Abstract
Inverse consistency is a desirable property for image registration. We propose a simple technique to make a neural registration network inverse consistent by construction, as a consequence of its structure, as long as it parameterizes its output transform by a Lie group. We extend this technique to multi-step neural registration by composing many such networks in a way that preserves inverse consistency. This multi-step approach also allows for inverse-consistent coarse to fine registration. We evaluate our technique on synthetic 2-D data and four 3-D medical image registration tasks and obtain excellent registration accuracy while assuring inverse consistency .
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
Similar content being viewed by others
Notes
- 1.
Although in infinite dimensions, the name Lie algebra does not apply, in our case we only need the notions of the exponential map and tangent space at identity to preserve the inverse consistency property.
- 2.
Specifically, \(\texttt {networks.tallUNet2}\) and \(\texttt {networks.ConvolutionalMatrixNet}\) from the library icon_registration version 1.1.1 on pypi.
- 3.
- 4.
- 5.
Due to changes in the OASIS-1 data, our test set slightly differs from [14]. We evaluate all methods using our testing protocol so that results are consistent.
References
Arsigny, V., Commowick, O., Pennec, X., Ayache, N.: A Log-Euclidean framework for statistics on diffeomorphisms. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4190, pp. 924–931. Springer, Heidelberg (2006). https://doi.org/10.1007/11866565_113
Avants, B.B., Epstein, C.L., Grossman, M., Gee, J.C.: Symmetric diffeomorphic image registration with cross-correlation: evaluating automated labeling of elderly and neurodegenerative brain. Media 12(1), 26–41 (2008)
Balakrishnan, G., Zhao, A., Sabuncu, M.R., Guttag, J., Dalca, A.V.: VoxelMorph: a learning framework for deformable medical image registration. TMI 38(8), 1788–1800 (2019)
Castillo, R., et al.: A reference dataset for deformable image registration spatial accuracy evaluation using the COPDgene study archive. Phys. Med. Biol. 58(9), 2861 (2013)
Christensen, G.E., Johnson, H.J.: Consistent image registration. TMI 20(7), 568–582 (2001)
Eade, E.: Lie groups for 2D and 3D transformations (2013). http://ethaneade.com/lie.pdf. Revised Dec 117, 118
Greer, H., Kwitt, R., Vialard, F.X., Niethammer, M.: ICON: learning regular maps through inverse consistency. In: ICCV (2021)
Hoffmann, M., Billot, B., Greve, D.N., Iglesias, J.E., Fischl, B., Dalca, A.V.: SynthMorph: learning contrast-invariant registration without acquired images. TMI 41(3), 543–558 (2022)
Hoopes, A., Hoffmann, M., Greve, D.N., Fischl, B., Guttag, J., Dalca, A.V.: Learning the effect of registration hyperparameters with HyperMorph. arXiv preprint arXiv:2203.16680 (2022)
Iglesias, J.E.: EasyReg: a ready-to-use deep learning tool for symmetric affine and nonlinear brain MRI registration (2023)
Lie, S.: Theorie der transformationsgruppen i. Math. Ann. 16, 441–528 (1880)
Marcus, D.S., Wang, T.H., Parker, J., Csernansky, J.G., Morris, J.C., Buckner, R.L.: Open access series of imaging studies (OASIS): cross-sectional MRI data in young, middle aged, nondemented, and demented older adults. J. Cogn. Neurosci. 19(9), 1498–1507 (2007)
Mok, T.C.W., Chung, A.C.S.: Large deformation diffeomorphic image registration with Laplacian pyramid networks. In: Martel, A.L., et al. (eds.) MICCAI 2020. LNCS, vol. 12263, pp. 211–221. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-59716-0_21
Mok, T.C., Chung, A.C.: Fast symmetric diffeomorphic image registration with convolutional neural networks. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (2020)
Nazib, A., Fookes, C., Salvado, O., Perrin, D.: A multiple decoder CNN for inverse consistent 3D image registration. In: 2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI), pp. 904–907 (2021). https://doi.org/10.1109/ISBI48211.2021.9433911
Nevitt, M.C., Felson, D.T., Lester, G.: The osteoarthritis initiative. Protocol Cohort Study 1 (2006)
Petersen, R., et al.: Alzheimer’s disease neuroimaging initiative (ADNI): clinical characterization. Neurology 74(3), 201–209 (2010). https://doi.org/10.1212/WNL.0b013e3181cb3e25
Regan, E.A., et al.: Genetic epidemiology of COPD (COPDGene) study design. COPD: J. Chronic Obstr. Pulm. Dis. 7(1), 32–43 (2011)
Reuter, M., Rosas, H.D., Fischl, B.: Highly accurate inverse consistent registration: a robust approach. NeuroImage 53(4), 1181–1196 (2010). https://doi.org/10.1016/j.neuroimage.2010.07.020. https://www.sciencedirect.com/science/article/pii/S1053811910009717
Rushmore, R.J., et al.: Anatomically curated segmentation of human subcortical structures in high resolution magnetic resonance imaging: an open science approach. Front. Neuroanat. 16 (2022)
Rushmore, R.J., et al.: HOA-2/SubcorticalParcellations: release-50-subjects-1.1.0 (2022). https://doi.org/10.5281/zenodo.7080547
Shen, Z., Han, X., Xu, Z., Niethammer, M.: Networks for joint affine and non-parametric image registration. In: CVPR (2019)
Tian, L., et al.: GradICON: approximate diffeomorphisms via gradient inverse consistency (2022). https://doi.org/10.48550/ARXIV.2206.05897
Van Essen, D.C., et al.: The human connectome project: a data acquisition perspective. Neuroimage 62(4), 2222–2231 (2012)
Vishnevskiy, V., Gass, T., Szekely, G., Tanner, C., Goksel, O.: Isotropic total variation regularization of displacements in parametric image registration. TMI 36(2), 385–395 (2017)
Wang, D., et al.: PLOSL: population learning followed by one shot learning pulmonary image registration using tissue volume preserving and vesselness constraints. Media 79, 102434 (2022)
Zhang, J.: Inverse-consistent deep networks for unsupervised deformable image registration. CoRR abs/1809.03443 (2018). http://arxiv.org/abs/1809.03443
Acknowledgements
This research was supported by NIH awards RF1MH126732, 1R01-AR072013, 1R01-HL149877, 1R01 EB028283, R41-MH118845, R01MH112748, 5R21LM013670, R01NS125307, 2-R41-MH118845; by the Austrian Science Fund: FWF P31799-N38; and by the Land Salzburg (WISS 2025): 20102-F1901166-KZP, 20204-WISS/225/197-2019. The work expresses the views of the authors and not of the funding agencies. The authors have no conflicts of interest.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Greer, H. et al. (2023). Inverse Consistency by Construction for Multistep Deep Registration. In: Greenspan, H., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2023. MICCAI 2023. Lecture Notes in Computer Science, vol 14229. Springer, Cham. https://doi.org/10.1007/978-3-031-43999-5_65
Download citation
DOI: https://doi.org/10.1007/978-3-031-43999-5_65
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-43998-8
Online ISBN: 978-3-031-43999-5
eBook Packages: Computer ScienceComputer Science (R0)
