It is commonly used in image registration and relies on a frequency-domain representation of the data, usually calculated by fast Fourier transforms.
The term is applied particularly to a subset of cross-correlation techniques that isolate the phase information from the Fourier-space representation of the cross-correlogram.
: Obtain the normalized cross-correlation by applying the inverse Fourier transform.
Commonly, interpolation methods are used to estimate the peak location in the cross-correlogram to non-integer values, despite the fact that the data are discrete, and this procedure is often termed 'subpixel registration'.
A large variety of subpixel interpolation methods are given in the technical literature.
An especially popular FT-based estimator is given by Foroosh et al.[1] In this method, the subpixel peak location is approximated by a simple formula involving peak pixel value and the values of its nearest neighbors, where
Some methods shift the peak in Fourier space and apply non-linear optimization to maximize the correlogram peak, but these tend to be very slow since they must apply an inverse Fourier transform or its equivalent in the objective function.
[2] It is also possible to infer the peak location from phase characteristics in Fourier space without the inverse transformation, as noted by Stone.
[3] These methods usually use a linear least squares (LLS) fit of the phase angles to a planar model.
The long latency of the phase angle computation in these methods is a disadvantage, but the speed can sometimes be comparable to the Foroosh et al. method depending on the image size.
This fact also may limit the usefulness of high numerical accuracy in an algorithm, since the uncertainty due to interpolation method choice may be larger than any numerical or approximation error in the particular method.
The inverse Fourier transform of a complex exponential is a Dirac delta function, i.e. a single peak: This result could have been obtained by calculating the cross correlation directly.
The advantage of this method is that the discrete Fourier transform and its inverse can be performed using the fast Fourier transform, which is much faster than correlation for large images.
Unlike many spatial-domain algorithms, the phase correlation method is resilient to noise, occlusions, and other defects typical of medical or satellite images.
Due to properties of the Fourier transform, the rotation and scaling parameters can be determined in a manner invariant to translation.
will not be a simple delta function, which will reduce the performance of the method.
In such cases, a window function (such as a Gaussian or Tukey window) should be employed during the Fourier transform to reduce edge effects, or the images should be zero padded so that the edge effects can be ignored.
Phase correlation is the preferred method for television standards conversion, as it leaves the fewest artifacts.