SU-E-J-93: Fourier Transform-Based Medical Image Registration

To evaluate the use of a Fast Fourier Transform (FFT) based pattern-matching algorithm for two-dimensional translational and rotational medical image registration.

The FFT pattern matching algorithm is based on the Fourier shift theorem. Briefly, image registration is accomplished by obtaining the Fourier Transform (FT) of two images, taking the normalized cross-correlation of the two FT, and performing an inverse FT on this correlation matrix. This results in a Dirchlet delta function that has a maximum value at a location corresponding to the translational shift between the two images. Rotational registration can also be achieved by performing this algorithm on the polar transformation of the FT images. The FT registration method was evaluated through the use of clinical images with induced translational and rotational shifts.

Over a range of induced shifts of +/-10 mm in both the x and y directions, and induced rotations of +/-10 degrees, all recovered rotations were within 0.1 degree of the induced rotation, and all recovered translations were within 0.5 mm of the induced translation. The computational time of the FT registration on a 1024×1024 image was approximately 2.23 sec.

An FFT based image registration algorithm is computationally efficient and provides a high degree of accuracy for two dimensional image registrations. The FFT registration approach provides a distinct analytical solution and does not rely on iterative methods to converge on a solution. In addition, the discrete nature of the FFT means that the accuracy of the solution is directly related to the size of the pixels in the images. The equivalent of sub-pixel registration can be achieved by simply resizing the image to a larger matrix (i.e. 512×512 to 1024×1024).