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Deterministic approaches using iterative optimisation have been historicallysuccessful in diffeomorphic image registration (DiffIR). Although theseapproaches are highly accurate, they typically carry a significantcomputational burden. Recent developments in stochastic approaches based ondeep learning have achieved sub-second runtimes for DiffIR with competitiveregistration accuracy, offering a fast alternative to conventional iterativemethods. In this paper, we attempt to reduce this difference in speed whilstretaining the performance advantage of iterative approaches in DiffIR. We firstpropose a simple iterative scheme that functionally composes intermediatenon-stationary velocity fields to handle large deformations in images whilstguaranteeing diffeomorphisms in the resultant deformation. We then propose aconvex optimisation model that uses a regularisation term of arbitrary order toimpose smoothness on these velocity fields and solve this model with a fastalgorithm that combines Nesterov gradient descent and the alternating directionmethod of multipliers (ADMM). Finally, we leverage the computational power ofGPU to implement this accelerated ADMM solver on a 3D cardiac MRI dataset,further reducing runtime to less than 2 seconds. In addition to producingstrictly diffeomorphic deformations, our methods outperform bothstate-of-the-art deep learning-based and iterative DiffIR approaches in termsof dice and Hausdorff scores, with speed approaching the inference time of deeplearning-based methods.

Nesterov Accelerated ADMM for Fast Diffeomorphic Image Registration