Applying Ateb–Gabor Filters to Biometric Imaging Problems

Abstract

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.

Some Remarks on Smooth Mappings of Hilbert and Banach Spaces and Their Local Convexity Property

“…In particular, in [7][8][9], the convexity property was effectively applied toward solving existence problems for both functional-difference inclusions and kinetic equations of statistical physics. It proved to be especially fruitful for the theory of nonlinear differential-operator equations [10][11][12], control theory, and optimization theory [13,14]. Some interesting and important local convexity properties, relevant to mappings of Hilbert spaces, were initially discussed in [3], and later generalized and studied in [15][16][17], devoted to the closedness of quadratic mappings on a separable Hilbert space.…”