Abstract
Here we present an algorithm for the simultaneous registration of N longitudinal image pairs such that information acquired by each pair is used to constrain the registration of each other pair. More specifically, in the geodesic shooting setting for Large Deformation Diffeomorphic Metric Mappings (LDDMM) an average of the initial momenta characterizing the N transformations is maintained throughout and updates to individual momenta are constrained to be similar to this average. In this way, the N registrations are coupled and explore the space of diffeomorphisms as a group, the variance of which is constrained to be small. Our approach is motivated by the observation that transformations learned from images in the same diagnostic category share characteristics. The group-wise consistency prior serves to strengthen the contribution of the common signal among the N image pairs to the transformation for a specific pair, relative to features particular to that pair. We tested the algorithm on 57 longitudinal image pairs of Alzheimer’s Disease patients from the Alzheimer’s Disease Neuroimaging Initiative and evaluated the ability of the algorithm to produce momenta that better represent the long term biological processes occurring in the underlying anatomy. We found that for many image pairs, momenta learned with the group-wise prior better predict a third time point image unobserved in the registration.
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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). doi:10.1023/B:VISI.0000043755.93987.aa
Brun, C.C., Lepore, N., Pennec, X., Chou, Y.Y., Lee, A.D., de Zubicaray, G.I., McMahon, K., Wright, M.J., Gee, J.C., Thompson, P.M.: A nonconservative lagrangian framework for statistical fluid registration - safira. IEEE Trans. Med. Imaging 30(2), 184–202 (2011)
Iglesias, J., Liu, C., Thompson, P., Tu, Z.: Robust brain extraction across datasets and comparison with publicly available methods. IEEE Trans. Med. Imaging 30(9), 1617–1634 (2011)
James, W., Stein, C.: Estimation with quadratic loss. In: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1. Contributions to the Theory of Statistics, pp. 361–379. University of California Press, Berkeley (1961). http://projecteuclid.org/euclid.bsmsp/1200512173
Lorenzi, M., Pennec, X., Frisoni, G.B., Ayache, N.: Disentangling normal aging from Alzheimer’s disease in structural MR images. Neurobiol. Aging 36, S42–S52 (2014)
Miller, M.I., Trouvé, A., Younes, L.: Geodesic shooting for computational anatomy. J. Math. Imaging Vis. 24(2), 209–228 (2006)
Niethammer, M., Huang, Y., Vialard, F.-X.: Geodesic regression for image time-series. In: Fichtinger, G., Martel, A., Peters, T. (eds.) MICCAI 2011, Part II. LNCS, vol. 6892, pp. 655–662. Springer, Heidelberg (2011)
Pennec, X., Stefanescu, R., Arsigny, V., Fillard, P., Ayache, N.: Riemannian elasticity: a statistical regularization framework for non-linear registration. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3750, pp. 943–950. Springer, Heidelberg (2005)
Singh, N., Hinkle, J., Joshi, S., Fletcher, P.T.: A hierarchical geodesic model for diffeomorphic longitudinal shape analysis. In: Gee, J.C., Joshi, S., Pohl, K.M., Wells, W.M., Zöllei, L. (eds.) IPMI 2013. LNCS, vol. 7917, pp. 560–571. Springer, Heidelberg (2013)
Trouve, A.: Diffeomorphisms groups and pattern matching in image analysis. Int. J. Comput. Vis. 28, 213–221 (1998)
Tustison, N.J., Avants, B.B., Cook, P.A., Kim, J., Whyte, J., Gee, J.C., Stone, J.R.: Logical circularity in voxel-based analysis: normalization strategy may induce statistical bias. Hum. Brain Mapp. 35, 745–759 (2012)
Vialard, F.X., Risser, L., Rueckert, D., Cotter, C.J.: Diffeomorphic 3D image registration via geodesic shooting using an efficient adjoint calculation. Int. J. Comput. Vis. 97(2), 229–241 (2012). doi:10.1007/s11263-011-0481-8
Wei, L., Awate, S., Anderson, J., Fletcher, T.: A functional network estimation method of resting-state fMRI using a hierarchical markov random field. NeuroImage 100, 520–534 (2014)
Yanovsky, I., Thompson, P.M., Osher, S., Leow, A.D.: Topology preserving log-unbiased nonlinear image registration: theory and implementation. In: CVPR, IEEE Computer Society (2007)
Younes, L., Qiu, A., Winslow, R.L., Miller, M.I.: Transport of relational structures in groups of diffeomorphisms. J. Math. Imaging Vis. 32(1), 41–56 (2008)
Zhang, M., Singh, N., Fletcher, P.T.: Bayesian estimation of regularization and atlas building in diffeomorphic image registration. In: Gee, J.C., Joshi, S., Pohl, K.M., Wells, W.M., Zöllei, L. (eds.) IPMI 2013. LNCS, vol. 7917, pp. 37–48. Springer, Heidelberg (2013)
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Fleishman, G.M., Gutman, B.A., Fletcher, P.T., Thompson, P.M. (2015). Simultaneous Longitudinal Registration with Group-Wise Similarity Prior. In: Ourselin, S., Alexander, D., Westin, CF., Cardoso, M. (eds) Information Processing in Medical Imaging. IPMI 2015. Lecture Notes in Computer Science(), vol 9123. Springer, Cham. https://doi.org/10.1007/978-3-319-19992-4_59
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DOI: https://doi.org/10.1007/978-3-319-19992-4_59
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