On the first variation of a varifold, Annals of Mathematics, vol.95, issue.3, 1972. ,
Plateau's Problem: An Invitation to Varifold Geometry, Mathematical Library, 1966. ,
Shape deformation analysis from the optimal control viewpoint, Journal de Mathématiques Pures et Appliquées, vol.104, issue.1, pp.139-178, 2015. ,
Theory of reproducing kernels, Transactions of the American Mathematical Society, vol.68, pp.337-404, 1950. ,
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
, Vector valued reproducing kernel Hilbert spaces and universality, 2008.
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
Kernel operations on the gpu, with autodiff, without memory overflows, pp.2018-2030 ,
KeOps: Calcul rapide sur GPU dans les espacesàespaces`espacesà noyaux, Proceedings of Journées de Statistique de la SFdS, 2018. ,
Analysis of geometric and functionnal shapes with extension of currents, 2013. ,
The varifold representation of nonoriented shapes for diffeomorphic registration, SIAM J. Imaging Sciences, vol.6, issue.4, pp.2547-2580, 2013. ,
Stability of curvature measures, 2008. ,
DOI : 10.1111/j.1467-8659.2009.01525.x
URL : https://hal.archives-ouvertes.fr/inria-00344903
, Stability of Curvature Measures. Computer Graphics Forum, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00344903
MeshLab: an Open-Source Mesh Processing Tool, Eurographics Italian Chapter Conference. The Eurographics Association, 2008. ,
Restricted Delaunay Triangulations And Normal Cycle, p.3, 2003. ,
DOI : 10.1145/777837.777839
Second fundamental measure of geometric sets and local approximation of curvatures, J. Differential Geom, vol.74, issue.3, pp.363-394, 2006. ,
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. ,
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. ,
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
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
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
Curvature measures, Trans. Amer. Maths. Soc, vol.93, 1959. ,
DOI : 10.2307/1993504
Geometric Measure Theory, 1969. ,
Normal and integral currents, Annals of Mathematics, vol.72, pp.458-520, 1960. ,
DOI : 10.2307/1970227
Optimal Transport for Diffeomorphic Registration, MICCAI 2017, Proc. MICCAI 2017, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01540455
Transport par difféomorphismes de points, de mesures et de courants pour la comparaison de formes et l'anatomie numérique, vol.13, 2005. ,
Large deformation diffeomorphic metric curve mapping, International Journal of Computer Vision, vol.80, issue.3, pp.317-336, 2008. ,
Computational anatomy: An emerging discipline, Q. Appl. Math, vol.4, pp.617-694, 1998. ,
, Evidence of structural remodeling in the dyssynchronous failing heart, vol.98, pp.125-132, 2006.
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
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
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
On the limited memory BFGS method for large scale optimization, Mathematical Programming, vol.45, issue.1-3, pp.503-528, 1989. ,
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
Geodesic Shooting for Computational Anatomy, Journal of Mathematical Imaging and Vision, vol.24, issue.2, pp.209-228, 2006. ,
, , 2008.
Automatic differentiation in pytorch, 2017. ,
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
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. ,
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. ,
Modèle de cycles normaux pour l'analyse des dformations, Université Paris Descartes, 2017. ,
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
GSI'17: Geometric Science Information, 2017. ,
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. ,
50 years sets with positive reach, a survey, Surveys in Mathematics and its Applications, vol.3, 2008. ,
Information Processing in Medical Imaging, no. 3565 in Lecture Notes in Computer Science, pp.381-392, 2005. ,
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. ,
, Shapes and Diffeomorphisms, 2010.
Integral and current representation of Federer's curvature measure, Arch. Maths, vol.23, pp.557-567, 1986. ,
Curvatures and currents for unions of set with positive reach, Geometriae Dedicata, vol.23, pp.155-171, 1987. ,