A study of sub-pixel motion estimation using phase correlation

Abstract

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.

Performance of correlation approaches for the evaluation of spatial distortion reductions

“…However, three broadly used sub-pixel precise DIC techniques and one enhancement were tested as pre-processing validation tools. Those are the two-dimensional Gaussian peak fit (Argyriou and Vlachos 2006;Debella-Gilo and Kääb 2011;Nobach and Honkanen 2005), the poly phase technique from Foroosh et al (2006), the iterative phase approach from Averbuch and Keller (2002) and its proposed enhancement. Other modern techniques, from e.g Stone et al (2001); Tzimiropoulos et al (2011), were not compared due to the overlap of compared methods and used samples.…”

Optical flow estimation using Fourier Mellin Transform

“…We employ a recently proposed method in [2] to obtain high accuracy sub-pixel motion estimates for our algorithm. We can increase the accuracy of the rotation and scale parameters by using high resolution for the log polar coordinates in Section 2.…”

“…However, such methods are computationally expensive and require the storage of a significant amount of data. In [2], a method of calculating subpixel accuracy by fitting a modified sinc function to the peaks of the phase correlation was proposed:…”

“…As a result, a more accurate estimation of the optical flow can be achieved. We also estimate the optical flow to sub-pixel accuracy based on a recently proposed algorithm that uses a 2D sinc function in fitting the phase correlation outputs [2]. Furthermore, a vector weighted average filter that uses phase correlation scores from the FMT as weighting coefficients is proposed in order to smooth the optical flow.…”

“…Its most important advantage is its immunity to illumination changes and moving shadows because the phase correlation function is normalized by the Fourier magnitude [2]. Furthermore, as the phase correlation method is performed in the frequency domain, it is much more computationally efficient than the block matching method [20].…”