mikov,Elena A. Ilyina,Natalya V. Dyorina,Anatoliy B. Belyavskiy
|dblpUrl=https://dblp.org/rec/conf/aist/LogunovaPMIDB16
}}
==The Results of Sulfur Print Image Classification of Section Images==
https://ceur-ws.org/Vol-1710/paper17.pdf
The Results of Sulfur Print Image Classification
of Section Images
O. S. Logunova1 , I. A. Posokhov1 , A. Y. Mikov1 , E. A. Ilina1 , N. V. Dyorina1 ,
and A. B. Belyavskiy1
Nosov Magnitogorsk State Technical University, Magnitogorsk, Russia,
logunova66@mail.ru
Abstract. The article deals with mathematical and algorithmic support
for sulfur prints image classification based on fuzzy sets and rules of ac-
cessories using peer inspections. In the study of the causes of unambigu-
ous classification the authors have introduced codomains of membership
function form: single classification, empty set, complete absorption and
unambiguous classification. The article conceived the concept of equi-
librium and nonequilibrium membership functions. The results showed
unambiguous classification of 100% images. The research was carried
out in 2011–2015. The proposed technique is applicable to the classifica-
tion of static images to assess the structure of materials using combined
methods.
Key words: data validity, image classification, fuzzy sets, tenancy rules.
1 Challenge problem
One of information sources about the quality of continuously cast billet is sul-
furic prints. The reliability of the information is determined by the methods of
irregular shape objects recognition in the image of sulfur prints. The authors
carried out the investigation for the identification of objects in an image using
statistical methods [1], morphological operations [2] and adaptive fuzzy trees
with a dynamic structure [3]. However, the known image recognition procedures
set out in [4–6], do not provide getting accurate information without resulting
images prior classification. There is an actual problem of improving the infor-
mation reliability obtained during continuous casting sulfur prints recognition.
Nowadays, active research is being carried out in the field of classification
of images and objects including in the structure. Among the known solutions,
we can specify the results of the studies which are conducted in many countries
around the world, including Russia. One of the approaches to solve the classifica-
tion problem remains creating a library of images according to the categories. For
example, in [7] the seven categories of images were studied to construct a vector
classification system. The paper demonstrates the selection theory with linear
shared objects in an optimal hyper plane. The authors conducted more than
2670 tests with classes: airplanes, birds, boats, buildings, fish, people, and vehi-
cles. In the study the authors used Laplacian of Gaussian distribution as a core.
When constructing the classifier the authors achieved a classification accuracy
of 11 to 16%. The authors in [8] suggest using Support Vector Machines (SVM)
for multipoint images classification. The paper presents the method of hyper
plan choice. However, the authors do not speak about the problems in methods
using in increasing hyper plans number. Quite a lot of works is dedicated to the
human face recognition and its elements. For this purpose the authors propose
the use of automatic classification based on the map of the characteristic points.
For example, in [9] we offer the use of two-dimensional wavelet transform based
on the envelope wave to highlight the main points of the face. This method ap-
plication resulted in 82% level of correct identification of the person’s face. The
disadvantage of this method is the image quality sensitivity and mimic changes
of the main face elements. One of object classification methods is to define the
feature points of the predetermined textures [10, 11]. In [7] the authors advance
an approximate base model of image segmentation based on point’s brightness
assessment. The authors of the work used an algorithm to image the brain. The
result was a classification of images with different textures of up to 84.4%. In [11]
we considered the statistical approach to texture classification of the individual
images, which is based on determining the lighting quality, camera position and
image processing conditions. The method is based on the use of the filter resis-
tant to the image rotation, the image histogram evaluation and the histogram
shape evaluation. The basic decision-making procedure has been adopted the
class picture k-means (k-Means), which appears sensitive to the choice of the
original condensation centers. The image classification problem was solved by
the same ways both with the help of fuzzy sets and fuzzy logic. The first studies
on the machine use for the fuzzy image classification appeared in the late 80’s
and early 90-ies of the 20th century and demonstrated good recognition results of
cartographic images with regularly shaped objects [12–14]. The presented funda-
mentals have been developed in recent studies [15–17]. However, despite many
existing research the problems of classifying the image with lots of irregular
shaped objects, low contrast, low quality and contrast remain unsolved [18–20].
The aim of the article is the development of software for sulfur prints
image classification for the further effective application of segmentation methods.
2 Factorable image classification technique
Three stages have been included in the image classification technique. Each
subsequent stage of the classification is provided to use for the images in the
field of unambiguous identity in accordance with the evaluation of the previous
step. Each shaped stage is different from the previous one by the number of
identification codes and the complexity of the membership functions belonging
to each class. The first stage uses the rules for identifying the image, built on
the basis of the three formative characteristics of the histogram: the position
of the threshold luminance; position of maximum brightness to the left of the
threshold; position of the maximum brightness to the right of the threshold.
The second stage, by increasing the number of identification codes from 3 to
256, uses three measures of similarities, describing the dispersion to evaluate the
scattering distance relative to the average value of each class. The third stage is
used only for the images that lacked unambiguous identity of the previous two
stages. Considering lack of the possibility to identify the images on the basis
of deterministic parameters of the histogram, we decided to perform linguistic
variables, terms and rules to identify images into the classes. The techniques
built on fuzzy rules include expert assessments and allow taking into account
the insights in the process formalization.
Considering 31% of the images after the application of the two techniques
based on the forming characteristics of histograms and distance remain in an
unambiguous identity we developed the technique for sulfur print image classi-
fication based on fuzzy sets and fuzzy logic rules.
In order to solve the problem of image classification we introduce the struc-
tured linguistic variable – Image, which in its composition has four components:
m, M , T , where T is an abscissa of the point for the position of the brightness
threshold; m is an abscissa of the point of the brightness maximum to the left of
the threshold; M is an abscissa of the point position of the brightness maximum
to the right of the threshold. Fig. 1 illustrates the structure of the linguistic
variable Image indicating all the components.
A special feature of the variable Image is three elements describing the for-
mative characteristics, for which the terms and the membership function should
be defined. Each of the components of the linguistic variable Image takes three
values: “Belongs to class A”; “Belongs to class B ”; “Belongs to class C ”, which
form a set of terms (Fig. 1).When describing the single reference histogram
there are four types of regions: of unambiguous identification (Fig. 2 ), of mul-
tiple identities (areas overlapping Fig. 3 ), the region of “empty set”, which does
not include any of the reference images and the region “total absorption”. For
each of the cases the authors have written the membership function in a general
form µi ,i = 1; 3, where i – notation for classes.
Fig. 1. Structure of the linguistic variable Image
If you have a unique identification of all three classes it is possible to get the
pattern of membership function shown in Fig. 2. In Fig. 2 we introduced the
notation: x is the considered component of the linguistic variable, [0; 255] is the
domain of the membership function according to the region of the brightness
histogram existence.
Fig. 2. Formation scheme of the membership function for the unambiguous identity
areas
The condition for the scheme existence shown in Fig. 2 appears intervals
order of the selected histogram characteristics. Consequently the condition of
ordering the formative characteristics is:
x1min < x1max < x2min < x2max < x3min < x3max . (1)
The ambiguous classification cases for the two groups remain after the second
stage of the classification technique. There is an interval for two overlapping
areas in which there are two solutions for the variable Image belonging to the
considered classes. Fig. 3 illustrates a diagram of the two areas intersection in
the process of image classification.
Fig. 3. The scheme of ambiguous identify region intersection
In the case shown in Fig. 3 , there is an intersection region at the range
[x2min ; x1max ] and the condition has been disturbed (1). Therefore, the ax-
iomatic form of membership function must be taken for this interval.
The simplest version of the membership function form is the linear “equilib-
rium” model (Fig. 4a) and more complex option for strengthening the proba-
bility of membership in the class through the combination of the two quadratic
functions (Fig. 4b) – “non-equilibrium” model. The point of these functions in-
tersection is determined in the course of adaptation or learning classification
system.
Fig. 4. The formation scheme of the membership functions for overlapping areas:
a – equilibrium model; b – non-equilibrium model
Fig. 4 additionally introduces the notation: M is the membership function
intersection point for the ambiguous classification region; xM is abscissa of the
membership function intersection point.
The abscissa of the point M can be displaced from its equilibrium position
as to the left as to the right, keeping the ordinate. Saving the ordinate makes it
possible to determine the analytical record of parabolic membership functions
in the training system. We wrote the analytic form of the membership function
for the equilibrium and nonequilibrium model.
For the function µi in the interval x(i+1)min ; x(i)max we try to use a canon-
ical equation of the line passing
through the two points with the coordinates
x(i+1)min ; 1 and x(i)min ; 0 for the analytical records as shown in Fig. 4a.
As a result, the membership function becomes:
1, x ∈ x(i) min ; x(i+1) min ;
1
µi = − x + L, x ∈ x(i+1) min ; x(i) max ;
Q
0, x ∈ x(i) max ; x(i+1) max .
Similarly, using the same notation, we obtain
1,
x ∈ x(i) min ; x(i+1) min ;
1
µi+1 = − x − R, x ∈ x(i+1) min ; x(i) max ;
Q
0, x ∈ x(i) max ; x(i+1) max ,
x(i+1)min
where R = and Q = x(i)max − x(i+1)min .
x(i)max − x(i+1)min
In the case of a non-equilibrium model for the function µi on the interval
x(i+1)min ; x(i)max we use the equation
of a parabola
through the three points
with the coordinates x(i+1)min ; 1 , x(i)min ; 0 and (xM ; 0,5), for the analytical
records as shown in Fig. 4b. The abscissa xM is set interactively at training the
classification system and it is considered known in advance.
While forming histogram there is brightness, according to which none of
reference images is classified, but any new image may have the characteristics
of those areas (Fig. 5). For these areas membership functions should also be
recorded, which can be constructed on the same principle as that of the ambigu-
ous identity regions. And the order of the interval boundaries must match the
expression (1).
Fig. 5. Arrangement of “empty set” areas
In this case, it suffices to consider the area between the two non-overlapping
intervals (Fig. 6). We wrote the analytical form of the membership function to
each model.
We used the canonical equation of the line passing through two points with
the coordinates x(i)max ; 1 and x(i+1)min ; 0 for the analytical records for the
function µi in the interval x(i)max ; x(i+1)min as shown in Fig. 6a.
As a result, the membership function µi becomes:
1, x ∈ x(i)min ; x(i) max ;
1
µi = x − R, x ∈ x(i) max ; x(i+1)min ;
Q
0, x ∈ x(i) min ; x(i+1) max .
Fig. 6. The formation scheme of the membership functions for overlapping areas:
a – equilibrium model; b – non-equilibrium model
Similarly, using the same notation, we obtain
1, x ∈ x(i)min ; x(i) max ;
1
µi+1 = − x − R, x ∈ x(i) max ; x(i+1)min ;
Q
0, x ∈ x(i+1) min ; x(i+1) max ,
x(i)max
where L = and Q = x(i)max − x(i+1)min .
x(i)max − x(i+1)min
In the case of a non-equilibrium
model for the function µi we should use
the range x(i)max ; x(i+1) min as the equationof a parabola passing
through the
three points with the coordinates x(i)max ; 1 , x(i+1)min ; 0 and (xM ; 0,5), for
the analytical records as shown in Fig. 6b. The abscissa xM is set interactively
at training the classification system and is considered known in advance.
Membership function pattern for the region of “total absorption” in accor-
dance with the formative characteristics of the histogram. “Total absorption”
area occurs during the segments order violation (1). There are two variants of
the “total absorption” region creation: the overlap of the first interval (Fig. 7a)
and the second interval overlap (Fig. 7b).
In this case, it is necessary to assign axiomatic value of the membership
function for the absorption region. As one of the possible options, we assume
that:
– when the following condition is satisfied x(i+1) min ; x(i+1)max ∈ x(i) min ; x(i)max
(Fig. 8)
(
1, x ∈ x(i) min ; x(i+1)min ∪ x(i+1) max ; x(i)max ;
µi =
0, x ∈ x(i+1) min ; x(i+1)max ,
and
µi+1 = 0, ∀ x;
– when the following condition is satisfied (Fig. 8) x(i) min ; x(i)max ∈ x(i+1) min ; x(i+1)max
(Fig. 8)
(
1, x ∈ x(i+1) min ; x(i)min ∪ x(i) max ; x(i+1)max ;
µi+1 =
0, x ∈ x(i) min ; x(i)max ,
and µi = 0, ∀ x;
Fig. 7. Formation scheme of the “total absorption” region: a – overlapping by the first
interval; b – overlapping by the second interval
In fact, zero membership function on one of the intervals excludes this area
from consideration when deciding on the accessories image to one of the classes.
The size of this area is less than 4% of the membership function domain. Inter-
mittent “failure” in the values of the membership function occurs at the specified
interval.
3 The results of the membership function construction
Using membership functions we perform their construction for the classification
of images that were not clearly classified in the first two stages. After the two
stages there were cases of ambiguous image classification between classes A and
C, B and C. We will consider each case individually for each component of the
variable Image.
Let us build the membership functions for the classes A and C. The member-
ship function for the parameters on the left maximum and a brightness threshold
is characterized by the presence of three areas of “empty set”, which do not cause
ambiguous identity of the image (Fig. 8), and allow you to uniquely classify new
images coming in the system. In Fig. 9 we can observe µM C function failure of
the range M ∈ (MAmin ; MAmax ). Thus, the membership functions are:
– membership function for a maximum on the left (Fig. 8):
1
m, 0 ≤ m < 147;
147
1, 147 ≤ m ≤ 185;
µmC = 1
− + 4,78, 185 < m < 234;
49
0, 234 ≤ m ≤ 255,
0,
0 ≤ m < 147;
1
m − 3,78, 185 ≤ m ≤ 234;
µmA = 49
1, 234 < m < 239;
1
− m + 15,94, 239 ≤ m ≤ 255,
16
Fig. 8. Equilibrium membership function pattern for the brightness maximum on the
left
– membership functions for the brightness threshold (Fig. 9):
1
T, 0 ≤ T < 193;
193
1, 193 ≤ T ≤ 207;
µT C = 1
− T + 7,9, 207 < T < 237;
30
0, 237 ≤ T ≤ 255,
0, 0 ≤ T ≤ 207;
1
− T − 7,9, 207 < T < 237;
µT A = 30
1,
237 ≤ T ≤ 240;
1
− T + 15, 240 < T ≤ 255;
15
Fig. 9. Equilibrium membership function pattern for the brightness maximum on the
right
– membership functions for maximum brightness on the right:
1
T, 0 ≤ M < 238;
238
1, 238 ≤ M < 240 or 244 < M ≤ 248;
µT C = 1
− T + 36,43, 248 < M < 255;
7
0, 240 ≤ M ≤ 244,
µM A = 0, ∀M ∈ [0; 255] .
For each component of the variable Image let us accept membership rules:
the Image belongs to class Ki , if the membership function value for the class
Ki is at least 0.5.
For each variable Image we obtain values of three components, which include
the picture to one of two classes according to the introduced rule.
Table 1 defines decision rules in the image classification according to mem-
bership between classes A or C. Table 2 shows an example of calculation and
the membership conclusion of one of the images, which was originally, identified
ambiguously, to classes A and C. After applying the technique based on fuzzy
sets and expert decision rules we adopted an unambiguous solution concerning
the image membership to class A.
In the tables class 0 is entered to indicate the interval of “total absorption”.
Tables are filled in a survey of experts – specialists in the evaluation of the
work piece quality during the training of decision-making on sulfur print images
classification.
Table 1. Decision rules in ambiguous classification between A and C
Class me mbership according to the component
Rule number Conclusion
m T M
1 A A 0 A
2 A C 0 A
3 C C 0 C
4 C A 0 A
5 C C C C
6 C A C C
7 A C C C
8 A A C A
Table 2. Example of making decisions based on the rules of Table 1
Function value
Component Notation Class Conclusion
µA µC
m 237 1 0 A A
T 200 0,31 0,69 C A
M 242 0 0 0 A
4 Conclusions
In order to resolve ambiguous sulfur prints image classification the authors
proposed the technique of stage classification, which includes three stages of
decision-making according to the formative characteristics of the brightness his-
togram, to the distance measures up to the reference histograms and fuzzy mem-
bership function with the use of expert logic inference rules. Each subsequent
stage is used in the presence of ambiguous classification in the previous step.
The authors offered the technique based on the theory of fuzzy sets for complex-
structured linguistic variable comprising three components: a brightness maxi-
mum on the right, brightness threshold, and a brightness maximum on the left to
resolve ambiguous identity regions of the image. Term-sets, which define entered
membership classes, have been introduced for each component. The proposed
mathematical software in describing the membership functions introduces the
notions of equilibrium and non-equilibrium models, it performs a generalized
technique of these models construction and its application in sulfur prints image
classification. When constructing membership functions of fuzzy sets the authors
conceived the concept of “empty set” and “total absorption” areas, which allowed
identifying ambiguously the images from the new retrospective dataflow.
References
1. Posokhov, I.A., Logunova, O.S.: The method of constructing the membership
function to classify images based on histograms. CEUR Workshop Proceedings (3)
(2014) P. 133–145
2. Posokhov, I.A., Logunova, O.S.: Tehnologija obrabotki izobrazhenij zagotovok
na osnove operacij morfologicheskogo analiza. Matematicheskoe i programmnoe
obespechenie sistem v promyshlennoj i social’noj sferah (1–2) (2011) P. 191–196
3. Logunova, O.S., Matsko, I.I., Posokhov, I.A., Lukaynov, S.I.: Automatic system for
intelligent support of continuous cast billet production control processes. The Inter-
national Journal of Advanced Manufacturing Technology (74(9)) (2014) P. 1407–
1418
4. Gonsales, R.: Cifrovaja obrabotka izobrazhenij. M. (2005) 1072 p.
5. Prjett, U.: Cifrovaja obrabotka izobrazhenij. M. (1982) 312 p.
6. Shapiro, L., Stokman, D.: Komp’juternoe zrenie. SPb. (2006) 752 p.
7. Chapelle, O., Haffner, P., Vapnik, V.: Support vector machines for histogram-
based image classification. IEEE Transactions on neural networks (10(5)) (1999)
P. 1055–1064
8. Foody, G.A.: A relative evaluation of multiclass image classificafion by suuport
vector machines. IEEE Transactions on geoscience and remote sensing (42(6))
(2004) P. 1335–1343
9. Lyons, M.J., Budynek, J., Akamatsu, S.: Automatic classification of single facial
images. IEEE Transactions on pattern analysis and machine intelligence (21(12))
(1999) P. 1357–1362
10. Leemput, K.V., Maes, F., Vandermeulen, D., Suetens, P.: Automated model-based
tissue classification of mr images of the brain. IEEE Transactions on medical
imaging (18(10)) (1999) P. 897–908
11. Varma, M.A., Zisserman, A.: Statistical approach to texture classification from
single images. International Journal of Computer Vision (62(1/2)) (2005) P. 61–81
12. Wang, F.: Fuzzy supervised classification of remote sensingimages. IEEE Trans-
actions on geoscience and remote sensing (28(2)) (1990) P. 194–201
13. Wang, F., Newkirk, R.: Design and implementation of knowledge-base system for
remotely sensed change detection. J. Imaging Techn. (13) (1987) P. 116–122
14. Cannon, R.L., Dave, J.V., Bezdek, J.C., Kolsky, H.G.: Segmentation of a the-
matic mapper image using the fuzzy c-means clustering algorithm. IEEE Trans.
Geosci.Remote Sensing (GE-24) (1986) P. 400–408
15. Morlini, I.A., Zani, S.: New class of weighted similarity indices using polytomous
variables. Journal of Classification (29(2)) (2012) P. 199–226
16. Giordani, P., Kiers, H.: Findclus: Fuzzy individual differences clustering. Journal
of Classification (29(2)) (2012) P. 170–198
17. Contreras, P., Murtagh, F.: Fast, linear time hierarchical clustering using the baire
metric. Journal of Classification (29(2)) (2012) P. 118–143
18. Bar-Hen, A., Gey, S., Poggi, J.M.: Influence measures for cart classification trees.
Journal of Classification (32(1)) (2012) P. 21–45
19. Shestakov, A.L., Sviridjuk, G.A.: O novoj koncepcii belogo shuma. Obozrenie
prikladnoj i promyshlennoj matematik (19(2)) (2012) P. 287–288
20. Shestakov, A.L., Sviridjuk, G.A., Hudjakov, J.V.: Dinamicheskie izmerenija v pros-
transtvah “shumov”. Vestnik Juzhno-Ural’skogo gosu-darstvennogo universiteta.
Serija: Komp’juternye tehnologii, upravlenie, radiojelektronika (13(2)) (2013) P. 4–
11