=Paper= {{Paper |id=Vol-2830/paper10 |storemode=property |title=Research and Analysis of Breast X-Rays Based on Intelligent Technologies |pdfUrl=https://ceur-ws.org/Vol-2830/paper10.pdf |volume=Vol-2830 |authors=Rimma Tomakova,Ilia Egorov,Aleksandra Brezhneva }} ==Research and Analysis of Breast X-Rays Based on Intelligent Technologies== https://ceur-ws.org/Vol-2830/paper10.pdf

Research and Analysis of Breast X-Rays Based on
Intelligent Technologies

Rimma Tomakova 1[0000-0003-152-4714], Ilia Egorov 1[0000-0002-1238-3243], and
Aleksandra Brezhneva 2[0000-0001-5226-329X]
1
Southwest State University, 50 Let Oktyabrya str., 94, Kursk, 305040, Russia
rtomakova@mail.ru, egorov.ilia1996@mail.ru
2
Plekhanov Russian University of Economics,
36 Stremyanny lane, Moscow, 115998, Russia
Brezhneva.AN@rea.ru

Abstract. The principles of forming an automated classification system for
breast radiographs are considered.
Classification of selected segments in x-ray images is implemented using
intelligent technologies based on neural network analysis. For this purpose, 120
images were selected from the MIAS database with morphological data, on the
basis of which a training sample was formed. The volume of the training
sample is 370 segments, of which 250 segments are characterized by the state
of norm and 120 segments contain pathologies. Each analyzed image block
corresponds to a predictor described by a three-component vector. The first
indicator that evaluates the segment of morphological education is the statistical
characteristic of the mode, the second indicator is the mathematical expectation,
and the third component of the indicator is the standard deviation.
The software is implemented in the MATLAB2018b environment. The results
of the quality classification of the developed software product on control
samples are presented. For this purpose, 50 images of mammograms of the
breast from the MIAS database were studied: 25 in the normal state and 25 with
pathology. The values of positive and negative classification results are
established. Diagnostic sensitivity was DH=84%, diagnostic specificity of
DS=96%, diagnostic efficiency of DE=90%.
Keywords: breast x-ray, segmentation, neural network classifier, homogeneity
criterion, automated system.

1 Introduction

Ecological problems of regions, a wrong way of life and unproductive conduct
instrumental in growth of oncologic diseases. Breast cancer is one of the most
common cancers currently in the worldwide. Every year in Russia, about 60 thousand

Proceedings of the 10th International Scientific and Practical Conference named after A. I. Kitov
"Information Technologies and Mathematical Methods in Economics and Management
(IT&MM-2020)", October 15-16, 2020, Moscow, Russia
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Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

CEUR Workshop Proceedings (CEUR-WS.org)
women diagnosed with breast cancer are admitted to the dispensary, and about 600
thousand patients continue to be monitored by oncologists. The main method for
detecting breast tumors is mammography [1]. Since 2017, Russia has been one of the
leading manufacturers of high-tech medical equipment and information systems for
mammology. The detector "Solo DM-MT", produced by JSC "Medical Technologies
Ltd", which can be used in analog and digital mammography, is widely used.

2 Literature Review

As you know, the main developers of applied software for mammogram processing
in the world are the companies such as: AccuDetect, The MAMMEX MammoCAD,
Syngo Breast Care, Fujifilm's Digital Mammography System [2, 3, 4, 5]. One of the
disadvantages of these software products is the closure of program code, which leads
to instability and unpredictability in the use of the software. In this regard, in 2018,
the Ministry of Digital Development, Communications and Mass Media approved
plans for the transition to domestic software developed for the Ministry of Health of
Russia. In world practice, recognition methods based on boosting technology and
neural network models of classifiers are used for automated image processing [4,5].
Currently, hybrid technologies have become widespread, which allow combining the
technologies of trained classifiers and soft computing technologies [6,8]. The
recognition problem is most successfully solved using neural network models . The
development of methods and algorithms for the identification and classification of
images are devoted to the works of A.N. Galushkina, A.N. Gorban, T. Kohonen, F.
Wasserman, and J. Hopfield. However, there is no unified methodology for solving
applied problems of image classification using artificial neural networks (ANNs). In
this regard, it is advisable, in relation to each specific task, to choose not only their
architecture, but also the method of forming the space of informative features and the
method of teaching ANNs [6,7,8].
Therefore, the purpose of the research is to develop an automated classification
system for the analysis of mammograms.
To achieve this purpose, the following tasks were set: highlighting the area of
interest that corresponds to the instructions of a mammologist; decomposition of the
mammogram into cascading windows for subsequent classification of the selected
image areas.

3 Materials and methods

Methods of segmentation of complexly structured images are used to study
mammogram images [7,8,9]. The image is divided into segments homogeneous in
texture or brightness, their homogeneity index is a priori set. A characteristic feature
of the homogeneous segment is the impossibility of separating another segment out it,
on the basis of the established criterion of homogeneity [7,8,9,10]. To select segments
based on the cascade segmentation method [6,11,12,13], software modules were
developed. These modules are combined into an automated system for the
classification of images of X-ray images of the breast (ASCIX).
The significant part of the software modules is developed in the MATLAB2018b
environment. The choice of the Matlab 2018b environment for development is due to
the fact that it has an extensive toolkit for implementing processing procedures and
classification images. In addition, the selected software architecture of the automated
system for the classification of images of X-ray images of the mammary gland makes
it easy to add and / or modify software modules. Structural scheme is shown in Figure
1.
It consists of three main modules: the Cascading Window Formation Module
(CWFM), the Cascading Window Combining Module (CWCM), and the
Classification and Decision Making Module (CDMM).The purpose of the first of
them (CWFM) is that it implements the procedure for segmentation of the breast
radiograph using the "top-down" technology described in [6]. In CWFM, the halftone
raster image of a breast radiograph is decomposed into segments distributed over
hierarchical levels. The criterion of the transition of the segment from one hierarchical
level to another (the criterion of indivisibility of the block) is the homogeneity index
of brightness of the pixels of the analyzed segment. Wherein, the indivisible segment
is assigned a code corresponding to the hierarchical level on which it is located. The
segment code is determined by the route the segment moves through the hierarchical
levels. The route ends with the procedure for assigning the segment the status of
"indivisible". The generated code allows you to determine the relating "indivisible"
blocks. The blocks can then be merged if they meet the merge criterion.
The second module (CWCM) is designed to form the final configuration of the
segments. The preparation for the subsequent classification of segments takes place in
this module. The module (CWCM) is configured to enlarge the segments that meet a
certain homogeneity criterion. The homogeneity criterion can be built on the basis of
the brightness characteristics of the segments or on the basis of their texture
characteristics.
The third module (CDMM) performs a dual-alternative classification of the image
segments of the radiograph into two classes: "there is an area of interest", "there is no
area of interest". The third module (CDMM) performs a dual-alternative classification
of the image segments of the radiograph into two classes: "there is an area of
interest", "there is no area of interest". For implementation the classification from
attributes of pixels included in the segment, a vector of informative features is
formed. Methods and algorithms for creating this vector are described in sufficient
detail in [14,15,16,17,18]. In this case, the classification of segment possible that fall
into the class "there is an area of interest" into classes "there is a pathology" - " there
is no pathology".
Mammographic
examination data Automated system

The Cascading Window The Classification and Decision
The uploading of the Combining Module (CWCM) Making Module (CDMM)
mammographic image
Writing down of the Loading of the
Decision received segments into extended segments
maker the memory
Entering the
uniformity criterion
The determination of
Defining attributes
the homogeneity of the
segments Writing down
The database of The segmentation into the patient
mammograms method to cascade database
breast Windows Classification (there is
Searching for adjacent
an area of interest/ there
blocks
is no area)
Writing down of the
extended segments
into the memory DM Confirming
Loading of the Displaying the result
the DM result
The Cascading Window segments on the screen
Formation Module (CWFM)

MATLAB 2018b

Fig. 1. Structural scheme of an automated mammographic image classification system

To involve the decision-maker (DM) in process of classifications, the classified
segments are binarized or presented in the form of a "heat map". The latter way of
representing classified segments is expedient when using neural networks with a
linear activation function as classifiers. In this case, the proximity of the output of the
neural network to one (proximity to the class "pathology") corresponds to the
proximity of the pixel shading of the segment to the red color. Such method of data
presentation allows the decision-makers both to participate in the process of making
diagnostic decisions together with a computer, and to form a database for an
automated system.

4 Formation of a training sample for the classification of breast
diseases based on intelligent technologies

The observational study was carried out to calculate the informative features which
are necessary for the functioning of an intelligent system. For this, the test
radiographic images of the breast were used from the DDSM database with confirmed
diagnoses, which were used as input data in automated system (ASCIX).
The cluster method of sampling was applied in the process of which two classes of
analyzed image segments were formed. Class C1 - contains image segments
characterized by the state of the norm. Class C2 -segments are presented that have
morphological formations caused by pathological processes. A case-control study was
conducted to develop a dual-alternative classifier. For this purpose, 120 images were
selected from the DDSM database with morphological formations. Based on these
images, a training sample was formed with a volume of 370 segments. Fragments of
test images of reference samples for class C1 and C1 are shown in Figure 2.
а)

Fig. 2. Examples of test segments of X-ray images of the breast: a) - norm; b) – pathology

The appointment of the training sample is to establish indicators that characterize
the condition of the examined patient. It represents 250 segments of normal breast
radiographs and 120 segments contain morphological neoplasms caused by
pathological processes. Due to it, two criteria were developed: "norm" - there is no
area of interest, "pathology" - there is an area of interest.
Each segment corresponds to the predictor P2, described by the vector of three
components. In experimental studies, the statistical characteristic Mo - mode (X1)
was chosen as the first indicator evaluating the segment of morphological formation.
The second indicator is M - expectation value (X2). The third component of the
indicator is SD - mean square deviation (X3).
Table 1 shows fragments of the calculated values: mode, expectation value and
mean square deviation for class C1 segments (there are absent morphological
formations with pathology), as well as for C2 class segments (have morphological
neoplasms caused by pathological processes).

Table 1. Fragment of the table of experimental data with informative signs for segments of
class С1 and segments of class С1
informative signs of class С1 informative signs of class С2
№
X1 X2 X3 X1 X2 X3
1 2 3 4 2 3 4
1 107 106 16,67 174 186 39,9
2 99 88 29,35 170 184 67,11
3 107 99 19,75 177 208 64,01
4 117 93 25,69 198 168 43,01
5 60 52 25,87 188 201 53,73
6 99 93 22,02 170 156 43,83
7 94 96 20,06 146 160 40,94
8 89 96 17,01 170 205 44,33
9 89 95 19,23 185 182 48,16
10 94 100 19,53 158 150 40,03
11 40 46 31,73 153 173 42,74
12 54 45 29,27 151 145 41,41
13 77 79 16,37 159 187 42,81
14 89 79 29,22 174 212 31,83
15 99 77 30,58 169 182 37,49

The analysis of the experimental data in Table 1 indicates that for the segments in
the normal state (class С1), the mode values do not exceed 143, for the expectation
value 153, and for the mean square deviation 36.71.
The averaged values of the mode, mathematical expectation and standard deviation
are - 93.50, 88.47, 25.12, respectively.
For segments in which there are morphological formations caused by pathological
processes (class С2), the mode values do not exceed 250, the expectation value is 227,
and for the mean square deviation, 67.11. The averaged values of the mode,
mathematical expectation and standard deviation are - 176.40, 183.10, 32.15
respectively.
Figure 3 shows the fragments of the studied image segments for the class of norm,
as well as its histogram, as well as a fragment of the segment containing the
morphological neoplasm and the corresponding histogram.
Мо = 109
СКО = 39,35
М = 94

a) b)

Мо = 170
СКО = 64,05
М = 136

c) d)
Fig.3. Fragment of the studied segments and their histograms:
a) a fragment of a segment in a normal state; b) the histogram of this segment; c) a fragment
of a segment containing a morphological neoplasm; d) histogram of a segment containing a
morphological neoplasm

If we accept a priori the law on normality of component distribution of the vector
P2, then each class is specified by the three-dimensional normal distribution of the
joint probability density of the components of the vector P2. The normal character of
such distribution is confirmed by checking its individual components and by the
consequence of the central limit theorem [21, 22].
To check the sample for compliance with the normal distribution law, the
STATISTICA program was used. With the aim of preliminary analysis, histograms
and quantile - quantile of graphics were built.
Figure 4 shows the graphs of histograms of indicators: mathematical expectation,
standard deviation for classes С1 and С2. From the graphs of the histograms it
conclusion follows that the obtained data correspond to the Gaussian curve, but there
are outliers and anomalous values at the edges of the distribution.
a) b)

c) d)
Fig. 4. Histogram of the normal distribution: a) expectation value for class С1;
b) expectation value for class С2; c) mean square deviation for class С1;
d) mean square deviation for class С2

Figure 5 depicted the quantile-quantile plots for three indicators: mode, expectation
value, mean square deviation for classesС1 and С2.
From the quantile-quantile plots, it conclusion follows that all points lie along the
line, which does not contradict the normal distribution law.
a) b)

c) d)

e) f)

Fig. 5. Quantile-quantile graphs: a) the mode for class С1 b) the mode for class С2; c) for the
expectation value of class С1; d) for the expectation value of class С2; e) for the mean square
deviation of class С1; f) for the mean square deviation of class С2
For justification compliance with the normal distribution law, an additional check
was carried out using the Kolmogorov – Smirnov test [22] with a confidence level of
0.95. Using the STATISTICA program, the Kolmogorov-Smirnov criterion was
calculated, the results of which are presented in Table 2.

Table 2. The results of checking three indicators for classes С1 and С2 using the STATISTICA
program

Variable Normality tests (spreadsheet 3)

N Max D Kolmogorov-
Smirnov
Mode of class С1 250 0,082 p< 0,10

Expectation value of class С1 250 0,081 p< 0,10
(М1)
Mean square deviation of 250 0,079 p< 0,10
classС1 (СКО1)
Mode of class С2 120 0,118 p< 0,10

Expectation value of class С2 120 0,112 p< 0,10
(М 2)
Mean square deviation of 120 0,117 p< 0,10
class С2 (СКО 2)

In the third column of the table shows the calculated sample values of D, and the
fourth column shows that all criteria are normally distributed, since the value of the
probability p is less than 0.1, which corresponds to a confidence level of 0.95.
To verify that the program is calculated correctly, it is necessary to compare the
obtained sampled values of D with the critical value of the Kolmogorov-Smirnov
criterion for a confidence level of 0.95. The calculation of the critical value is carried
out according to the formula [22]:

where α is the eve of sig ifica ce of the distributio ; is the samp e size.
For a sample of 250 values, corresponding to class C1, the critical value is equal
0 1921, and for a sample of 120 values, belonging to class C2, the critical
value is 11 243. If , then the hypothesis is accepted, if , then the
hypothesis is rejected [22]. Since all the calculated sample values of D are less than
the critical values, then, therefore, the hypothesis is accepted, the samples are
normally distributed.
5 Results

To assess the quality of mammograms segmentation by the proposed method, we
used collections of X-ray images of the mammary gland from the Digital Database for
Screening Mammography –DDSM, created on the basis of the University of South
Florida and the University of Washington School of Medicine (available at:
http://marathon.csee.usf.edu/ Mammography / Database.html). The database
contains both normal cases obtained during the screening examination with the result
"normal", and cancer cases confirmed by the results of further research.
50 images of mammograms of the mammary gland were selected from the
database, of which the presence of malignant neoplasms was proved in 25 cases by
specialists. Computer programs included in the automated system (Fig. 1) provide the
selection of segments on the X-ray image that be o g to the c ass “there is a area of
i terest”. Moreover, the dis ocatio of these segme ts shou d co firm the dis ocation
of segments with neoplasms, which were identified by a mammologist.
Figure 6 shows the results of classification of X-ray images from the control
sample into the classes "there is an area of interest" - "there is no area of interest". If
the computer detects an area of interest on the X-ray image, then the patient is
assigned additional examinations.

a) b) c) d)

Fig. 6. Results of image segmentation: a) the original image "no area of interest";
b) processed image according to the criterion "no area of interest"; c) the original
image “there is an area of interest.”; d) processed image accordi g to the criterio
"there is an area of interest."

Table 3 shows the indicators of the quality of diagnostics of X-ray images from the
control sample. According to the indicator of diagnostic sensitivity (DH), the
intelligent system showed a result of 0.84, and according to the indicator, diagnostic
specificity (DS) - 0.96.
Table 3. Results of control tests of the automated system
Observation result
Condition Total
Positive Negative
there is an area of interest 21 4 25

no area of interest 1 24 25

Total 22 28 50

6 Discussion
Analysis and experimental studies of the known methods of segmentation of
halftone raster images have shown that they all have certain drawbacks and cannot be
used directly for segmentation of radiographs. Therefore, the segmentation algorithm
should be built on a hierarchical principle. The lower hierarchy should contain
intelligent agents that provide an improvement in the quality of segmentation by
reducing the transition area between segments and increasing the brightness of border
pixels. Taking into account D. Hubel's research, it is advisable to use morphological
operators for preliminary processing of radiographs. The structure was developed of
an intelligent system for the classification of radiographs based on the procedure for
forming the selection of an area of interest and were developed uniformity criterions
of the selected areas.

7 Conclusion

The approbation of the presented automated system and its software modules
showed that out of 50 X-ray images, 45 were classified correctly, which amounted to
90% of the control sample. Moreover, false positive results accounted for 4% of the
training sample. According to this indicator, the presented system surpasses the
known ones by 2 ... 4%. In addition, there are reserves for reducing this indicator to
increase the sensitivity threshold for individual segments. This is due to the fact that
in order to send the patient to have an additional examination, it is enough to find only
one segment on the image of the breast radiograph that satisfies the given condition,
which makes it possible to increase both the diagnostic sensitivity and the diagnostic
specificity.
References

1. Boyd H.F., Gio Y., Martin L.J., et. al. Mammographic density and the risk and detection of
breast cancer// Engl. JMed. 2007. V. 356. P.227-229.
2. Medical device companies. Scanis // MedWOWGlobal. - K.: Copyright, 2014. - URL:
http://ru.medwowglobal.com/company/scanis/91190 (accesed 15.09.2019).
3. Computer-Aided Detection for Digital Mammography syngo MammoCAD // Siemens. –
Copyright, 2008. - P. 1-8. - URL:
http://www.medical.siemens.com/siemens/en_INT/gg_sps_FBAs/files/brochures/cad/finalpd
fMammoCAD.pdf (accesed 29.10.2019).
4. FUJIFILM Digital Mammography CAD // Fujifilm Europe. - М.: Copyright, 2019. - URL:
http://www.fujifilm.eu/eu/products/medical-systems/products/p/fujifilm-digital-
mammography-cad/ (accesed 15.05.2019).
5. Medical Imaging // Parascript. - М.: Copyright, 2019. - URL:
http://www.parascript.com/medical-imaging/ (accesed 10.04.2019).
6. Tomakova R.A., Filist S.A., Pykhtin A.I. Development And Research Of Methods And
Algorithms For Intelligent Systems For Complex Structured Images Classification// Journal
of Engineering and Applied Sciences. 2017. V. 12. 22. P. 6039-6041.
7. Filist S.A. Dabagov A.R., Malutina I.A. Method for cascade segmentation of radiographs of
the breast// [Proceedings of Southwestern state University. Series: Management, computer
engineering, computer science. Medical instrumentation.- 2019. - T.9 №1(30). - pp. 49-61.
8. Ledeneva T.M., Podvalny S.L., Stryukov R.K., Degtyarev S.V. Fuzzy modeling of medical
expert systems // Biomedical Radioelectronics. 2016. №9. P. 16-24.
9. Filist S.A. Multilayer morphological operators for the segmentation of complexly structured
raster halftone images [Text] / S.A. Filist, A.R. Dabagov, I.A. Malutina, etc. // Proceedings
of Southwestern state University. Series: Management, computer engineering, computer
science. Medical instrumentation.- 2019. - T.9 №3. - pp. 44-63.
10. Rajashekaran, S., Vijayalksmi, G.A. Neural Networks, Fuzzy Logic and Genetic Algorithms:
Synthesis and Applications, 2nd Edition. Prentice-Hall, 2017. - 572 p.
11. Yan, Zhicheng, et al. "Hd-cnn: Hierarchical deep convolutional neural network for image
classification." International Conference on Computer Vision (ICCV). Vol. 2. 2015. 435-443.
12. Bernikov V.V., Preobrazhensky A.P., Choporov O.N. Possibilities for Parallelizing Image
Processing Using OPENCV and PENMP // Modeling, Optimization and Information
Tech o ogies. 2019.T.9. №. 2 (25). pp. 110-126.
13. Titov D.V., Bekhtin Y.S., Egoshina I.L., Kaperko A.F. Processing of multi-spectral images
for so vi g the recog itio prob em // Te ecommu icatio s. 201 . №5. pp. 35-38.
14. Korsunov N.I., Toropchin D.A. The method of finding the spam images based on the hash of
the key points of the image//I ter atio a Jour a of Computi g. 2016. Т. 15. № 4. С. 259-
264.
15. Filist S.A., Tomakova R.A., Degtyarev S.V., Rybochkin A.F. Hybrid Intelligent Models For
Chest X-Ray Image Segmentation//Biomedical Engineering. 2018. V. 51. 5. P. 358-363.
16. Korsunov N.I., Toropchin D.A. Image classification method based on clustering complex
objects // Scientific Bulletin of Belgorod State University. Series: Economics. Informatics.
2016. №23 (244). P. 100-103.
17. Tomakova R.A., Filist S.A., Pykhtin A.I. Automatic Fluorography Segmentation Method
Based On Histogram Of Brightness Submission In Sliding Window//International Journal of
Pharmacy and Technology. 2017. V. 9. 1. P. 28220-28228.
18. Filist S.A., Ali Qaboos, Kuzmin A.A. Formation of an attribute space for classification
problems of complexly structured images based on spectral windows and neural network
structures. Proceedings of Southwestern state University. Series: Management, computer
technology, informatics. Medical instrumentation. 2016. №4 (67). P. 56-68.
19. Korsunov N.I., Toropchin D.A. A method for constructing a spam filter for searching for
fuzzy duplicates of images // Information Systems and Technologies. 2017. №1(99). P. 13-
20.
20. Korsunov N.I., Ushakova S.N. The structure of the neurocomputer signal classification
system // Scientific Bulletin of Belgorod State University. Series: Economics. Informatics.
2019.T. 46. №.3. P. 496-502.
21. Dabagov, A.R. Automated classification system for breast radiographs [Text] / Dabagov
A.R., Gorbunov V.A., Filist S.A., Malyutina I.A., Kondrashov D.S. // Medical equipment. -
2019. - №6 (318). - P. 39-41.
22. Dabagov, A.R. Automatic classifier of X-ray images using transparency masks / A.R.
Dabagov, A.S. Bugaev // Proceedings of Southwestern state University. Series
Management, computer technology, informatics. Medical instrumentation. - 2019. - №.4. -
P. 106-125.
23. Dabagov, A.R. A four-stage algorithm for processing X-ray images in the systems of
intelligent support for the classification of mammograms [Text] / A.R. Dabagov // System
analysis and control in biomedical systems. - 2019. - T. 1 , №4. - P. 117 - 127.
24. Zhilyakov E.G., Chernomorets A.A., Bolgova E.V., Kovalenko A.N. Image decomposition
on the orthogonal basis of subband matrics eigenvectors//Journal of Engineering and
App ied Scie ces. 2017. Т. 12. № 12. P. 3194-3197.
25. Akimov A.V., Donskikh A.O., Sirota A.A. Models and algorithms for recognizing digital
images under the influence of deforming and additive distortions // Bulletin of Voronezh
State University. Series: System Analysis and Information Technology. 2018. №1. P. 104-
118.
26. Savvin S.V., Sirota A.A. Superpixel segmentation methods and their application for the
analysis of images with heterogeneous texture // Bulletin of the Voronezh State University.
Series: System Analysis and Information Technology. 2016. № 4. P. 165-172.
27. Zhilyakov E.G., Konstantinov I.S., Chernomorets A.A. Decomposition of images into
additive compo e ts//I ter atio a Jour a of Imagi g a d Robotics. 2016. Т.16. №1. P. 1-8.
28. Akimov A.V., Sirota A.A. Synthesis and Analysis of Algorithms for Digital Signal
Recognition in Conditions of Deforming Distortions and Additive Noise Radioelectronics
a d Commu icatio s Systems. 2017. Т.60. №10. P. 45 -468.
29. Zhilyakov E.G., Chernomorets A.A., Bolgova E.V. On informational subdomains of spatial
frequencies of images // Scientific news of Belgorod State University. Series: Economics.
Informatics. 2016. №23 (244). P. 87-92.
30. Egoshina I.L. Complexation of Optical, Ultrasond and X-Ray Images in Intraoperatitive
Navigatio Systems //Bu eti of the Russia Academy of Scie ces: Physics. 201 . Т. 2. №
12. P. 1542-1546.
31. Bernikov V.V., Preobrazhensky A.P., Choporov O.N. Analysis of algorithms for detecting
moving objects in the video image / Modeling, optimization and information technologies.
2018. T.6. №.3 (22). P. 223-233.
32. Donskikh A.O., Sirota A.A. Training of deep neural networks in a small sample for the
classification of biological objects by multiplicative measurements // Bulletin of Voronezh
State University. Series: System Analysis and Information Technology. 2019. №4. P. 109-
118.
33. Zhilyakov E.G., Chernomorets A.A., Bolgova E.V., Oleynik I.I., Chernomorets D.A. Hidden
Data Embedding Method Based on the Image Projections onto the Eigenvectors of
Subinterval Matrices// International Journal of Engineering and Technology(UAE). 201 . Т.
7. № 3. P. 72-80.
34. Podvalny S.L., Mugatina V.M., Vasiliev E.M. Faceted neural networks in pattern
recognition problems. // Mathematical methods in engineering and technology. - ММТ.
2020. T.6. P.90-95.
35. Levenkov K.O., Korovin E.N., Novikova E.I. Neural network modeling of the process of
choosing a treatment regimen for patients with chronic pyelonephritis and urolithiasis //
Modeling, optimization and information technologies. 2018.T.6, №23 P. 61-71.