Vector fields created by Fourier transform of video signals

Abstract

The power spectrum and autocorrelation are widely used in video signals processing. The phase-frequency spectrum contains more information than the amplitude spectrum. However, the amplitude spectrum is used more often in the video signal process. It is possible to combine the advantages of these two spectra to obtain a vector function such as phase-energy spectrum. This spectrum is sensitive even to a small difference in pixel brightness but at the same time it is as stable as the power spectrum. In this paper, we explored the properties of the phase-power spectrum and related amplitude of partials vector field. We showed that phase-power spectrum has conservative as well as solenoidal components and so it creates curl’s vector field. We also found the components of phase-power spectra that contain pixels with a different degree of contrast on the uniform background. We showed the possibility to use solenoidal component of the phase-power vector field to find the circulation (i.e. field work). We concluded that the circulation along any of brightness contour constants, which is symmetrical to the origin, is equal zero. We explored two-dimensional vector field of the phase-power spectrum. Finally, we determined an effect of pixels with different degree of brightness and their relative position to the image’s edges on vector field’s components formation.