<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Visible Structures Highlighting Model Analysis Aimed at Object Image Detection Problem</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>I R Saifudinov</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>V V Mokshin</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>P I Tutubalin</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>L M Sharnin</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>D G Hohlov</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Kazan National Research Technical University named after A. N. Tupolev - KAI</institution>
          ,
          <addr-line>Karl Marx str. 10, Kazan, Russia, 420111</addr-line>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2018</year>
      </pub-date>
      <fpage>139</fpage>
      <lpage>148</lpage>
      <abstract>
        <p>The research considers an approach to solving the problem of reducing the data processed in mobile platforms oriented video-analytic systems. Different models of human visual attention has been analyzed and also classified according to the image segmentation. The results obtained are presented in the form of the method used for isolating the borders of the most significant object in the image. They are based on the optimization the length and curvature values of the object borders. This approach allows to filter significant structures in the image and process them with the help of image segmentation techniques. The method was evaluated according to usage the accuracy criterion along with other methods in delineation of boundaries: threshold value, morphological processing and watershed. Software and hardware system for registering dump trucks has been improved. It gives the possibility to automatize the process of registration dump trucks, training them during the construction of roads.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>
        1. Introduction
Automated video surveillance systems (video analytics) used in many spheres of human activity,
likewise state institutions and manufacturing enterprises are extremely popular nowadays. The systems
usage allows to create options for events automatic alarm, efficiency in employees labour
improvement by means of direct control of the performing activity.Herewith, because of the large
number of tasks solved in video analytics, as well as their multi-criteria, autonomy tendency, and
indistinct nature of tasks, there is a certain necessity to find the effective approach for highlighting
image visible structures that allows to work on the basis of mobile platforms. The attempt for analysis
of various tasks has been made in the research. [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], [
        <xref ref-type="bibr" rid="ref6 ref7 ref8">6-8</xref>
        ].
      </p>
      <p>
        The method of highlighting of visible structures in an image based on visibility measuring of length
and curvature of the curve that is similar to the concept suggested by Lowe [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] has been taken into
consideration. The research deals with the measure of visibility according to the criterion of false
positive detection in comparison to the method of delimiting contour of object [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. In addition to the
evaluation of the method, it is compared with the segmentation and accuracy of other methods of
optimization of significant information.
      </p>
    </sec>
    <sec id="sec-2">
      <title>2. Visibility network construction</title>
      <p>
        Orientation elements are the basic computational elements of the network [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. Each element   is
connected with a processor that normally can perform certain calculations based on the conditions and
those with  denotation performed by the neighbour processor. This defines a single network
containing  2 processing blocks with the local communication. In the current implementation,  is
equal to 48, which provides a reasonable angular resolution. Let's appeal to the associated orientation
sequence of the elements   , … ,   + , , where each element is a linear segment or interval, like length
of a curve N. (curves can be continuous or with any number of intervals). The optimization task is
formulated to maximize the value of Ф
 above overall length of a curve N, starting with   .
      </p>
      <p>max
(  +1,…,  + )∈  (  )
Ф
 (  , … ,   + )
where   (  ) is a number of all possible length of a curve N, starting with   .</p>
      <p>For a certain of measures class Ф(∙), the calculation of Ф

can be obtained by simple local
computations made repeatedly. To illustrate, let’s take the first curves three elements long only.
In this case:</p>
      <p>max
(  +1,  +2)∈ 2(  )</p>
      <p>Ф2(  ,   +1,   +2)
where   is defined by   +1 (one of   's k of neighbours) and   +2 (  +1 neighbour) for a given
element so that the rate Ф2(  ,   +1,   +2) will be in its maximum. Simple approach (brute-force
method) in the analysis of  2 value in different curves will be required anew. Suppose, however, that
Ф2 corresponds to the condition of:
 2(  )
max Ф2(  ,   +1,   +2) = max Ф1(</p>
      <p>, max Ф1(  +1,   +2))
  +1
  +2
In this case, the maximization of the rate Ф2 can be achieved by application of Ф1 used repeatedly
over shorter curves. The general approach can be formulated the same way, e.i:
max  (  ) Ф</p>
      <p>(  , … ,   + ) = max  +1 ∈  (  ) Ф1(  , max  −1(  +1) Ф −1(  +1, … ,   + ))
where  ( 
) is equal to  1(  ). Thus, the searching area required for each length of a curve N is being
(1)
reduced, from   to 
, instead of</p>
      <p>which is essential for a brute-force method approach. The
concept (1) is related to the optimality principle, underlining for all multistage decision-making
processes. This is a special case in dynamic programming in particular. It refers to the
family of
functions that follows concept (1) of extensible functions.</p>
      <p>There are two factors that are essential for visibility measure. The first one is related to the length
of a curve, and the second factor is related to its shape. The length of a curve is determined by the
number of its elements that have a factual curve (rather than an interval) passing through these
elements. They are called active elements. Whereas elements that are associated with intervals are
referred to as virtual elements where local visibility   corresponds to   . If   is the active element,
then   has positive value, which is equal to 1 and 0 for the virtual element   . A measure associated
with the length of a curve   , … ,   + is determined by the equation:
along the curve.</p>
      <p>The measure rate above(2) presents the sum of the local values of the visibility of active elements
Then, the attenuation function associated with the curve   , … ,   is defined as follows:
where   , = 1. The measure in (2) is modified by the attenuation coefficients is:
The measure rate in equation (3) is weighted contribution of the local visibility values   along a
curve, that are in reverse dependency to a number of virtual elements along   , … ,   . To measure the
shape of a curve, measure that in reverse dependency to the total curvature of a curve is used. The
total curvature of γ is defined as ∫ (
P is known as the local curvature at this point (the reciprocal value of the radius of curvature R). It is
necessary to use the total curvature to obtain a measure that is limited and in the position of reverse
dependency to the total curvature. The next measure is relevant to the following:
 )  , where  ( ) is a slope along a curve and 
at the point
(4)
(5)
(6)</p>
      <p>In order to obtain a discrete approximation to the measure in (4), we denote   to indicate
orientation difference between the k-th element and its successor and ∆ as length of the orientation
element. A discrete approximation to full curvature of a measure along   , …   , will be:
where
  , is the weight of each value of local visibility 
 along a curve. A measure that shows a high rate
for long curves with low overall curvature is now defined as:
exp
− ∫ ( )</p>
      <p>2
  , +1 = exp−
∑   ,   ,</p>
      <p>, =
∏   , +1</p>
    </sec>
    <sec id="sec-3">
      <title>3. Analysis of the visibility network: discussion and results</title>
      <p>To analyse visibility network we compared the percentage of false positive detections. Test samples
located around the perimeter of circle at equal intervals consist of short, oriented segments in the field
of segments with random position and orientation as it shown in figure 1.
sorted in ascending order according to their visibility of the most (ϕ1) and less (ϕ ) noticeable
segments. For given m form segments, false-positive are defined as noise segments, which are
assigned a visibility greater than ϕ</p>
      <p>+1. A false positive estimate for each method was calculated for
samples consisting of different numbers of shape and noise segments rate. A false positive rate for
each combination (for example, 20 shape segments and 70 noise segments) was estimated by
averaging false positive value by means of more than ten attempts with different noise samples. The
picture in the right side of Figure 2 is the graph of false positive rate percentage for a circle with
twenty segments.</p>
      <p>Each method can be accomplished well enough (less than 10% of false positives) at a low noise
level (40 noise segments or less). The results of methods applied begin to diverge at higher noise
levels. It should be noted that threshold processing is superior to morphological processing while
watershed is relative to the approach suggested, although the latter is more expensive to calculate.
And, finally, at lower signal-to-noise ratios watershed and the proposed approach have significantly
lower false-positive estimates. The next comparison was identical to the first one, but shape segments
are formed by an unlimited sinusoid (Figure 2).</p>
      <p>In the right half of Figure 2 is a graph of the percentage of false positives relative to the number of
noise segments for a ten segment sinusoidal curve. Comparatively low indicators of the proposed
method compared with other methods can be attributed to its apparent dependence on closure.
However, it still outperforms the threshold processing for higher signal-to-noise ratios and has an error
rate comparable to threshold processing (i.e., within 5%) at lower signal-to-noise ratios.</p>
      <p>In the third comparison a field consisting of correlated noises (i.e., a dipole) was used (Figure 3).
The dipole consists of two collinear segments separated by an interval equal to the distance between
neighboring segments of the circle. Since the two segments forming the dipole are collinear, the
degree of closeness between the segments forming the dipole is greater than between the adjacent
segments of the circle. Therefore, it is impossible to distinguish noise segments from the shape
segments using only a local measurement. From the graph it can be seen that the methods of threshold
processing and morphological processing have almost a 100% false positive level, whereas the
watershed and the proposed method are much better able to cope with this task.</p>
      <p>In the fourth comparison (Figure 4), ten segments are used. This is a complex picture, because the
sampling frequency is so small, so that there is only one segment at 36 degrees of the circle. Most of
methods do not work well even at relatively high signal-to-noise ratios. For noise level 80, threshold
processing and the morphological processing method are performed at 90% false positive level. The
watershed method is performed a bit better, with a false-positive level of 70%. In contrast, the
falsepositive level for the proposed method is less than 5%.</p>
      <p>Let's consider practical use examples of the specified methods in the decision of the object
segmentation problem on the image in the video-analytical system focused on mobile platforms for the
account number of transportations dump trucks. The image segmentation results are shown below.
Segmentation for threshold processing is shown in Figure 5.</p>
      <p>Segmentation for the watershed is shown in Figure 6. The results of morphological processing
segmentation are shown in Figure 7.</p>
      <p>The results of the proposed method segmentation for isolating significant structures are shown in
Figure 8.</p>
      <p>
        The proposed method of identifying significant structures was compared with other measures that
calculate the optimal structure: contrast discrimination, a combined approach to optimization [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ];
quantitative indicators of changes based on the organization of functions: eigenvalues and
eigenvectors [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ] and stochastic areas of completion: a neural model of illusory shape of the contour
and significance [
        <xref ref-type="bibr" rid="ref20 ref21 ref22 ref23">20-23</xref>
        ]. Let us consider examples of practical use of these methods in solving the
problem of segmentation of important structures in the image.
      </p>
      <p>To get an idea of the strengths and weaknesses of boundary selection measures, it is useful to apply
them to a simple test scheme consisting of edges from a circle (thirty, twenty, or ten evenly spaced
samples) against a background of one hundred edges of random position and orientation. Three test
patterns are shown in figure 9. To visualize the values assigned to each edge, the edges are displayed
as rectangles with lengths and widths proportional to the original significance values.</p>
      <p>a) b) c)
Figure 9. (a) thirty edge circle against the background of a hundred edges of noise. (b) twenty edge
circle. (C) ten edge circle.</p>
      <p>First, let us consider the results of measuring the method of contrast discrimination. It is important
to note that the previously described modified optimization problem is solved. That is,    is
optimized for all vectors,  ∈ {0,1} and | | =  where  - is the total number of edges and m is the
number of edges. Since the method is given the number of edges, it has a significant advantage over
other measures, and these results should be interpreted accordingly. Segmentation for thirty and
twenty edge circles is shown in Fig.10 (a) and (b). With the exception of excluding one edge of the
circle in the 1 hour orientation, and including a false 10-hour edge, the method calculates perfect
segmentation. However, the results are in ten regional districts (see figure 10 (c)) show that the
method could not separate the circle from the lantern.</p>
      <p>To better visualize the large range of significance values calculated by the quantitative change
measure method, the length and width of the rectangles are drawn proportionally to the log(1.0 +
106 ∙ xi), where xi - is the significance of the edge i. In Fig. 11 (a) results for the thirty edge circle
calculated using the quantitative change method are shown. In General, the edges of the circle are set
to a larger value than the edges of the background. However, it is observed that the significance values
in the upper left part of the circle are much larger than the values in the lower right corner. If the
eigenvector with the highest positive real eigenvalue is interpreted as a limited distribution of random
walks between edges, it is seen that this distribution is dominated by random walks (with reversals in
the direction) through the parasitic edge at the 10 o'clock position. Because the measure does not
provide tangential continuity or closure, the effect of one inconveniently positioned edge can be
profound. For Fig.11 (b) and (c) the asymmetry becomes very pronounced as the circle sample
becomes less frequent. The consequence of this is that the measure has failed to isolate the circle from
its base, even in the case where a very simple method such as stochastic completion areas has a small
problem (see Figure 12 (b)).</p>
      <p>a) b) c)
Figure 11. The values of significance, (a) calculated by the quantitative change in the indicators for
the thirty edge circle, (b) for the twenty edge circle, and (C) for the ten edge circle.</p>
      <p>For figure 12 (a) and (b) significance maps for thirty and twenty edge circles calculated by the
stochastic completion regions are shown. With the exception of the false 10-hour edge, all edges of the
background are assigned gaps with a small value. The contrast between the values calculated by this
method and the estimated quantitative indicators of changes is quite impressive. The difference in the
power of discrimination is due solely to the use of directivity and the multiplication of vector x by
vector x in this method. This multiplication imposes a restriction that the edge must form a bridge
between the other two. The result is intervals with a larger range of values than those with only x or x
components . However, this limitation is not enough to distinguish the edges of the ten edge circles
from the background borders. A significance map calculated as the stochastic completion regions for
the ten edge circle is shown in figure 12 (c). A significant number of background edges have gaps
comparable to those assigned to the edges of the circle.</p>
      <p>a) b) c)
Figure 12. The significance values calculated by the stochastic completion regions, (a) for the thirty
edge circle, (b) for the twenty edge circle, and (c) for the ten edge circle.</p>
      <p>a) b) c)
Figure 13. The values of significance calculated by the proposed approach, (a) for the thirty edge
circle, (b) for the twenty edge circle, and (c) for the ten edge circle.</p>
      <p>Finally, figure 13 (a-c) shows significance maps calculated using the proposed approach. With the
exception of the false 10-hour edge, all edges of the background are assigned intervals with a small
value. This is true even for ten edge circles, which no other measure could segment from the
background.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Conclusions</title>
      <p>
        In addition to comparing false positive detection, Table 1 shows the time required to run the
algorithms on the Android 5.0 operating system. With a resolution of 640x480 pixels. It can be seen
from the table that the proposed method for identifying significant structures shows the fastest and
least resource-consuming results. Thus, the proposed model for significant structures identifying is an
effective tool for primary segmentation of images in video-analytical systems oriented at mobile
platforms. As results have shown, the method of isolating notable structures showed the most accurate
results. The method of selecting notable structures is based on the measure of visibility calculation that
includes applies the principle of dynamic programming [
        <xref ref-type="bibr" rid="ref15 ref5">5, 15</xref>
        ]. Also it would be used queueing
system to analyse such kind models [
        <xref ref-type="bibr" rid="ref16 ref17">16-17</xref>
        ]. Two internal properties of the network of significance,
such as extensibility and geometric convergence, allow us to optimize the measure of significance and
effectively restore optimal curves (in polynomial time).
      </p>
      <p>At the same time, they restrict the range of possible functions that can be used as a measure of
significance, so the method has some limitations with scale invariance, fusion of curves, and grouping
in the presence of compounds. In addition, overcoming overlapping problems will require
asymptotically increasing the complexity of the method, since the discretization is closely related with
using dynamic programming to effectively optimize the chosen measure.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <surname>Moksin</surname>
            <given-names>V V</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Saifudinov</surname>
            <given-names>I R</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Kirpichnikov A P and Sharnin L M 2016</surname>
          </string-name>
          <article-title>Vehicle recognition based on heuristic data and machine learning Bull</article-title>
          . Kazan Techn. Univ.
          <volume>19</volume>
          (
          <issue>5</issue>
          )
          <fpage>130</fpage>
          -
          <lpage>137</lpage>
          (in Russian)
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <surname>Saifudinov</surname>
            <given-names>I R</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Mokshin</surname>
            <given-names>V V</given-names>
          </string-name>
          and
          <string-name>
            <surname>Kirpichnikov A P 2017</surname>
          </string-name>
          <article-title>Grouping contours of objects of structural images based on the network of element visibility Bull. Kazan Techn</article-title>
          . Univ.
          <volume>20</volume>
          (
          <issue>9</issue>
          )
          <fpage>120</fpage>
          -
          <lpage>123</lpage>
          (in Russian)
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <surname>Treisman</surname>
            <given-names>A 1982</given-names>
          </string-name>
          <string-name>
            <surname>Perceptual</surname>
          </string-name>
          <article-title>Grouping and Attention in Visual Search for Features and</article-title>
          for
          <source>Objects Journal of Experimental Psychology: Human Perception and Performance</source>
          <volume>8</volume>
          (
          <issue>2</issue>
          )
          <fpage>194</fpage>
          -
          <lpage>214</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <surname>Lowe D G 1985 Perceptual Organization and Visual Recognition</surname>
          </string-name>
          (Kluwer Academic Publishers, Boston)
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <surname>Kormen</surname>
            <given-names>T</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Leiserson</surname>
            <given-names>Ch</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Rivest</surname>
            <given-names>R</given-names>
          </string-name>
          and
          <string-name>
            <surname>Shtaine K 2005 Dynamic Programming</surname>
          </string-name>
          <article-title>Algorithms: construction and analysis (Introduction to Algorithms) (Moscow: Williams) p 1296 (in Russia)</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <surname>Gorilik</surname>
            <given-names>A L</given-names>
          </string-name>
          and
          <string-name>
            <surname>Skripkin</surname>
            <given-names>V A</given-names>
          </string-name>
          <year>1989</year>
          <article-title>Recognition methods (Higher School Publishing) p 232 (in Russia)</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <surname>Vapnik</surname>
            <given-names>V N</given-names>
          </string-name>
          and
          <string-name>
            <surname>Chervonenkis</surname>
            <given-names>A I</given-names>
          </string-name>
          <year>1974</year>
          <article-title>Theory of pattern recognition (Moscow: Science) p 416 (in Russia)</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <surname>Nesteruk</surname>
            <given-names>V F</given-names>
          </string-name>
          and
          <string-name>
            <surname>Sokolova</surname>
            <given-names>V A</given-names>
          </string-name>
          <year>1980</year>
          <article-title>Questions of the theory of perception of subject images and a quantitative assessment of their contrast</article-title>
          <source>Optoelectronic Industry</source>
          <volume>5</volume>
          <fpage>11</fpage>
          -
          <lpage>13</lpage>
          (in Russia)
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <surname>Shashua</surname>
            <given-names>A</given-names>
          </string-name>
          and
          <string-name>
            <surname>Ullman</surname>
            <given-names>S 1988</given-names>
          </string-name>
          <article-title>Structural saliency: The detection of globally salient structures using a locally connected network 2nd Intl</article-title>
          .
          <source>Conf. on Computer Vision</source>
          (ICCV '88), Clearwater, FL
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <surname>Laurent</surname>
            <given-names>H</given-names>
          </string-name>
          and
          <string-name>
            <surname>Radu H 1993 Figure-Ground</surname>
            <given-names>Discrimination</given-names>
          </string-name>
          : a
          <source>Combinatorial Optimization Approach IEEE Transactions on Pattern Analysis and Machine Intelligence</source>
          ,
          <source>Institute of Electrical and Electronics Engineers</source>
          <volume>15</volume>
          (
          <issue>9</issue>
          )
          <fpage>899</fpage>
          -
          <lpage>914</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <surname>Sarkar</surname>
            <given-names>S</given-names>
          </string-name>
          and
          <string-name>
            <surname>Boyer K L 1996</surname>
          </string-name>
          <article-title>Quantitative measures of change based on feature organization: Eigenvalues and eigenvectors Computer Vision</article-title>
          and Pattern Recognition 40 DOI: 10.1109/CVPR.
          <year>1996</year>
          .517115
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <surname>Williams L R and Jacobs D W 1997 Stochastic Completion</surname>
          </string-name>
          <article-title>Fields: A Neural Model of Illusory Contour Shape</article-title>
          and
          <source>Salience Neural Computation</source>
          <volume>9</volume>
          (
          <issue>4</issue>
          )
          <fpage>837</fpage>
          -
          <lpage>858</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [13]
          <string-name>
            <surname>Shakowat</surname>
            <given-names>M</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Sarker</surname>
            <given-names>Z</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Tan W H and Logeswaran R 2007</surname>
          </string-name>
          <article-title>Morphological based technique for image segmentation</article-title>
          <source>International Journal of Information Technology</source>
          <volume>14</volume>
          (
          <issue>1</issue>
          )
          <fpage>55</fpage>
          -
          <lpage>80</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          [14]
          <string-name>
            <surname>Sahoo P K 1988</surname>
          </string-name>
          <article-title>A survey of thresholding techniques Computer Vision</article-title>
          ,
          <source>Graphics and Image Processing</source>
          <volume>41</volume>
          <fpage>233</fpage>
          -
          <lpage>260</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          [15]
          <string-name>
            <surname>Rutkowski</surname>
            <given-names>W S</given-names>
          </string-name>
          <year>1979</year>
          <source>Shape completion Comput Vis Graph Image Process</source>
          <volume>9</volume>
          <fpage>89</fpage>
          -
          <lpage>101</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation>
          [16]
          <string-name>
            <surname>Yakimov</surname>
            <given-names>I</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Kirpichnikov</surname>
            <given-names>A</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Mokshin</surname>
            <given-names>V</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Yakhina</surname>
            <given-names>Z</given-names>
          </string-name>
          and
          <string-name>
            <surname>Gainullin</surname>
            <given-names>R 2017</given-names>
          </string-name>
          <article-title>The comparison of structured modeling and simulation modeling of queueing systems Communications in Computer and Information Science (CCIS) 800 DOI:</article-title>
          10.1007/978-3-
          <fpage>319</fpage>
          -68069-9_
          <fpage>21</fpage>
        </mixed-citation>
      </ref>
      <ref id="ref17">
        <mixed-citation>
          [17]
          <string-name>
            <surname>Tutubalin</surname>
            <given-names>P I</given-names>
          </string-name>
          and
          <string-name>
            <surname>Mokshin</surname>
            <given-names>V V</given-names>
          </string-name>
          <year>2017</year>
          <article-title>The Evaluation of the cryptographic strength of asymmetric encryption algorithms IEEE Second Russia</article-title>
          and Pacific Conference on Computer Technology and Applications (RPC)
          <fpage>180</fpage>
          -
          <lpage>183</lpage>
          DOI: 10.1109/RPC.
          <year>2017</year>
          .8168094
        </mixed-citation>
      </ref>
      <ref id="ref18">
        <mixed-citation>
          [18]
          <string-name>
            <surname>Laurent</surname>
            <given-names>H</given-names>
          </string-name>
          and
          <string-name>
            <surname>Radu H 1993 Figure-Ground</surname>
            <given-names>Discrimination</given-names>
          </string-name>
          : a
          <source>Combinatorial Optimization Approach IEEE Transactions on Pattern Analysis and Machine Intelligence</source>
          ,
          <source>Institute of Electrical and Electronics Engineers</source>
          <volume>15</volume>
          (
          <issue>9</issue>
          )
          <fpage>899</fpage>
          -
          <lpage>914</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref19">
        <mixed-citation>
          [19]
          <string-name>
            <surname>Sarkar</surname>
            <given-names>S</given-names>
          </string-name>
          and
          <string-name>
            <surname>Boyer K L 1998</surname>
          </string-name>
          <article-title>Quantitative measures of change based on feature organization: Eigenvalues and eigenvectors Computer Vision</article-title>
          and
          <source>Pattern Recognition</source>
          <volume>7</volume>
          (
          <issue>1</issue>
          )
          <fpage>110</fpage>
          -
          <lpage>136</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref20">
        <mixed-citation>
          [20]
          <string-name>
            <surname>Williams</surname>
            <given-names>L R</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Jacobs D W 1997 Stochastic Completion</surname>
          </string-name>
          <article-title>Fields: A Neural Model of Illusory Contour Shape</article-title>
          and
          <source>Salience Neural Computation</source>
          <volume>9</volume>
          (
          <issue>4</issue>
          )
          <fpage>837</fpage>
          -
          <lpage>858</lpage>
        </mixed-citation>
      </ref>
      <ref id="ref21">
        <mixed-citation>
          [21]
          <string-name>
            <surname>Borisova</surname>
            <given-names>I V</given-names>
          </string-name>
          ,
          <article-title>legkii V N and Kravec S A 2017 The application of the brightness gradient orientation for automatic object tracking systems</article-title>
          <source>Computer Optics</source>
          <volume>41</volume>
          (
          <issue>6</issue>
          )
          <fpage>931</fpage>
          -
          <lpage>937</lpage>
          DOI: 10.18287/
          <fpage>2412</fpage>
          -6179-2017-41-6-
          <fpage>931</fpage>
          -937
        </mixed-citation>
      </ref>
      <ref id="ref22">
        <mixed-citation>
          [22]
          <string-name>
            <surname>Myasnikov</surname>
            <given-names>E V</given-names>
          </string-name>
          <year>2017</year>
          <article-title>Hyperspectral image segmentation using dimensionality reduction and classical segmentation approaches</article-title>
          <source>Computer Optics</source>
          <volume>41</volume>
          (
          <issue>4</issue>
          )
          <fpage>564</fpage>
          -
          <lpage>572</lpage>
          DOI: 10.18287/
          <fpage>2412</fpage>
          -6179- 2017-41-4-
          <fpage>564</fpage>
          -572
        </mixed-citation>
      </ref>
      <ref id="ref23">
        <mixed-citation>
          [23]
          <string-name>
            <surname>Goshin</surname>
            <given-names>Y V</given-names>
          </string-name>
          and
          <article-title>Kotov A P 2017 Parallel implementation of a multi-view image segmentation algorithm using the hough transform</article-title>
          <source>Computer Optics</source>
          <volume>41</volume>
          (
          <issue>4</issue>
          )
          <fpage>588</fpage>
          -
          <lpage>591</lpage>
          DOI: 10.18287/
          <fpage>2412</fpage>
          - 6179-2017-41-4-
          <fpage>588</fpage>
          -591
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>