Displacement estimation by the phase-shiftings of Fourier transform in present white noise

Displacement estimation is a fundamental problem in Real-time video image processing. It can be typically approached by theories based on features in spatial domain. This paper presents an algorithm which improves the theory for estimating the moving object's displacement in spatial domain by its Fourier transform frequency spectrum. Because of the characters of Fourier transform, the result is based on all the features in the image. Utilizing shift theorem of Fourier transform and auto-registration, the algorithm employs the phase spectrum difference in polar coordinate of two frame images sequence with the moving target.The method needn't transform frequency spectrum to spatial domain after calculation comparing with the traditional algorithm which has to search Direc peak, and it reduces processing time. Since the technique proposed uses all the image information, including all the white noise in the image especially, and it's hard to overcome the aliasing from noises, but the technique can be an effective way to analyze the result in little white noise by the different characters between high and low frequency bands. It can give the displacement of moving target within 1 pixel of accuracy. Experimental evidence of this performance is presented, and the mathematical reasons behind these characteristics are explained in depth. It is proved that the algorithm is fast and simple and can be used in image tracking and video image processing.