Image/patient registration from (partial) projection data by the Fourier phase matching method

Abstract

A technique for 2D or 3D image/patient registration, PFPM (projection based Fourier phase matching method), is proposed. This technique provides image/patient registration directly from sequential tomographic projection data. The method can also deal with image files by generating 2D Radon transforms slice by slice. The registration in projection space is done by calculating a Fourier invariant (FI) descriptor for each one-dimensional projection datum, and then registering the FI descriptor by the Fourier phase matching (FPM) method. The algorithm has been tested on both synthetic and experimental data. When dealing with translated, rotated and uniformly scaled 2D image registration, the performance of the PFPM method is comparable to that of the IFPM (image based Fourier phase matching) method in robustness, efficiency, insensitivity to the offset between images, and registration time. The advantages of the former are that subpixel resolution is feasible, and it is more insensitive to image noise due to the averaging effect of the projection acquisition. Furthermore, the PFPM method offers the ability to generalize to 3D image/patient registration and to register partial projection data. By applying patient registration directly from tomographic projection data, image reconstruction is not needed in the therapy set-up verification, thus reducing computational time and artefacts. In addition, real time registration is feasible. Registration from partial projection data meets the geometry and dose requirements in many application cases and makes dynamic set-up verification possible in tomotherapy.

CT image registration in sinogram space

“…Similar to that studied by Lu et al, 17 the sinogram-based registration can be extended to 3D motion with six degrees of freedom under the assumption of small angle rotations ͑pitch or yaw͒ on a direction perpendicular to the central axis. Because of the limited practical usage of the approximation scheme, the details are presented in the Appendix .…”

“…Because of the limited practical usage of the approximation scheme, the details are presented in the Appendix . The derivation is essentially the same as that of Lu et al, 17 except that here it is done in the real space instead of the Fourier space.…”

“…Previously, registrations in projection data space have been investigated using Radon and Fourier transforms. [14][15][16][17][18] While this method is general, the inherent mathematical complexity makes it conceptually less intuitive and difficult to implement. Particularly, continuous and smooth images functions were assumed in order to perform the Fourier transformations and this made it problematic to register the case with metal implants.…”

“…Particularly, continuous and smooth images functions were assumed in order to perform the Fourier transformations and this made it problematic to register the case with metal implants. In order to be mathematically manageable, assumptions such as small rotation angles, 17 are often introduced, which further limits the inverse based approach.…”

Estimation of affine transformations directly from tomographic projections in two and three dimensions

“…In [11][12][13], a projection-based registration of two-dimensional datasets using rigid body transformation is discussed. In [14], these ideas are extended to three-dimensional datasets, allowing (non-uniform) scaling, translation and rotation as degrees of freedom. Due to the use of a Fourier phase matching method, this approach is very fast, but has the disadvantage that the maximum rotation angle around the x and y axis must be less than 10 • .…”