Nonrigid registration of dynamic medical imaging data using nD + t B-splines and a groupwise optimization approach

Registration results for a synthetic image (left top) using a reference time point method, a consecutive time point method, a groupwise method and the cyclic and non-cyclic versions of the proposed method. The optimal transformation should describe a cosinus in the Y-direction and a flat line in the X-direction. [Display omitted] ►The development and evaluation of a registration method for motion estimation combining a Lagrangian nD + t B-spline transformation model, a global cost function and global optimizati on strategy. ►The possibility to include a cyclic motion constraint that is strictly enforced by the transformation model. ►The quantitative comparison of the proposed technique with three well-known techniques. ► The software developed for this publication is publicly available. A registration method for motion estimation in dynamic medical imaging data is proposed. Registration is performed directly on the dynamic image, thus avoiding a bias towards a specifically chosen reference time point. Both spatial and temporal smoothness of the transformations are taken into account. Optionally, cyclic motion can be imposed, which can be useful for visualization (viewing the segmentation sequentially) or model building purposes. The method is based on a 3D (2D + time) or 4D (3D + time) free-form B-spline deformation model, a similarity metric that minimizes the intensity variances over time and constrained optimization using a stochastic gradient descent method with adaptive step size estimation. The method was quantitatively compared with existing registration techniques on synthetic data and 3D + t computed tomography data of the lungs. This showed subvoxel accuracy while delivering smooth transformations, and high consistency of the registration results. Furthermore, the accuracy of semi-automatic derivation of left ventricular volume curves from 3D + t computed tomography angiography data of the heart was evaluated. On average, the deviation from the curves derived from the manual annotations was approximately 3%. The potential of the method for other imaging modalities was shown on 2D + t ultrasound and 2D + t magnetic resonance images. The software is publicly available as an extension to the registration package elastix.