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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Fingerprint Recognition Technology with Ateb-Gabor Filtration</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Lviv Polytechnic National University</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Bandery str.</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ukraine mariia.a.nazarkevych@lpnu.ua</string-name>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Comenius University in Bratislava</institution>
          ,
          <addr-line>Bratislava</addr-line>
          ,
          <country country="SK">Slovakia</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Taras Shevchenko National University of Kyiv</institution>
          ,
          <addr-line>64/13, Volodymyrska Street, City of Kyiv, Ukraine, 01601 Kyiv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <fpage>0000</fpage>
      <lpage>0002</lpage>
      <abstract>
        <p>The identification of fingerprints in the security information system is investigated. Fingerprint scanning was performed, papillae thinning was performed, Sherlock and Monroe fields were orientated, Ateb-Gabor filtration was performed, and three-dimensional Ateb-Gabor properties were investigated for different rational parameters. Their effect on filtering and subsequently on identification is revealed. Ateb-Habor filtering for biometric prints is applied, which significantly extends classic filtering by implementing a broader set of filters and providing a comprehensive approach to identification. The skeleton was executed using the Hilditch algorithm. The next step is to create the direction fields, using the method proposed by Sherlock and Monroe when forming the direction field of the papillary lines. Uses an average spine / trough nine pixels period. This imitates a sensor with the discriminability of 500 dpi. Frequency in areas decreases depending on position. The Hilditch algorithm generates a vector image. This image is in the form of a loaded graph - that is, found endpoints, points of intersection of the top of the graph and the lines and arcs of the edges of the graph.</p>
      </abstract>
      <kwd-group>
        <kwd>Fingerprint</kwd>
        <kwd>identification</kwd>
        <kwd>Gabor filtering</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>Fingerprint identification has become widely used lately. Various types of sensors —
optical, capacities, ultrasonic and thermal — are used to obtain digital images of
fingerprints. To date, the most common fingerprint imaging sensors are optical sensors.</p>
      <p>There are two main categories of fingerprint comparison methods — the
comparison of defined points and the comparison of the whole pattern of the fingerprint — a
template-on. The pattern identification method compares two images to see its
resemblance. This method is typically used in fingerprint identification systems (show
Fig.1). More commonly used technology is recognition based on point-by-point
comparisons.</p>
    </sec>
    <sec id="sec-2">
      <title>Minus thinning method for biometric images</title>
      <p>
        Skeletonize algorithms are determined on consistent deletion of outline points.
These points get rid of and the line becomes thinned out. The thinning algorithm is the
removing of edge points where throughout the image moves mask 3 × 3. These set of
rules apply to every 3X3 window. Consider building a skeleton using the Hilditch
algorithm (show Fig.2). The algorithm is designed to work with binary images. The
algorithm is to scan the post-iterative pixel matrix of the image mask position and the
consistent change of black pixels on white. The algorithm was described in [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ].
      </p>
    </sec>
    <sec id="sec-3">
      <title>Constructing a fingerprint with directions</title>
      <p>
        To create the direction field, we use the method proposed by Sherlock and Monroe in
forming the direction field of the papillary lines. As stated in [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ], the description of
minutia is classified as spine completion, bifurcation or divergent fork, application,
convergence fork, inter junction or bridge, fragment or short spine, hook or spur,
return, rejected interrupts, intersection, point, dashed spine [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ].
      </p>
      <p>
        The Sherlock and Monroe method was proposed in [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] to form the directional field
of papillary lines. The model proposed by Sherlock and Monroe allows you to create a
direction field based on minute position information. The creation of papillary lines on
the basis of the direction field and the density field is as follows: the original image
containing some isolated singularities is gradually enlarged by the use of an
AtebGabor filter tuned to a certain density level.
      </p>
      <p>
        The orientation model proposed by Sherlock and Monroe [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] provides an image of
the orientation of the papillary lines taking into account the features of the nucleus and
the delta of the fingerprint (show Fig.3). In this model, each element of the direction
field is measured by its value. The local orientation of the papillary line is defined as
the phase of the rational function module, is in the same location as the fingerprint
nuclei and deltas (show Fig.4). The orientation for each point is determined by the
formula:
,
(1)
where    - functions defined for different deltas and nuclei
      </p>
      <p>
        … ,
   - j-е nuclei end    - i-delta in the complex plane [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ].
      </p>
      <p>The overall periodicity is selected consonant to the frequency distribution of the
comb lines in actual fingerprints. Uses an average spine / trough period of nine pixels.
This creates a sensor effect with a resolution of 500 dpi. Frequency in areas decreases
depending on position.</p>
      <p>The Sherlock and Monroe model is used as follows. The fingerprint is filtered by
Ateb-Gabor. Further, thinning is carried out. The positions of nuclei and deltas are
specified. A field of directions is built later.
2.1</p>
      <sec id="sec-3-1">
        <title>Gabor filtering</title>
        <p>Gabor wavelets are widely used for filtering fingerprints, and Gabor characteristics
are recognized as the best representation for fingerprint recognition in terms of
recognition factor. Moreover, it is demonstrated with resistance to changes in lighting and
noise. When only one reference image is available per scanned image, they offer an
adaptive weighted sub-Gabor's array for representing and recognizing fingerprints.</p>
        <p>
          In [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ], Gabor specifics were receiving for the classification of a classified
representation. The main disadvantage of Gabor methods is the size of the Gabor function
whose space is much larger as the images are collected by the Gabor filter bank. To
solve this problem, the Adaboost algorithm and Entropy and Genetic Algorithms (GA)
[
          <xref ref-type="bibr" rid="ref8">8</xref>
          ] are used to choose the most significant features of Gabor. But it is very difficult to
choose the best method from the many Gabor features. [
          <xref ref-type="bibr" rid="ref9">9</xref>
          ]. In addition, the removal of
Gabor's functions is very intensive, so these functions are not used for applications
nowadays [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ]. A simplified version of the Gabor wavelets was introduced in [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ].
Unfortunately, Gabor simplified features are more sensitive to changes in lighting than
original Gabor features.
        </p>
        <p>Gabor filters are typically used for texture analysis, edge detection, feature
extraction, unevenness estimation (in stereo), and more. Gabor filters include special classes
of bandpass filters that pass a certain frequency band and reject others.</p>
        <p>Images are filtered by Gabor filters in much the same way as conventional filters.
We have a mask, the more precise term for it will be the "convolution core" that
represents the filter. By mask we mean that we have a two-dimensional array. We use
twodimensional images. In these images, each pixel is assigned a weight value. The above
array moves on each pixel of the image and performs a convolution operation. When
applied to an image, the Gabor filter gives the greatest response at the edges and in
places where the texture changes. The following images show the test image and its
transformation after applying the filter.</p>
        <p>The Gabor filter responds to changes in edges and textures. The filter responds well
to the spatial location of the function. This occurs when coagulation kernels are applied
in the spatial domain, in the frequency domains.</p>
        <p>The method based on the application of the Gabor filter is quite simple and
effective in constructing images of papillary lines. An iterative change of an input image
containing one or more isolated sources causes the image to grow with local
orientation. As a result, a consistent and very realistic picture of the papillary lines gradually
emerges. In this case, in the random positions of the fingerprint appear minute different
types.
2.2</p>
      </sec>
      <sec id="sec-3-2">
        <title>Three-dimensional Ateb-Gabor filters</title>
        <p>
          Gabor filtering [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ] applies image modification. It is carried out by filtration, which
is divided into the real and imaginary part. The real part of the Gabor filter kernel is
realized by the cosine function. The imaginary part is constructed as a replacement of
the cosine by the sine.
        </p>
        <p>
          In this work we propose to use a Ateb-Gabor filtering to filter biometric
fingerprints, which greatly expands classic filtering, implementing a wider set of filters and
providing a comprehensive approach. Filtration [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ] is described by the formula:
(2)
where
where, φ - the parameter of data compression and scaling, σ - gaussian nucleus
standart deviation; m, n - the rational numbers periodical Ateb-function; ψ – lagging;
θ - parallel bandwidth of normal orientation; λ - the wavelength of the harmonic
function. The filter results are shown in Fig. 5 - m=9, n=0.5, =1, π, Fig. 6
m=3, n=5, =1, π, Fig. 7 - m=3, n=7, =1, π, Fig. 8 - m=3, n=11,
=1, π.
        </p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>Skeletonize</title>
      <p>Skeletonize transforms objects in images into a type of skeleton. This is distorted to
represent the topology of the object by performing sequential image passages. Each
time, pixel boundaries are identified and deleted, provided that they do not disrupt the
object. Many skeletonization algorithms have been developed as an iterative sequential
deletion of points on contours. Thinning algorithms, in particular Hilditch, work to
eliminate boundary points so that the 3 × 3 window moves across the pixels of the
image and the contents of the window apply the rules. Skeletonization works when
sequentially scaling images and then removing pixels at the edge of an object. This
lasts as long as there are no more pixels at the edge of the image. It works like a mask.
The search table is then used to write to pixels of values 0, 1, 2, or 3 that are selectively
deleted during iterations.</p>
      <p>
        Thinning algorithms are considered in the work of Rutovitz [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ], who first
proposed the algorithm, which works as a definition of the intersection number, and
allows you to perform parallel operations. This method can perform the entire
tourniquet.
      </p>
      <p>
        Another well-known algorithm is the Hilditch algorithm [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ]. The wave algorithm
is also known. It forms a vector image of the image in the form of a loaded graph - that
is, the definition of endpoints, intersection points of the vertex of the graph, and arcs
and lines bordering the edges of the graph.
      </p>
      <p>
        And work with thin vector elements was developed in [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ], which was
complicated by latent elements that were poorly printable. The application of machine learning
methods is devoted to the work [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ], which is based on the training of data neural
networks and the pre-filtering of images. And the work [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ] describes the recognition in
the video stream that is relevant and relevant to this study to change key images. The
development of information technology for data transmission and optimization based
on combinatorial methods is devoted to [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ], where the optimization algorithms are
taken. In [
        <xref ref-type="bibr" rid="ref18 ref19">18, 19</xref>
        ], the issue of image resolution enhancement, which took place when
identifying finger biometric, was considered.
      </p>
    </sec>
    <sec id="sec-5">
      <title>Fingerprint histogram alignment</title>
      <p>Histogram alignment is a nonlinear process. Separating channels and aligning each
channel individually is not a good way of leveling contrast. Alignment includes image
intensity values, not color components.</p>
      <p>This should be used to ensure that the intensity value is evenly balanced and does
not in any way disturb the color balance. Therefore, the first step is to rebuild the color
space from RGB into one of the color spaces, where the pixel intensity values are
separated from the color components.The binarization results are shown in Figure 9. The
initial image in grayscale is to the left Fig. 9a. In Figs. 9b shows an increase in
countergrowth, 9c shows segmentation, which consists of splitting a digital image into several
segments. This is done to simplify and change the presentation of the image to
facilitate its analysis. In Figs. 9d shows local normalization, which is to bring the image
back to the origin that is acceptable for recognition. In Figs. 9e shows a Gabor filter
transceiver. In Fig.10 show is image filtering: a - adding a processed image,
bbinarization; c - median filtration; d- function extrac, e -filtered image.</p>
      <p>
        If there are many colors in the image, the splitting method will cause a color
imbalance. After the images were processed, they were subject to RSA encryption according
to the algorithms [
        <xref ref-type="bibr" rid="ref20 ref21">20, 21</xref>
        ]. For grayscale images, work is devoted to the gray range
[
        <xref ref-type="bibr" rid="ref22">22</xref>
        ]. In [
        <xref ref-type="bibr" rid="ref23">23</xref>
        ], a method for identifying biometric images is presented.
Fig. 9. Fingerprint histogram alignment: a Input image, b - Contrast enhancement; c –
Segmentation; d - Local normalization; e - Gabor
      </p>
    </sec>
    <sec id="sec-6">
      <title>Conclusions</title>
      <p>Biometric fingerprints were identified and recognition was based on new filtering
techniques. Biometrics were scanned, and papillae were thinned using the Hilditch
algorithm. This method produces a vector representation of the image in the form of
downloaded graphs. This is done to separate the end points, that is, the points of
intersection of the top of the graph and the lines and arcs that contain the edges of the
graph.</p>
      <p>Field orientation was performed using the Sherlock and Monroe method.
AtebGabor-based filtering is implemented. Ateb-Gabor properties were investigated for
various rational parameters and their effect on filtering was carried out.
Fig. 10. Image filtering: a - adding a processed image, b-binarization; c - median filtration;
dfunction extrac, e -filtered image</p>
    </sec>
  </body>
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