W. Allard, On the first variation of a varifold, Annals of Mathematics, vol.95, issue.3, 1972.

F. Almgren, Plateau's Problem: An Invitation to Varifold Geometry, Mathematical Library, 1966.

S. Arguilì-ere, E. Trélat, A. Trouvé, and L. Younès, Shape deformation analysis from the optimal control viewpoint, Journal de Mathématiques Pures et Appliquées, vol.104, issue.1, pp.139-178, 2015.

N. Aronszajn, Theory of reproducing kernels, Transactions of the American Mathematical Society, vol.68, pp.337-404, 1950.

B. Buet, G. P. Leonardi, and S. Masnou, A varifold approach to surface approximation, Archive for Rational Mechanics and Analysis, vol.226, issue.2, pp.639-694, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02141325

C. Carmeli, E. De-vito, A. Toigo, and V. Umanit, Vector valued reproducing kernel Hilbert spaces and universality, 2008.

B. Charlier, N. Charon, and A. Trouvé, The fshape framework for the variability analysis of functional shapes, Foundations of Computational Mathematics, pp.1-71, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00981805

B. Charlier, J. Feydy, and J. Glaunès, Kernel operations on the gpu, with autodiff, without memory overflows, pp.2018-2030

B. Charlier, J. Feydy, and J. Glaunès, KeOps: Calcul rapide sur GPU dans les espacesàespaces`espacesà noyaux, Proceedings of Journées de Statistique de la SFdS, 2018.

N. Charon, Analysis of geometric and functionnal shapes with extension of currents, 2013.

N. Charon and A. Trouvé, The varifold representation of nonoriented shapes for diffeomorphic registration, SIAM J. Imaging Sciences, vol.6, issue.4, pp.2547-2580, 2013.

F. Chazal, D. Cohen-steiner, A. Lieutier, and B. Thibert, Stability of curvature measures, 2008.
DOI : 10.1111/j.1467-8659.2009.01525.x

URL : https://hal.archives-ouvertes.fr/inria-00344903

F. Chazal, D. Cohen-steiner, A. Lieutier, and B. Thibert, Stability of Curvature Measures. Computer Graphics Forum, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00344903

P. Cignoni, M. Callieri, M. Corsini, M. Dellepiane, F. Ganovelli et al., MeshLab: an Open-Source Mesh Processing Tool, Eurographics Italian Chapter Conference. The Eurographics Association, 2008.

D. Cohen-steiner and J. M. Morvan, Restricted Delaunay Triangulations And Normal Cycle, p.3, 2003.
DOI : 10.1145/777837.777839

D. Cohen-steiner and J. M. Morvan, Second fundamental measure of geometric sets and local approximation of curvatures, J. Differential Geom, vol.74, issue.3, pp.363-394, 2006.

J. Csernansky, L. Wang, J. Swank, J. Miller, M. Gado et al., Preclinical detection of alzheimer's disease: hippocampal shape and volume predict dementia onset in the elderly, NeuroImage, vol.25, issue.3, pp.783-792, 2005.

J. G. Csernansky, L. Wang, S. C. Joshi, J. T. Ratnanather, and M. I. Miller, Computational anatomy and neuropsychiatric disease: probabilistic assessment of variation and statistical inference of group difference, hemispheric asymmetry, and time-dependent change, NeuroImage, vol.23, pp.56-68, 2004.

S. Durrleman, S. Allassonnì-ere, and S. Joshi, Sparse adaptive parameterization of variability in image ensembles, International Journal of Computer Vision, vol.101, issue.1, pp.161-183, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00817565

S. Durrleman, P. Fillard, X. Pennec, A. Trouv, and N. Ayache, Registration, atlas estimation and variability analysis of white matter fiber bundles modeled as currents, NeuroImage, vol.55, issue.3, pp.1073-1090, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00816044

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

H. Federer, Curvature measures, Trans. Amer. Maths. Soc, vol.93, 1959.
DOI : 10.2307/1993504

H. Federer, Geometric Measure Theory, 1969.

H. Federer and W. Fleming, Normal and integral currents, Annals of Mathematics, vol.72, pp.458-520, 1960.
DOI : 10.2307/1970227

J. Feydy, B. Charlier, F. X. Vialard, and G. Peyré, Optimal Transport for Diffeomorphic Registration, MICCAI 2017, Proc. MICCAI 2017, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01540455

J. Glaunès, Transport par difféomorphismes de points, de mesures et de courants pour la comparaison de formes et l'anatomie numérique, vol.13, 2005.

J. Glaunès, A. Qiu, M. Miller, and L. Younes, Large deformation diffeomorphic metric curve mapping, International Journal of Computer Vision, vol.80, issue.3, pp.317-336, 2008.

U. Grenander and M. I. Miller, Computational anatomy: An emerging discipline, Q. Appl. Math, vol.4, pp.617-694, 1998.

P. A. Helm, L. Younes, M. F. Beg, D. B. Ennis, C. Leclercq et al., Evidence of structural remodeling in the dyssynchronous failing heart, vol.98, pp.125-132, 2006.

I. Kaltenmark, B. Charlier, and N. Charon, A general framework for curve and surface comparison and registration with oriented varifolds, The IEEE Conference on Computer Vision and Pattern Recognition (CVPR, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01817514

S. Lee, N. Charon, B. Charlier, K. Popuri, E. Lebed et al., Atlas-based shape analysis and classification of retinal optical coherence tomography images using the functional shape (fshape) framework, Medical Image Analysis, vol.35, pp.570-581, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01817551

S. Lee, M. L. Heisler, K. Popuri, N. Charon, B. Charlier et al., Age and glaucoma-related characteristics in retinal nerve fiber layer and choroid: Localized morphometrics and visualization using functional shapes registration, Frontiers in Neuroscience, vol.11, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01817576

D. C. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization, Mathematical Programming, vol.45, issue.1-3, pp.503-528, 1989.

T. Mansi, I. Voigt, B. Leonardi, X. Pennec, S. Durrleman et al., A statistical model for quantification and prediction of cardiac remodelling: Application to tetralogy of fallot, IEEE Transactions on Medical Imaging, vol.30, issue.9, pp.1605-1616, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00616185

M. I. Miller, A. Trouvé, and L. Younes, Geodesic Shooting for Computational Anatomy, Journal of Mathematical Imaging and Vision, vol.24, issue.2, pp.209-228, 2006.

J. M. Morvan, , 2008.

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang et al., Automatic differentiation in pytorch, 2017.

X. Pennec, Intrinsic statistics on riemannian manifolds: Basic tools for geometric measurements, Journal of Mathematical Imaging and Vision, vol.25, issue.1, pp.127-154, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00614994

A. Qiu, L. Younes, M. I. Miller, and J. G. Csernansky, Parallel transport in diffeomorphisms distinguishes the time-dependent pattern of hippocampal surface deformation due to healthy aging and the dementia of the alzheimer's type, NeuroImage, vol.40, issue.1, pp.68-76, 2008.

J. Rataj and M. Zähle, Curvatures and currents for unions of sets with positive reach, ii, Annals of Global Analysis and Geometry, vol.20, issue.1, pp.1-21, 2001.

P. Roussillon, Modèle de cycles normaux pour l'analyse des dformations, Université Paris Descartes, 2017.

P. Roussillon and J. Glaunès, Kernel metrics on normal cycles and application to curve matching, SIAM J. Imaging Sciences, vol.9, 1991.
URL : https://hal.archives-ouvertes.fr/hal-01305806

P. Roussillon and J. Glaunès, GSI'17: Geometric Science Information, 2017.

X. Tang, D. Holland, A. M. Dale, L. Younes, and M. I. Miller, for the Alzheimer's Disease Neuroimaging Initiative: Shape abnormalities of subcortical and ventricular structures in mild cognitive impairment and alzheimer's disease: Detecting, quantifying, and predicting, Human Brain Mapping, vol.35, issue.8, pp.3701-3725, 2014.

C. Thäle, 50 years sets with positive reach, a survey, Surveys in Mathematics and its Applications, vol.3, 2008.

M. Vaillant and J. Glaunès, Information Processing in Medical Imaging, no. 3565 in Lecture Notes in Computer Science, pp.381-392, 2005.

L. Wang, F. Beg, T. Ratnanather, C. Ceritoglu, L. Younes et al., Large deformation diffeomorphism and momentum based hippocampal shape discrimination in dementia of the alzheimer type, IEEE Transactions on Medical Imaging, vol.26, issue.4, pp.462-470, 2007.

L. Younès, Shapes and Diffeomorphisms, 2010.

M. Zähle, Integral and current representation of Federer's curvature measure, Arch. Maths, vol.23, pp.557-567, 1986.

M. Zähle, Curvatures and currents for unions of set with positive reach, Geometriae Dedicata, vol.23, pp.155-171, 1987.