Abstract
Deterministic approaches using iterative optimisation have been historically successful in diffeomorphic image registration (DiffIR). Although these approaches are highly accurate, they typically carry a significant computational burden. Recent developments in stochastic approaches based on deep learning have achieved sub-second runtimes for DiffIR with competitive registration accuracy, offering a fast alternative to conventional iterative methods. In this paper, we attempt to reduce this difference in speed whilst retaining the performance advantage of iterative approaches in DiffIR. We first propose a simple iterative scheme that functionally composes intermediate non-stationary velocity fields to handle large deformations in images whilst guaranteeing diffeomorphisms in the resultant deformation. We then propose a convex optimisation model that uses a regularisation term of arbitrary order to impose smoothness on these velocity fields and solve this model with a fast algorithm that combines Nesterov gradient descent and the alternating direction method of multipliers (ADMM). Finally, we leverage the computational power of GPU to implement this accelerated ADMM solver on a 3D cardiac MRI dataset, further reducing runtime to less than 2 s. In addition to producing strictly diffeomorphic deformations, our methods outperform both state-of-the-art deep learning-based and iterative DiffIR approaches in terms of dice and Hausdorff scores, with speed approaching the inference time of deep learning-based methods.
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Notes
- 1.
Momentum is the dual form of velocity. They are connected by a symmetric, positive semi-definite Laplacian operator as defined in Eq. (6).
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Acknowledgements
The research is supported by the BHF Accelerator Award (AA/18/2/34218), the Ramsay Research Fund from the School of Computer Science at the University of Birmingham and the Wellcome Trust Institutional Strategic Support Fund: Digital Health Pilot Grant.
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Thorley, A. et al. (2021). Nesterov Accelerated ADMM for Fast Diffeomorphic Image Registration. In: de Bruijne, M., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2021. MICCAI 2021. Lecture Notes in Computer Science(), vol 12904. Springer, Cham. https://doi.org/10.1007/978-3-030-87202-1_15
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