=Paper= {{Paper |id=Vol-2105/10000477 |storemode=property |title=None |pdfUrl=https://ceur-ws.org/Vol-2105/10000477.pdf |volume=Vol-2105 }} ==None== https://ceur-ws.org/Vol-2105/10000477.pdf 
     Development of the Ateb-Gabor Filtration Method
             in Biometric Protection Systems

                                  Nazarkevych Mariya 1
                   1 Lviv Polytechnic National University, Lviv, Ukraine

                         mariia.a.nazarkevych@lpnu.ua



      Abstract. The Gabor filter for biometric images has been investigated. Intro-
      duced a new Ateb-Gabor filter to improve the quality of fingerprint images. The
      sequence of filtration and recognition of biometric data is developed. For relia-
      ble fingerprint recognition, image correction is required, since interference
      caused by scanning may distort the lines of the imprints, which creates errors in
      recognition. The mathematical apparatus of the Ateb-functions provides addi-
      tional functions for controlling Gabor's filtration, since it has a wider range of
      filtering options. It has been shown that the use of the Ateb-Gabor filter has a
      more controlling influence on the image, because in addition there are two pa-
      rameters of rational numbers that considerably extends the filtration process.
      The method of filtering images based on the Gabor filter using Ateb-functions
      is developed. At present, work is being done on the application of a new filter to
      biometric images, bringing it to a finished software product. A two-dimensional
      Gabor filter is also developed, which in the future will allow people to recog-
      nize faces.


      Keywords: Ateb-Gabor; Gabor Filter; Image processing.


1     Introduction

With the development of information technology, biometrics has become an essential
part of our everyday lives. Biometric identification systems require constant im-
provement since they work fairly slowly and often give the wrong results. new meth-
ods have been developed for fingerprint analysis, which scans them without any con-
tact [1]. Similarly, the scanning and recognition technologies in 3D space appeared
[2]. As a result, professional systems for recognition were developed [3]. Using the
technology of the "large data" processing, modern surveillance systems and access
control systems identify individual fragments of biometrics more accurately, and
technologies for identifying specific people in the stream are developed [4].
2      Gabor Filters and Image Processing

One of the most popular methods for selecting the edges in the image is the use of
Gabor filters [5]. The real part of the nucleus of the Gabor filter are constructed using
[6]. To construct an imaginary part of the Gabor filter, it is necessary to replace the
cosine function with the sine calculation in the above formula.


3      Filtration

The filtration process involves the convolution of the filter and the input signal in the
spatial domain. In this paper, it was done in the Wolfram Mathematica 11 computing
environment [7]. Multiplication in the spatial domain is equivalent to convolution in
the frequency domain [8].

                                                π‘Ÿ = π‘–π‘šπ‘Žπ‘”π‘’ βˆ— π‘“π‘–π‘™π‘‘π‘’π‘Ÿ                     (3)

where r - is the result of filtration; * - convolution and π‘“π‘–π‘™π‘‘π‘’π‘Ÿ - Fourier transform of
the Gabor filter. The Fourier transform of the Gabor filter is a Gaussian signal [8],
whose center is located at the center frequency of the filter. As a result of multiplica-
tion in the frequency domain, the amplitude of the output frequency close to the si-
nusoidal signal increases, while others decreases.


3.1    Implementation of the Gabor filter
The width and height of the filter are determined by the width and height of the
Gaussian component. Determining the correct width and height for the Gabor filter is
essential while designing new filters. Experimentally established [9] that a good filter,
capable of detecting narrow edges at a certain frequency should have boundaries in
the plane z = 0 and also it should have two negative and one positive peak.


3.2    Generalized One-Dimensional Ateb-Gabor Filter
We construct a generalized one-dimensional Gabor filter basing on the Ateb-functions
[10]. It will look like:
                                           πœ”2
                      𝑔(π‘š, 𝑛, πœ”) = 𝑒
                                       βˆ’
                                           2𝜎 2 ca (π‘š, 𝑛, 2    , ,  ),
where 𝜎 - is the standard deviation of the Gaussian nucleus, which determines the
amplitude of the function, πœ” - is the frequency of oscillations, which is defined as
πœ” = 1/𝑇 , Π΄Π΅ T(m, n) – is the period of Ateb function ca (π‘š, 𝑛, 2  , ,  ), 2  βˆ’
 period of Ateb-function.
    The experimental results of the filtration are shown in the figure below. In fig.1 a is
filtered by an ordinary Gabor filter, and fig.1 b filter is Ateb-Gabor with m=n=3 with
the best results of filtration.
                          a                                  b
          Fig.1. Filtration a) ordinary Gabor filter b) Ateb-Gabor filter with m=n=3

   The optimal correlation between frequency and width of the Gabor filter has been
determined, which allowed performing filters automatically with the purpose of find-
ing the edges of objects with different frequencies, sizes and directions. The optimal
correlation is in each specific image of its own. The method of removing the average
component of the Gabor filter is proposed, which allows reducing the value of the
average filter to zero without deforming the filter. The results of numerous experi-
ments demonstrate the successful selection of edges in the image based on the results
obtained in the work of the Gabor filter parameters.


4      Image Processing Using the Gabor Filter

In each fingerprint, you can identify two types of attributes - global and local. Global
signs are those that are visible to the naked eye. Another type of attributes is local.
    They are selected because lines of the fingerprints are not straight. These points
provide unique fingerprint information in the process of identifying a person. Each
printout contains up to 70 minutia points [10].
    The implementation of the Gabor filter for images takes place in five steps.
Step1. Image normalization. Normalization of the image is necessary in order to set
the previous mean values and deviations.
Step2. Calculation of the orientation.The orientation image Img represents the ma-
trix N Γ— N, in which each component Img (i, j) shows the local orientation, angle of
inclination at a given point of the line with coordinates (i, j).
Step 3. Calculation of the frequency image. The frequency image is a matrix of size
N Γ— N, in which each component Img (i, j) shows the local frequency of the lines at a
given point, which is defined as the frequency of the crests directed along the orienta-
tion of the protrusion. On the next step, the skeletelization of the image is based on
the wave method [11].
Step4. Binarization of the image.
Step 5. Apply to the binary image of the Gabor filter. The filter is configured for
the local orientation of the speeches, applied to the pixels of the projections and vices
of the image.
5      Conclusions

The Gabor filter for biometric images has been developed. A new filter of Ateb-
Gabor has been investigated and its efficiency in application to biometrics has been
proved. Work is carried out to filter images and study their characteristics based on
one-dimensional and two-dimensional Gabor filter. We think that we will achieve
significant results in the near future. The use of a generalized Gabor filter will allow
for better filtration and have a large number of parameters to choose from for the best
filtering options. The change of the parameters m and n provides different values of
the period, which makes it possible to expand the number of filter options. To solve
the problem of fingerprint identification, the Ateb-Gabor function allows you to im-
prove identification, and, based on it, filtration of images with a large number of
ridges. This provides better characteristics than the usual one-dimensional Gabor
filter.


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