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TopAwaRe: Topology-Aware Registration

Part of the Lecture Notes in Computer Science book series (LNIP,volume 11765)


Deformable registration, or nonlinear alignment of images, is a fundamental preprocessing tool in medical imaging. State-of-the-art algorithms restrict to diffeomorphisms to regularize an otherwise ill-posed problem. In particular, such models assume that a one-to-one matching exists between any pair of images. In a range of real-life-applications, however, one image may contain objects that another does not. In such cases, the one-to-one assumption is routinely accepted as unavoidable, leading to inaccurate preprocessing and, thus, inaccuracies in the subsequent analysis. We present a novel, piecewise-diffeomorphic deformation framework which models topological changes as explicitly encoded discontinuities in the deformation fields. We thus preserve the regularization properties of diffeomorphic models while locally avoiding their erroneous one-to-one assumption. The entire model is GPU-implemented, and validated on intersubject 3D registration of T1-weighted brain MRI. Qualitative and quantitative results show our ability to improve performance in pathological cases containing topological inconsistencies.


  • Image registration
  • Diffeomorphisms
  • Topology-Aware

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  1. 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. Med. Image Anal. 12(1), 26–41 (2008)

    CrossRef  Google Scholar 

  2. Balakrishnan, G., Zhao, A., Sabuncu, M.R., Guttag, J., Dalca, A.V.: An unsupervised learning model for deformable medical image registration. In: Conference on Computer Vision and Pattern Recognition (CVPR), pp. 9252–9260(2018)

    Google Scholar 

  3. Beg, M.F., Miller, M.I., Trouvé, A., Younes, L.: Computing large deformation metric mappings via geodesic flows of diffeomorphisms. Int. J. Comput. Vis. 61(2), 139–157 (2005)

    CrossRef  Google Scholar 

  4. Berendsen, F.F., Kotte, A.N.T.J., Viergever, M.A., Pluim, J.P.W.: Registration of organs with sliding interfaces and changing topologies. In: SPIE, vol. 9034, pp. 90340E–90340E-7 (2014)

    Google Scholar 

  5. Delmon, V., Rit, S., Pinho, R., Sarrut, D.: Registration of sliding objects using direction dependent B-splines decomposition. Phys. Med. Biol. 58(5), 1303 (2013)

    CrossRef  Google Scholar 

  6. Kwon, D., Niethammer, M., Akbari, H., Bilello, M., Davatzikos, C., Pohl, K.M.: PORTR: pre-operative and post-recurrence brain tumor registration. IEEE TMI (3), 651–667

    Google Scholar 

  7. Landman, B.A., et al.: MICCAI 2012 Workshop on Multi-Atlas Labeling. CreateSpace, Scotts Valley (2012)

    Google Scholar 

  8. Mueller, S.G., et al.: Ways toward an early diagnosis in Alzheimer’s disease: the Alzheimer’s disease neuroimaging initiative (ADNI). Alzheimer’s Dement. 1(1), 55–66 (2005)

    CrossRef  Google Scholar 

  9. Papież, B.W., Heinrich, M.P., Fehrenbach, J., Risser, L., Schnabel, J.A.: An implicit sliding-motion preserving regularisation via bilateral filtering for deformable image registration. Med. Image Anal. 18(8), 1299–1311 (2014)

    CrossRef  Google Scholar 

  10. Risser, L., Baluwala, H.Y., Schnabel, J.A., Vialard, F.X.: Piecewise-diffeomorphic image registration: application to the motion estimation between 3D CT lung images with sliding conditions. Med. Image Anal. 17(2), 182–193 (2012)

    CrossRef  Google Scholar 

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This research was supported by the Lundbeck Foundation and by the Centre for Stochastic Geometry and Advanced Bioimaging, funded by a grant from the Villum Foundation.

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Correspondence to Aasa Feragen .

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Nielsen, R.K., Darkner, S., Feragen, A. (2019). TopAwaRe: Topology-Aware Registration. 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.

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-32244-1

  • Online ISBN: 978-3-030-32245-8

  • eBook Packages: Computer ScienceComputer Science (R0)