  We present a highly parallel method for accurate and efficient variational
deformable 3D image registration on a consumer-grade graphics processing unit
(GPU). We build on recent matrix-free variational approaches and specialize the
concepts to the massively-parallel manycore architecture provided by the GPU.
Compared to a parallel and optimized CPU implementation, this allows us to
achieve an average speedup of 32.53 on 986 real-world CT thorax-abdomen
follow-up scans. At a resolution of approximately $256^3$ voxels, the average
runtime is 1.99 seconds for the full registration. On the publicly available
DIR-lab benchmark, our method ranks third with respect to average landmark
error at an average runtime of 0.32 seconds.
