Abstract
Anatomically plausible image registration often requires volumetric preservation. Previous approaches to incompressible image registration have exploited relaxed constraints, ad hoc optimisation methods or practically intractable computational schemes. Divergence-free velocity fields have been used to achieve incompressibility in the continuous domain, although, after discretisation, no guarantees have been provided. In this paper, we introduce stationary velocity fields (SVFs) parameterised by divergence-conforming B-splines in the context of image registration. We demonstrate that sparse linear constraints on the parameters of such divergence-conforming B-Splines SVFs lead to being exactly divergence-free at any point of the continuous spatial domain. In contrast to previous approaches, our framework can easily take advantage of modern solvers for constrained optimisation, symmetric registration approaches, arbitrary image similarity and additional regularisation terms. We study the numerical incompressibility error for the transformation in the case of an Euler integration, which gives theoretical insights on the improved accuracy error over previous methods. We evaluate the proposed framework using synthetically deformed multimodal brain images, and the STACOM’11 myocardial tracking challenge. Accuracy measurements demonstrate that our method compares favourably with state-of-the-art methods whilst achieving volume preservation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aganj, I., Reuter, M., Sabuncu, M.R., Fischl, B.: Avoiding symmetry-breaking spatial non-uniformity in deformable image registration via a quasi-volume-preserving constraint. NeuroImage 106, 238–251 (2015)
Bistoquet, A., Oshinski, J., Škrinjar, O.: Myocardial deformation recovery from cine MRI using a nearly incompressible biventricular model. Med. Image Anal. 12, 69–85 (2008)
De Craene, M., et al.: Temporal diffeomorphic free-form deformation: application to motion and strain estimation from 3D echocardiography. Med. Image Anal. 16, 427–450 (2012)
Evans, J.A., Hughes, T.J.: Isogeometric divergence-conforming B-splines for the unsteady Navier-Stokes equations. J. Comput. Phys. 241, 141–167 (2013)
Heyde, B., Alessandrini, M., Hermans, J., Barbosa, D., Claus, P., D’hooge, J.: Anatomical image registration using volume conservation to assess cardiac deformation from 3D ultrasound recordings. Trans. Med. Imaging 35, 501–511 (2016)
Mang, A., Gholami, A., Davatzikos, C., Biros, G.: CLAIRE: a distributed-memory solver for constrained large deformation diffeomorphic image registration. arXiv preprint arXiv:1808.04487 (2018)
Mansi, T., Pennec, X., Sermesant, M., Delingette, H., Ayache, N.: ILogDemons: a demons-based registration algorithm for tracking incompressible elastic biological tissues. Int. J. Comput. Vis. 92, 92–111 (2011)
Modat, M., et al.: Fast free-form deformation using graphics processing units. Comput. Methods Programs Biomed. 98, 278–284 (2010)
Rohlfing, T., Maurer, C., Bluemke, D., Jacobs, M.: Volume-preserving nonrigid registration of MR breast images using free-form deformation with an incompressibility constraint. Trans. Med. Imaging 22, 730–741 (2003)
Tobon-Gomez, C., et al.: Benchmarking framework for myocardial tracking and deformation algorithms: an open access database. Med. Image Anal. 17, 632–648 (2013)
Wächter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106, 25–57 (2006)
Acknowledgments
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement TRABIT No 765148; Wellcome [203148/Z/16/Z; 203145Z/16/Z; WT101957], EPSRC [NS/A000049/1; NS/A000050/1; NS/A000027/1; EP/L016478/1]. TV is supported by a Medtronic/RAEng Research Chair [RCSRF1819\7\34].
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Fidon, L., Ebner, M., Garcia-Peraza-Herrera, L.C., Modat, M., Ourselin, S., Vercauteren, T. (2019). Incompressible Image Registration Using Divergence-Conforming B-Splines. In: Shen, D., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2019. MICCAI 2019. Lecture Notes in Computer Science(), vol 11765. Springer, Cham. https://doi.org/10.1007/978-3-030-32245-8_49
Download citation
DOI: https://doi.org/10.1007/978-3-030-32245-8_49
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32244-1
Online ISBN: 978-3-030-32245-8
eBook Packages: Computer ScienceComputer Science (R0)