Background: Systems of the Internet of Things are actively implementing biometric systems. For fast and high-quality recognition in sensory biometric control and management systems, skeletonization methods are used at the stage of fingerprint recognition. The analysis of the known skeletonization methods of Zhang-Suen, Hilditch, Ateb-Gabor with the wave skeletonization method has been carried out and it shows a good time and qualitative recognition results. Methods: The methods of Zhang-Suen, Hildich and thinning algorithm based on Ateb-Gabor filtration, which form the skeletons of biometric fingerprint images, are considered. The proposed thinning algorithm based on Ateb-Gabor filtration showed better efficiency because it is based on the best type of filtering, which is both a combination of the classic Gabor function and the harmonic Ateb function. The combination of this type of filtration makes it possible to more accurately form the surroundings where the skeleton is formed. Results: Along with the known ones, a new Ateb-Gabor filtering algorithm with the wave skeletonization method has been developed, the recognition results of which have better quality, which allows to increase the recognition quality from 3 to 10%. Conclusion: The Zhang-Suen algorithm is a 2-way algorithm, so for each iteration, it performs two sets of checks during which pixels are removed from the image. Zhang-Suen's algorithm works on a plot of black pixels with eight neighbors. This means that the pixels found along the edges of the image are not analyzed. Hilditch thinning algorithm occurs in several passages, where the algorithm checks all pixels and decides whether to replace a pixel from black to white if certain conditions are satisfied. This Ateb-Gabor filtering will provide better performance, as it allows to obtain more hollow shapes, organize a larger range of curves. Numerous experimental studies confirm the effectiveness of the proposed method.

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This article presents a new method of image filtering based on a new kind of image processing transformation, particularly the wavelet-Ateb–Gabor transformation, that is a wider basis for Gabor functions. Ateb functions are symmetric functions. The developed type of filtering makes it possible to perform image transformation and to obtain better biometric image recognition results than traditional filters allow. These results are possible due to the construction of various forms and sizes of the curves of the developed functions. Further, the wavelet transformation of Gabor filtering is investigated, and the time spent by the system on the operation is substantiated. The filtration is based on the images taken from NIST Special Database 302, that is publicly available. The reliability of the proposed method of wavelet-Ateb–Gabor filtering is proved by calculating and comparing the values of peak signal-to-noise ratio (PSNR) and mean square error (MSE) between two biometric images, one of which is filtered by the developed filtration method, and the other by the Gabor filter. The time characteristics of this filtering process are studied as well.

Biometric images were pre-processed and filtered in two ways, by wavelet- Gabor and wavelet Ateb-gabor filtration. Ateb-based Gabor filter is effective for filtration because it contains generalizations of trigonometric functions. The wavelet transform of Ateb-Gabor function was developed. The function dependence on seven parameters was shown, each of them significantly changes the filtering results of biometric images. The Ateb-Gabor wavelet research was performed. Graphic dependencies of the wavelet Gabor filter and the wavelet Ateb-Gabor filter were constructed. The appliance of wavelet transform makes it possible to reduce the complexity of calculating an Ateb-Gabor filter by simplifying function calculations and reducing filtering time. The complexities of algorithms for calculating the wavelet Gabor filter and the wavelet Ateb-Gabor filter have been evaluated. Ateb-Gabor filtration allows you to adjust the intensity of the entire image, and to change certain ranges, thereby changing certain areas of the image. Biometric images should have this property, on which the minucius should be contrasting and clear. Ateb functions have the property of changing two rational parameters, which will allow to make more flexible control of filtration. The properties of the Ateb function, as well as the possibility of changing the amplitude of the function, the oscillation frequency by the numerical values of the Ateb-Gabor filter, were investigated. By using the parameters of the Ateb function, you can get a much larger range of shapes and sizes, which expands the number of possible filtration options. You can also perform filtration once, taking into account the direction of the minucius and reliably determine the sharpness of the edges, rather than perform filtration many times. The reliability of results were tested using NIST Special Database 302 and good filtration results were shown. This is confirmed by the comparison experiment between the wavelet-Gabor filter and the wavelet Ateb-Gabor function based on the PSNR signal-to-noise ratio measurement.