Analysis of image registration noise due to rotationally dependent aliasing

Abstract

This paper investigates factors that degrade the precision of image registration based on phase correlation. The major sources of error are interpolation error and rotationally dependent aliasing. The latter error stems from the fact that the discrete-Fourier transform does not commute with the rotation of sampled-images, whereas in the continuous domain the corresponding operations do commute. We show through a series of examples how much the various sources of error contribute to phase-correlation registration, and we demonstrate constructive techniques for improving precision and signal to noise ratio in the registration process. Since rotationally dependent aliasing is exacerbated by the presence of high frequencies, the examples demonstrate that the use of a Blackman window removes spurious high frequencies in the spectral leakage created by the image boundary and greatly reduces aliasing effects. Since remaining aliasing effects are strongest in the low frequencies of the Fourier transform, their effects can be reduced to a negligible amount by removing frequencies within a radius of N/4 of the Fourier domain origin. A third technique is to perform phase correlation over half the Fourier plane rather than over the full plane, which more than doubles the signal-to-noise ratio of phase correlation. For an example image, the combination of techniques improved the phase-correlation signal-to-noise ratio from 8.5 to 172 and raised the peak from 0.348 to 0.885, which are substantially higher values than previously reported.