Extension of phase correlation to subpixel registration

Abstract

Abstract-In this paper, we have derived analytic expressions for the phase correlation of downsampled images. We have shown that for downsampled images the signal power in the phase correlation is not concentrated in a single peak, but rather in several coherent peaks mostly adjacent to each other. These coherent peaks correspond to the polyphase transform of a filtered unit impulse centered at the point of registration. The analytic results provide a closed-form solution to subpixel translation estimation, and are used for detailed error analysis. Excellent results have been obtained for subpixel translation estimation of images of different nature and across different spectral bands.

Subpixel Alignment of MRI Data Under Cartesian and Log-Polar Sampling

“…To demonstrate this, let us examine the phase difference function in (2). Inverse transforming this phase angle would yield…”

“…A discrete interpretation of this continuous-domain result is used in practice for image registration [1,5], which yields very good results, and was also extended to sub-pixel registration in [2]. However, for MRI, which provides directly the Fourier spectrum of the field of view, it would be interesting from both practical and computational points of view to estimate the shifts directly in the Fourier domain.…”

Robust Phase-Correlation Based Registration of Airborne Videos Using Motion Estimation

“…For subpixel displacements between the images, the delta function of the PC is spread over a small neighborhood, corresponding to a Dirichlet kernel (Foroosh et al 2002). The zero-padding of the normalized cross power spectrum Rðg; nÞ; as suggested by (Marcel et al 1997), involves the inverse Fourier transform of a large matrix.…”

Globally Optimal Multimodal Rigid Registration: An Analytic Solution using Edge Information

“…In this paper, we address the idea of computing the registration parameters for a multimodal registration scenario using only global operations. This type of globally-exhaustive registration has enjoyed much success in monomodal registration [1,2,3,4], but has yet to be deployed effectively in a multimodal environment.…”

“…This can be done in a few different ways. Probably the most popular is the phase correlation technique [1,2,4], whereby the corresponding Fourier coefficients of the two images are divided (canceling their magnitudes), leaving only their phase differences; the inverse FT of this phase image yields a single spike impulse whose location indicates the optimal shift of one image to align it with the other. Another approach is to compute either the cross-correlation [8] or sum of squared differences [9] cost function, using the maximum or the minimum (respectively) to indicate the correct shift.…”