A Study of Sub-pixel Motion Estimation using Phase Correlation

We propose a method for obtaining high-accuracy sub-pixel motion estimates using phase correlation. Our method is motivated by recently published analysis according to which the Fourier inverse of the normalized cross-power spectrum of pairs of images which have been mutually shifted by a fractional amount can be approximated by a two-dimensional sinc function. We use a modified version of such a function to obtain a sub-pixel estimate of motion by means of variable-separable fitting in the vicinity of the maximum peak of the phase correlation surface. We demonstrate that our method outperforms, in terms of sub-pixel accuracy, not only other surface fitting techniques but also the state-of-the-art in motion estimation using phase correlation including the technique that motivated our work in the first place. Furthermore our method performs particularly well in the presence of artificially induced additive white Gaussian noise and also offers better motion vector coherence in terms of zero-order entropy.