Medical Image Registration with Fourier basis Functions

Registration is one of the most interesting, yet challenging computer-aided tasks in medical image processing, aimed at bringing two or more data sets into spatial and/or temporal correlation. If the represented data are medical images, there are countless situations where it is of interest to attain such correlation, as it has become routine practice in many diagnostic and image-guided therapeutic procedures. For example, one of the most frequent clinical applications is to align two scans of a given patient, e.g. for easy identification of equivalent structures on both registered images, follow-up of disease, etc. Another use of image registration is commonplace during brain activation studies, where several functional Magnetic Resonance (fMRI) or Positron Emission Tomography (PET) scans are repeated on the same or different subjects while receiving sensorial or cognitive stimulations. In order to perform a statistical analysis on the brain images, it is often necessary to register all data sets with respect to a brain atlas. In this way, both statistical power and signal-to-noise ratio are enhanced in what is known as intramodality registration (Friston et al, 2006). One of the most exciting applications is inter-modality registration, e.g. correlating PET and MR (Magnetic Resonance) scans of a same subject, or PET vs. CT (Computed Tomography). PET imaging provides distinctive functional and metabolic information, but lacks the high anatomical resolution which is in turn provided by conventional MR or CT. Thus PET/CT registration is synergic, since it facilitates the location of malignancies in their anatomical context. Moreover, this modality combination is often useful for Radiotherapy Planning (Townsend, 2008). An automatic image registration algorithm normally includes a floating image to be aligned to the coordinate system of a reference image. To do this, a spatial transformation function – containing a number of parameters-, must be proposed and applied to the former data set. The parameters are chosen in such a way that a proposed similarity measure between both data sets is optimized. This measure may be –for example-, the Normalized Mutual Information (NMI) or the Cross Correlation Coefficient. Methods which apply rigid-body transformations perform reasonably well for registering images of the head (brain) and extremity portions. In a 3D space, a rigid-body transformation involves only six parameters, e.g. three translations (Δx, Δy, Δz) and three