Abstract
Deformable image registration is a fundamental step in many medical image analysis tasks and has attracted a large amount of research to develop efficient and accurate unsupervised machine learning approaches. Although much attention has been paid to finding suitable similarity measures, network architectures and training methods, much less research has been devoted to suitable regularization techniques to ensure the plausibility of the learned deformations.
In this paper, we propose implicitly solved regularizers for unsupervised and weakly supervised learning of deformable image registration. In place of pure gradient descent with automatic differentiation, we combine efficient implicit solvers for the regularization term with the established gradient-based optimization regarding the network parameters. As a result, our approach is broadly applicable and can be combined with a range of similarity measures and network architectures. Our experiments with state-of-the-art network architectures show that the proposed approach has the potential to increase the smoothness, i.e. the plausibility, of the learned deformations and the registration accuracy measured as dice overlaps. Furthermore, we show that due to efficient GPU implementations of the implicit solvers, this increase in plausibility and accuracy comes at almost no additional cost in terms of computational time.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Balakrishnan, G., Zhao, A., Sabuncu, M.R., Guttag, J., Dalca, A.V.: VoxelMorph: a learning framework for deformable medical image registration. IEEE Trans. Med. Imaging 38(8), 1788–1800 (2019)
Bhalodia, R., Elhabian, S.Y., Kavan, L., Whitaker, R.T.: A cooperative autoencoder for population-based regularization of CNN image registration. In: Shen, D., et al. (eds.) MICCAI 2019. LNCS, vol. 11765, pp. 391–400. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-32245-8_44
Burger, M., Modersitzki, J., Ruthotto, L.: A hyperelastic regularization energy for image registration. SIAM J. Sci. Comput. 35(1), B132–B148 (2013)
Cachier, P., Bardinet, E., Dormont, D., Pennec, X., Ayache, N.: Iconic feature based nonrigid registration: the PASHA algorithm. Comput. Vis. Image Underst. 89(2), 272–298 (2003)
Chen, J., Frey, E.C., He, Y., Segars, W.P., Li, Y., Du, Y.: TransMorph: transformer for unsupervised medical image registration. Med. Image Anal. 82, 102615 (2022)
Chen, J., He, Y., Frey, E., Li, Y., Du, Y.: ViT-V-Net: vision transformer for unsupervised volumetric medical image registration. arXiv preprint arXiv:2104.06468 (2022)
Cheng, X., Zhang, L., Zheng, Y.: Deep similarity learning for multimodal medical images. Comput. Methods Biomech. Biomed. Eng. Imag. Visualiz. 6(3), 248–252 (2018)
Christensen, G., Rabbitt, R., Miller, M.: Deformable templates using large deformation kinematics. IEEE Trans. Image Process. 5(10), 1435–1447 (1996)
Cohen, L.D.: Auxiliary variables and two-step iterative algorithms in computer vision problems. J. Math. Imaging Vision 6(1), 59–83 (1996)
Ferrante, E., Dokania, P.K., Silva, R.M., Paragios, N.: Weakly supervised learning of metric aggregations for deformable image registration. IEEE J. Biomed. Health Inform. 23(4), 1374–1384 (2019)
Fischer, B., Modersitzki, J.: A unified approach to fast image registration and a new curvature based registration technique. Linear Algebra Appl. 380, 107–124 (2004)
Fu, Y., Lei, Y., Wang, T., Curran, W.J., Liu, T., Yang, X.: Deep learning in medical image registration: a review. Phys. Med. Biol. 65(20), 20TR01 (2020)
Geman, D., Yang, C.: Nonlinear image recovery with half-quadratic regularization. IEEE Trans. Image Process. 4(7), 932–946 (1995)
Haskins, G., et al.: Learning deep similarity metric for 3D MR-TRUS image registration. Int. J. Comput. Assist. Radiol. Surg. 14(3), 417–425 (2019)
Hering, A., et al.: Learn2Reg: comprehensive multi-task medical image registration challenge, dataset and evaluation in the era of deep learning. IEEE Trans. Med. Imaging 1 (2022)
Hu, Y., et al.: Adversarial deformation regularization for training image registration neural networks. In: Frangi, A.F., et al. (eds.) MICCAI 2018. LNCS, vol. 11070, pp. 774–782. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00928-1_87
Hu, Y., et al.: Weakly-supervised convolutional neural networks for multimodal image registration. Med. Image Anal. 49, 1–13 (2018)
Ji, Y., et al.: Amos: a large-scale abdominal multi-organ benchmark for versatile medical image segmentation. Adv. Neural. Inf. Process. Syst. 35, 36722–36732 (2022)
Kim, B., Kim, D.H., Park, S.H., Kim, J., Lee, J.G., Ye, J.C.: CycleMorph: cycle consistent unsupervised deformable image registration. Med. Image Anal. 71, 102036 (2021)
Modersitzki, J.: Numerical methods for image registration. In: Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford (2003)
Mok, T.C.W., Chung, A.C.S.: Fast symmetric diffeomorphic image registration with convolutional neural networks. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 4644–4653 (2020)
Pace, D.F., Aylward, S.R., Niethammer, M.: A locally adaptive regularization based on anisotropic diffusion for deformable image registration of sliding organs. IEEE Trans. Med. Imaging 32(11), 2114–2126 (2013)
Paszke, A., et al.: Automatic differentiation in PyTorch. In: NIPS 2017 Workshop Autodiff (2017). https://openreview.net/forum?id=BJJsrmfCZ
Qin, C., Wang, S., Chen, C., Qiu, H., Bai, W., Rueckert, D.: Biomechanics-informed neural networks for myocardial motion tracking in MRI. In: Martel, A.L., et al. (eds.) MICCAI 2020. LNCS, vol. 12263, pp. 296–306. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-59716-0_29
Schmidt-Richberg, A., Werner, R., Handels, H., Ehrhardt, J.: Estimation of slipping organ motion by registration with direction-dependent regularization. Med. Image Anal. 16, 150–159 (2012)
de Vos, B.D., Berendsen, F.F., Viergever, M.A., Sokooti, H., Staring, M., Išgum, I.: A deep learning framework for unsupervised affine and deformable image registration. Med. Image Anal. 52, 128–143 (2019)
Wang, J., Zhang, M.: DeepFLASH: an efficient network for learning-based medical image registration. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 4444–4452 (2020)
Weickert, J., Romeny, B., Viergever, M.: Efficient and reliable schemes for nonlinear diffusion filtering. IEEE Trans. Image Process. 7(3), 398–410 (1998)
Werner, R., Schmidt-Richberg, A., Handels, H., Ehrhardt, J.: Estimation of lung motion fields in 4D CT data by variational non-linear intensity-based registration: a comparison and evaluation study. Phys. Med. Biol. 59(15), 4247–4260 (2014)
Xu, Z., et al.: Double-uncertainty guided spatial and temporal consistency regularization weighting for learning-based abdominal registration. In: Wang, L., Dou, Q., Fletcher, P.T., Speidel, S., Li, S. (eds.) Medical Image Computing and Computer Assisted Intervention, MICCAI 2022, LNCS, pp. 14–24. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-16446-0_2
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Ehrhardt, J., Handels, H. (2024). Implicitly Solved Regularization for Learning-Based Image Registration. In: Cao, X., Xu, X., Rekik, I., Cui, Z., Ouyang, X. (eds) Machine Learning in Medical Imaging. MLMI 2023. Lecture Notes in Computer Science, vol 14348. Springer, Cham. https://doi.org/10.1007/978-3-031-45673-2_14
Download citation
DOI: https://doi.org/10.1007/978-3-031-45673-2_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-45672-5
Online ISBN: 978-3-031-45673-2
eBook Packages: Computer ScienceComputer Science (R0)
