E. Stéphanie-allassonnière, A. Kuhn, and . Trouvé, Construction of Bayesian deformable models via a stochastic approximation algorithm: A convergence study, Bernoulli, vol.16, issue.3, pp.641-678, 2010.
DOI : 10.3150/09-BEJ229

L. Stéphanie-allassonnière, X. Devilliers, and . Pennec, Estimating the Template in the Total Space with the Fréchet Mean on Quotient Spaces may have a Bias: a Case Study on Vector Spaces Quotiented by the Group of Translations, Mathematical Foundations of Computational Anatomy (MFCA'15), 2015. (Authors given by alphabetic order, LD is in fact the prinicpal author). (Cited, pp.31-39, 2015.

]. S. Allassonnière, S. Durrleman, and E. Kuhn, Bayesian Mixed Effect Atlas Estimation with a Diffeomorphic Deformation Model, SIAM Journal on Imaging Sciences, vol.8, issue.3, pp.1367-1395, 2015.
DOI : 10.1137/140971762

X. Marc-arnaudon and . Li, Barycenters of measures transported by stochastic flows. Annals of probability, pp.1509-1543, 2005.

M. Faisal-beg, M. Miller, A. Trouvé, and L. Younes, Computing large deformation metric mappings via geodesic flows of diffeomorphisms, International journal of computer vision, vol.61, issue.35, pp.139-157, 2005.

R. Bhattacharya and V. Patrangenaru, Large sample theory of intrinsic and extrinsic sample means on manifolds???II, The Annals of Statistics, vol.33, issue.3, pp.1-29, 2003.
DOI : 10.1214/009053605000000093

R. Bhattacharya and V. Patrangenaru, Large sample theory of intrinsic and extrinsic sample means on manifolds???II, The Annals of Statistics, vol.33, issue.3, pp.1225-1259, 2005.
DOI : 10.1214/009053605000000093

A. Bhattacharya and R. Bhattacharya, Statistics on Riemannian manifolds: asymptotic distribution and curvature, Proceedings of the American Mathematical Society, vol.136, issue.08, pp.2959-2967, 2008.
DOI : 10.1090/S0002-9939-08-09445-8
URL : http://www.ams.org/proc/2008-136-08/S0002-9939-08-09445-8/S0002-9939-08-09445-8.pdf

L. Fred and . Bookstein, Size and shape spaces for landmark data in two dimensions, Statistical science, pp.181-222, 1986.

N. Bourbaki, Algebre: Chapitre 8, 2012.
DOI : 10.1007/978-3-540-35316-4

E. George and . Box, Science and statistics, Journal of the American Statistical Association, vol.71, issue.356, pp.791-799, 1976.

]. Cheng, L. Ian, X. Dryden, and . Huang, Bayesian Registration of Functions and Curves, Bayesian Analysis, vol.11, issue.2, pp.447-475, 2016.
DOI : 10.1214/15-BA957SUPP

]. Cleveland, W. Wu, and A. Srivastava, Norm-preserving constraint in the Fisher???Rao registration and its application in signal estimation, Journal of Nonparametric Statistics, vol.28, issue.2, pp.338-359, 2016.
DOI : 10.1007/s10827-012-0427-3

J. Cooley and J. Tukey, An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation, vol.19, issue.90, pp.297-301, 1965.
DOI : 10.1090/S0025-5718-1965-0178586-1

F. Timothy, S. Cootes, C. J. Marsland, K. Twining, . Smith et al., Groupwise diffeomorphic non-rigid registration for automatic model building, European conference on computer vision, pp.316-327, 2004.

S. Loïc-devilliers, A. Allassonnière, X. Trouvé, and . Pennec, Template Estimation in Computational Anatomy: Fr??chet Means Top and Quotient Spaces Are Not Consistent, SIAM Journal on Imaging Sciences, vol.10, issue.3, pp.1139-1169, 2017.
DOI : 10.1137/16M1083931

G. Lejeune and D. , Über die Reduction der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen, Journal für die reine und angewandte Mathematik, pp.209-227

J. Du, A. Hosseinbor, M. K. Chung, B. B. Bendlin, G. Suryawanshi et al., Diffeomorphic metric mapping and probabilistic atlas generation of hybrid diffusion imaging based on BFOR signal basis, Medical Image Analysis, vol.18, issue.7, pp.1002-1014, 2014.
DOI : 10.1016/j.media.2014.05.011

X. Stanley-durrleman, A. Pennec, N. Trouvé, and . Ayache, Statistical models of sets of curves and surfaces based on currents, Medical Image Analysis, vol.13, issue.5, pp.793-808, 2009.
DOI : 10.1016/j.media.2009.07.007

S. Stanley-durrleman, S. Allassonnière, and . Joshi, Sparse Adaptive Parameterization of Variability in Image Ensembles, International Journal of Computer Vision, vol.67, issue.2, pp.161-183, 2013.
DOI : 10.1111/j.1467-9868.2005.00503.x

S. Durrleman, M. Prastawa, N. Charon, J. Korenberg, S. Joshi et al., Morphometry of anatomical shape complexes with dense deformations and sparse parameters, NeuroImage, vol.101, issue.21, pp.35-49, 2014.
DOI : 10.1016/j.neuroimage.2014.06.043
URL : https://hal.archives-ouvertes.fr/hal-01015771

T. Fletcher, C. Lu, and S. Joshi, Statistics of shape via principal geodesic analysis on Lie groups, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings., p.17, 2003.
DOI : 10.1109/CVPR.2003.1211342

]. Fletcher, C. Lu, M. Stephen, S. Pizer, and . Joshi, Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape, IEEE Transactions on Medical Imaging, vol.23, issue.8, pp.995-1005, 2004.
DOI : 10.1109/TMI.2004.831793

K. Glasbey and . Mardia, A penalized likelihood approach to image warping, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.63, issue.3, pp.465-492, 2001.
DOI : 10.1111/1467-9868.00295

C. John and . Gower, Generalized procrustes analysis, Psychometrika, vol.40, issue.1, pp.33-51, 1975.

A. Guimond, J. Meunier, and J. Thirion, Average Brain Models: A Convergence Study, Computer Vision and Image Understanding, vol.77, issue.2, pp.192-210, 2000.
DOI : 10.1006/cviu.1999.0815
URL : https://hal.archives-ouvertes.fr/inria-00615030

M. Sebastian-hitziger, A. Clerc, S. Gramfort, C. Saillet, T. Bénar et al., Jitter-adaptive dictionary learning-application to multi-trial neuroelectric signals. arXiv preprint arXiv:1301, pp.20-88, 2013.

J. Sarang and M. Miller, Landmark matching via large deformation diffeomorphisms, IEEE Transactions on Image Processing, vol.9, issue.8, pp.1357-1370, 2000.

]. Joshi, B. Davis, M. Jomier, and G. Gerig, Unbiased diffeomorphic atlas construction for computational anatomy, NeuroImage, vol.23, issue.35, pp.151-160, 2004.
DOI : 10.1016/j.neuroimage.2004.07.068
URL : http://www.cs.unc.edu/~gerig/publications/NeuroImage04-Joshi.pdf

]. Karcher, Riemannian center of mass and mollifier smoothing . Communications on pure and applied mathematics, pp.509-541, 1977.

]. , K. , and K. Mardia, Consistency of Procrustes estimators, Bibliography Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.59, issue.38, pp.281-290, 1997.

S. Kullback and R. Leibler, On information and sufficiency . The annals of mathematical statistics, pp.79-86, 1951.
DOI : 10.1214/aoms/1177729694
URL : http://doi.org/10.1214/aoms/1177729694

E. Sebastian-kurtek, Z. Klassen, M. Ding, A. Avison, and . Srivastava, Parameterization-invariant shape statistics and probabilistic classification of anatomical surfaces, Biennial International Conference on Information Processing in Medical Imaging, pp.147-158, 2011.

A. Sebastian-kurtek, W. Srivastava, and . Wu, Signal Estimation Under Random Time-Warpings and Nonlinear Signal Alignment, Advances in Neural Information Processing Systems 24, pp.675-683, 2011.

L. Le, On the consistency of procrustean mean shapes, Advances in Applied Probability, vol.A, issue.01, pp.53-63, 1998.
DOI : 10.1002/cpa.3160300502

S. Sidonie-lefebvre, J. Allassonnière, T. Jakubowicz, E. Lasne, and . Moulines, Aircraft classification with a low resolution infrared sensor, Machine Vision and Applications, pp.175-186, 2012.
DOI : 10.1051/ps/2009001

H. Lombaert, L. Grady, X. Pennec, N. Ayache, and F. Cheriet, Spectral Log-Demons: Diffeomorphic Image Registration with Very Large Deformations, International Journal of Computer Vision, vol.14, issue.4, pp.1-18, 2013.
DOI : 10.1016/j.media.2010.04.003
URL : https://hal.archives-ouvertes.fr/hal-00979616

A. Michael-miller, L. Trouvé, and . Younes, Geodesic Shooting for Computational Anatomy, Journal of Mathematical Imaging and Vision, vol.13, issue.1???2, pp.209-228, 2006.
DOI : 10.1117/3.831079.ch3

N. Miolane, S. Holmes, and X. Pennec, Template Shape Estimation: Correcting an Asymptotic Bias, SIAM Journal on Imaging Sciences, vol.10, issue.2, pp.808-844, 2017.
DOI : 10.1137/16M1084493
URL : https://hal.archives-ouvertes.fr/hal-01350508

M. Rohé, M. Sermesant, and X. Pennec, Barycentric Subspace Analysis: A New Symmetric Group-Wise Paradigm for Cardiac Motion Tracking, International Conference on Medical Image Computing and Computer-Assisted Intervention, pp.300-307, 2016.
DOI : 10.1007/978-3-642-22092-0_53

K. Serdar, P. Balci, and . Golland, Discovering Modes of an Image Population through Mixture Modeling, Proceeding of the MICCAI conference, pp.381-389, 2008.

C. Seiler, X. Pennec, and M. Reyes, Capturing the multiscale anatomical shape variability with polyaffine transformation trees, Medical Image Analysis, vol.16, issue.7, pp.1371-1384, 2012.
DOI : 10.1016/j.media.2012.05.011
URL : https://hal.archives-ouvertes.fr/hal-00813866

]. Sommer, F. Lauze, S. Hauberg, and M. Nielsen, Manifold Valued Statistics, Exact Principal Geodesic Analysis and the Effect of Linear Approximations, Computer Vision?ECCV 2010, pp.43-56, 2010.
DOI : 10.1007/978-3-642-15567-3_4

]. Sommer, F. Lauze, and M. Nielsen, Optimization over geodesics for exact principal geodesic analysis, Advances in Computational Mathematics, vol.24, issue.2, pp.283-313, 2014.
DOI : 10.1016/j.cagd.2006.11.003

]. Thirion, Image matching as a diffusion process: an analogy with Maxwell's demons, Medical Image Analysis, vol.2, issue.3, pp.243-260, 1998.
DOI : 10.1016/S1361-8415(98)80022-4

]. Thompson, On growth and form. On growth and form, p.16, 1942.

T. William and J. W. Milnor, The geometry and topology of three-manifolds, 1979.

M. Vaillant and J. Glaunès, Surface matching via currents In Information processing in medical imaging, pp.1-5, 2005.

X. Tom-vercauteren and . Pennec, Diffeomorphic demons: Efficient non-parametric image registration, NeuroImage, vol.45, issue.1, pp.61-72, 2009.
DOI : 10.1016/j.neuroimage.2008.10.040

]. Voronoi, Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire. Recherches sur les parallélloèdres primitifs, Journal für die reine und angewandte Mathematik, pp.198-287, 1908.

N. Zhang, P. Singh, and . Fletcher, Bayesian Estimation of Regularization and Atlas Building in Diffeomorphic Image Registration, Information Processing in Medical Imaging, pp.37-48, 2013.
DOI : 10.1007/978-3-642-38868-2_4