On Comparing The Energy Concentration Of The Image Orthogonal Transforms

Evgeniy G. Zhilyakov, Andrey A. Chernomorets, Evgeniya V.Bolgova, Denis V.Ursol, Ekaterina I. Prokhorenko

In this article, we performed a study whose purpose is to compare the values of the so-called concentration of images energy in various subdomains of spatial frequencies into which we divided the domain of the analyzed image orthogonal transforms (such as discrete Fourier transform, discrete cosine transform, Haar transform, so-called integral Fourier transform and integral cosine transform). The concept of concentration of image energy in each frequency subdomain near zero frequency, proposed in this work, is one of the criteria for choosing a transformation for solving different image processing problems (for example, image compression or hidden embedding of control data into images etc.). For the considered orthogonal transformations, the values of the image energy concentration were obtained in subdomains of spatial frequencies of various sizes, while the concentration calculation process was performed both without subtracting the average brightness value of its pixels from the image and with removed average brightness value. The analysis of the values of the images energy concentration in the frequency domains of various sizes obtained by applying the considered transformations showed that in most cases, the results of the discrete cosine transformation have a greater value of the energy concentration. The analysis of the concentration values also showed that the results of the integral cosine transformation also have a significant concentration of their energy compared to other considered orthogonal transformations. It was also found that removing of the average brightness value from the image decreases the energy concentration values of the results of image orthogonal transformations. So, the using of discrete and so-called integral cosine image transform without removing image average brightness value is more preferable when solving different image processing tasks.

Volume 12 | Issue 6

Pages: 692-702

DOI: 10.5373/JARDCS/V12I6/S20201082