Використання швидких алгоритмів обчислення кореляції і згортки для підготовки еталонних зображень

Abstract

It is considered the several methods for calculating of the cross-correlation function and convolution of two images to solve the problem of reference image preparation for the correlation-extremal guidance system of the controlled aerial vehicles. During the flight the correlation-extremal guidance system performs a comparison of reference images of sighting surface, prepared before, and current images from the onboard sensors. To form optimal reference images the calculation of the cross-correlation function (or its analogues) of initial images and preliminary variants of reference images is executed repeatedly, so it takes considerably amount of time.In this work the formula of modified 2-D Hartley Transform with separated variables is obtained, so it is allows construct analytical expression of recursive base operation (analogue of the 2-D Fast Fourier Transform algorithm).The estimation of computational complexity of the cross-correlation function and convolution with using of algorithms of 2-D Discrete Fourier Transform (DFT), 2-D Fast Fourier Transform (FFT), 2-D Discrete Hartley Transform (DHT) and 2-D Fast Hartley Transform (FHT) is conducted.The obtained analytical expressions of the number of operations show that the using of modified 2-D FHT with separated variables allows to reduce amount of operations for the cross-correlation function of two images by one third. Moreover, the calculation of DHT and FHT is performed in the field of real numbers (in contrast to DFT and FFT), therefore it does not doubling of amount of RAM to store and operate of the real and imaginary components.The conducted studies show that since the initial images for reference images preparation are usually large enough, the using of modified 2-D FHT for cross-correlation function calculation allows to reduce the time of quality estimation and selecting of optimal reference image for the controlled aerial vehicle flight correction.