Mass-preserving motion correction of PET: Displacement field vs. spline transformation

In Positron Emission Tomography (PET), motion due to the cardiac and respiratory cycle causes blurred images. Different approaches for motion correction in PET vary in the general concept (optical flow or image registration) or, e.g., in the discretization of motion. Given our mass-preserving transformation model, we evaluate different motion models in this work: dense displacement field (compute for each voxel an individual displacement) vs. spline transformation (i.e. free-form deformation). Thereby a focus is put on the parametrization of the spline transformations where we optimize the number of spline coefficients and the regularization parameter. We make a quantitative comparison of the motion estimates of the different motion models based on data of the established XCAT software phantom. For both motion models (Displacement Field (DF) and Spline Transformation (ST)) the registration results are evaluated by 1) the total processing time and 2) the Euclidean distance to the ground-truth vectors provided by the XCAT phantom. We found that the spline transformation model is superior to the displacement field strategy in terms of processing time and accuracy.