Six parameter patient registration directly from projection data

Pre-reconstruction rigid body registration for positron emission tomography: An initial validation against ground truth

“…al., developed originally for CT ( [1], [2], [3]), to PET and expands on the details of its implementation. The method is arguably better suited to PET than CT as the fan beam geometry of the latter is assumed by the method to be sufficiently well approximated by parallel beam projection; in PET the projections are inherently parallel beam.…”

“…The ECAT is a fully 3D scanner, and, as the method is presently only implemented in 2D (The pinciple extends to 3D, with projections in a spherical-polar space, as discussed in [2]), several in-plane slices from the 3D sinogram were combined to form a single 2D sinogram corresponding to a cross-section through the centre of the phantom. The angular resolution of the sinograms are 1.25 degrees and, after reconstruction, the voxel spacing is 2.25mm.…”

Similarity transformation parameters recovery based on Radon transform. Application in image registration and object recognition

“…Then, as it can be seen, the rotation property of the Radon transform often given in the literature ðf 3 r ðp; ϕÞ ¼ f 3 ðp; ϕ À ϕ 0 ÞÞ is only valid if ϕ 0 rϕ r ϕ 0 þπ as it is deduced from the lower parts of Eqs. (8) and (9). It is worth noting that the rotation of image by an angle ϕ 0 leads to a shifting of its RT by the same amount for some parts of the sinogram (for ϕ 0 r ϕ r ϕ 0 þ π) while for the other parts (for ϕ 0 þ π r ϕ rϕ 0 ) the RT is shifted by the same quantity ϕ 0 7 π but after a symmetrical transformation of the sinogram.…”

“…However, results remain fairly weak on some images. For the tomographic registration purpose, the algorithm in [8] uses some properties of the Radon and Fourier transforms, such as the central slice and Fourier shift theorems to identify translational and angular offsets and then, the fitting is obtained by using the cross-correlation method. Related to the NDT community, the work in [9] is devoted to the application of the Fourier phase matching method in the registration of radiography and computed tomography projections which has the potential to allow automated metrology and defect detection.…”

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.…”