Deformable CT Registration Using Fourier Basis Functions in 3D

Non-rigid medical image registration is an essential tool when studying deformable regions such as thorax and abdomen. In this paper we propose an algorithm based on Fourier transformations with trigonometric Fourier basis functions at different orders combined with a subdivision scheme in order to attain spatial alignment of two corresponding Computed Tomography (CT) volumes, with small to moderate deformations. The performance of the algorithm was analyzed as a function of the transformation order (n) and the number of volume subdivisions along each axis (s). The results show that a suitable parameter choice is n=2, s=3-4. The algorithm was validated by “correcting” clinical images previously deformed with Thin-Plate Splines (TPS), and also applied to coregister different scans of a given subject after repositioning on the scanner bed. This method is automatic and does not require previous segmentation or landmark selection. Average registration errors with the optimal parameters were estimated in approximately 3 mm, and typical computing time is of the order of a few minutes in a standard personal computer. We have found that Fourier basis functions provide an efficient way to implement non-rigid registration.