Fast 4D elastic group-wise image registration. Convolutional interpolation revisited

Background and Objective:This paper proposes a new and highly efficient implementation of 3D+t groupwise registration based on the free-form deformation paradigm. Methods:Deformation is posed as a cascade of 1D convolutions, achieving great reduction in execution time for evaluation of transformations and gradients. Results:The proposed method has been applied to 4D cardiac MRI and 4D thoracic CT monomodal datasets. Results show an average runtime reduction above 90%, both in CPU and GPU executions, compared with the classical tensor product formulation. Conclusions:Our implementation, although fully developed for the metric sum of squared differences, can be extended to other metrics and its adaptation to multiresolution strategies is straightforward. Therefore, it can be extremely useful to speed up image registration procedures in different applications where high dimensional data are involved.