Abstract
Computing a concise representation of the anatomical variability found in large sets of images is an important first step in many statistical shape analyses. In this paper, we present a generative Bayesian approach for automatic dimensionality reduction of shape variability represented through diffeomorphic mappings. To achieve this, we develop a latent variable model for principal geodesic analysis (PGA) that provides a probabilistic framework for factor analysis on diffeomorphisms. Our key contribution is a Bayesian inference procedure for model parameter estimation and simultaneous detection of the effective dimensionality of the latent space. We evaluate our proposed model for atlas and principal geodesic estimation on the OASIS brain database of magnetic resonance images. We show that the automatically selected latent dimensions from our model are able to reconstruct unseen brain images with lower error than equivalent linear principal components analysis (LPCA) models in the image space, and it also outperforms tangent space PCA (TPCA) models in the diffeomorphism setting.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Allassonnière, S., Kuhn, E.: Stochastic algorithm for parameter estimation for dense deformable template mixture model. ESAIM-PS 14, 382–408 (2010)
Bishop, C.M.: Bayesian pca. Advances in Neural Information Processing Systems, 382–388 (1999)
Fletcher, P.T., Lu, C., Joshi, S.: Statistics of shape via principal geodesic analysis on Lie groups. In: Computer Vision and Pattern Recognition, pp. 95–101 (2003)
Gerber, S., Tasdizen, T., Fletcher, P.T., Joshi, S., Whitaker, R.: Manifold modeling for brain population analysis. Medical Image Analysis 14(5), 643–653 (2010)
Gori, P., et al.: Bayesian atlas estimation for the variability analysis of shape complexes. In: Mori, K., Sakuma, I., Sato, Y., Barillot, C., Navab, N. (eds.) MICCAI 2013, Part I. LNCS, vol. 8149, pp. 267–274. Springer, Heidelberg (2013)
Joshi, S., Davis, B., Jomier, M., Gerig, G.: Unbiased diffeomorphic atlas construction for computational anatomy. NeuroImage 23(suppl. 1), 151–160 (2004)
Ma, J., Miller, M.I., Trouvé, A., Younes, L.: Bayesian template estimation in computational anatomy. NeuroImage 42, 252–261 (2008)
Miller, M.I., Trouvé, A., Younes, L.: Geodesic shooting for computational anatomy. Journal of Mathematical Imaging and Vision 24(2), 209–228 (2006)
Qiu, A., Younes, L., Miller, M.I.: Principal component based diffeomorphic surface mapping. IEEE Transactions on Medical Imaging 31(2), 302–311 (2012)
Simpson, I.J.A., Schnabel, J.A., Groves, A.R., Andersson, J.L.R., Woolrich, M.W.: Probabilistic inference of regularisation in non-rigid registration. NeuroImage 59, 2438–2451 (2012)
Singh, N., Hinkle, J., Joshi, S., Fletcher, P.T.: A vector momenta formulation of diffeomorphisms for improved geodesic regression and atlas construction. In: International Symposium on Biomedical Imaging, pp. 1219–1222 (2013)
Twining, C.J., Cootes, T.F., Marsland, S., Petrovic, V., Schestowitz, R., Taylor, C.J.: A unified information-theoretic approach to groupwise non-rigid registration and model building. In: Christensen, G.E., Sonka, M. (eds.) IPMI 2005. LNCS, vol. 3565, pp. 1–14. Springer, Heidelberg (2005)
Vaillant, M., Miller, M.I., Younes, L., Trouvé, A.: Statistics on diffeomorphisms via tangent space representations. NeuroImage 23, S161–S169 (2004)
Vialard, F.X., Risser, L., Holm, D., Rueckert, D.: Diffeomorphic atlas estimation using Kärcher mean and geodesic shooting on volumetric images. In: MIUA (2011)
Vialard, F.X., Risser, L., Rueckert, D., Cotter, C.J.: Diffeomorphic 3d image registration via geodesic shooting using an efficient adjoint calculation. International Journal of Computer Vision, 229–241 (2012)
Younes, L., Arrate, F., Miller, M.: Evolutions equations in computational anatomy. NeuroImage, 40–50 (2009)
Zhang, M., Fletcher, P.T.: Probabilistic principal geodesic analysis. In: Advances in Neural Information Processing Systems, pp. 1178–1186 (2013)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Zhang, M., Fletcher, P.T. (2014). Bayesian Principal Geodesic Analysis in Diffeomorphic Image Registration. In: Golland, P., Hata, N., Barillot, C., Hornegger, J., Howe, R. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2014. MICCAI 2014. Lecture Notes in Computer Science, vol 8675. Springer, Cham. https://doi.org/10.1007/978-3-319-10443-0_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-10443-0_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10442-3
Online ISBN: 978-3-319-10443-0
eBook Packages: Computer ScienceComputer Science (R0)