Medical Image Registration Using the Fourier Transform

Abstract

A Fourier Transform (FT) based pattern-matching algorithm was adapted for use in medical image registration. This algorithm obtained the FT of two images, determined the normalized cross-power spectrum of the transformed images, and then applied an inverse FT. The result was a delta function with a maximum value at the location corresponding to the distance between the two images; a similar method was used to recover rotations. This algorithm was first tested using a simple two-dimensional image, with induced shifts of ±20 pixels and ±10 degrees. All translations were recovered with no error and all rotations were recovered within 0.18 degrees. Subsequently, this algorithm was tested on eight clinical kV images drawn from four different body sites. Twenty-five random shifts and rotations were applied to each image. The average mean error of the registration solution was −0.002 ± 0.077 mm in the x direction, 0.002 ± 0.075 mm in the y direction, and −0.012 ± 0.099 degrees. These initial results suggest that a FT algorithm has a high degree of accuracy when registering clinical kV images.