Nesterov accelerated ADMM for fast diffeomorphic image registration

Alexander Thorley, Xi Jia, Hyung Jin Chang, Boyang Liu, Karina Bunting, Victoria Stoll, Antonio de Marvao, Declan P. O’Regan, Georgios Gkoutos, Dipak Kotecha, Jinming Duan*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish
Title of host publicationMedical Image Computing and Computer Assisted Intervention – MICCAI 2021
Subtitle of host publication24th International Conference, Strasbourg, France, September 27–October 1, 2021, Proceedings, Part IV
EditorsMarleen de Bruijne, Philippe C. Cattin, Stéphane Cotin, Nicolas Padoy, Stefanie Speidel, Yefeng Zheng, Caroline Essert
Number of pages11
ISBN (Electronic)9783030872021
ISBN (Print)9783030872014
Publication statusPublished - 21 Sept 2021
Event24th International Conference on Medical Image Computing and Computer Assisted Intervention, MICCAI 2021 - Virtual, Online
Duration: 27 Sept 20211 Oct 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12904 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference24th International Conference on Medical Image Computing and Computer Assisted Intervention, MICCAI 2021
CityVirtual, Online

Bibliographical note

Funding Information:
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.

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.


  • ADMM
  • Diffeomorphism
  • Image registration

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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