C. Bibliographie-[-adpy12-]-marc-arnaudon, A. Dombry, L. Phan, and . Yang, Stochastic algorithms for computing means of probability measures, Stochastic Processes and their Applications, pp.1437-1455, 2012.

A. Abuzaina, S. Mark, . Nixon, N. John, and . Carter, Sphere Detection in Kinect Point Clouds via the 3D Hough Transform, pp.290-297, 2013.
DOI : 10.1007/978-3-642-40246-3_36

A. Al-sharadqah, Further statistical analysis of circle fitting, Electronic Journal of Statistics, vol.8, issue.2, pp.2741-2778, 2014.
DOI : 10.1214/14-EJS971

F. Bach, Adaptivity of averaged stochastic gradient descent to local strong convexity for logistic regression, The Journal of Machine Learning Research, vol.15, issue.1, pp.595-627, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00804431

G. Bbt-+-11-]-juan-lucas-bali, . Boente, E. David, J. Tyler, and . Wang, Robust functional principal components : A projection-pursuit approach. The Annals of Statistics, pp.2852-2882, 2011.

A. Balsubramani, S. Dasgupta, and Y. Freund, The fast convergence of incremental pca, Advances in Neural Information Processing Systems, pp.3174-3182, 2013.

N. Bartoli and P. D. Moral, Simulation et algorithmes stochastiques, Cépaduès éditions, p.5, 2001.

L. Breiman, H. Jerome, and . Friedman, Estimating Optimal Transformations for Multiple Regression and Correlation, Journal of the American Statistical Association, vol.41, issue.391, pp.580-598, 1985.
DOI : 10.1007/BF02296972

B. Bercu and P. Fraysse, A robbins?monro procedure for estimation in semiparametric regression models. The Annals of Statistics, pp.666-693, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00551832

H. Battey, J. Fan, H. Liu, J. Lu, and Z. Zhu, Distributed estimation and inference with statistical guarantees, 2015.

P. Billingsley, Convergence of probability measures, 2013.
DOI : 10.1002/9780470316962

F. Bach and E. Moulines, Non-strongly-convex smooth stochastic approximation with convergence rate O (1/n), Advances in Neural Information Processing Systems, pp.773-781, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00831977

A. Benveniste, M. Métivier, and P. Priouret, Adaptive Algorithms and Stochastic Approximations, Applications of Mathematics, vol.22, 1990.
DOI : 10.1007/978-3-642-75894-2

D. Bosq, Linear processes in function spaces, Lecture Notes in Statistics Theory and applications, vol.149, 2000.
DOI : 10.1007/978-1-4612-1154-9

L. Bottou, Large-scale machine learning with stochastic gradient descent, Proceedings of COMPSTAT'2010, pp.177-186, 2010.

A. Beck and D. Pan, On the Solution of the GPS Localization and Circle Fitting Problems, SIAM Journal on Optimization, vol.22, issue.1, pp.108-134, 2012.
DOI : 10.1137/100809908

D. Brazey and B. Portier, A New Spherical Mixture Model for Head Detection in Depth Images, SIAM Journal on Imaging Sciences, vol.7, issue.4, pp.2423-2447, 2014.
DOI : 10.1137/140951424

A. Beck and S. Sabach, Weiszfeld???s Method: Old and New Results, Journal of Optimization Theory and Applications, vol.30, issue.2, pp.1-40, 2015.
DOI : 10.1090/S0025-5718-1968-0232137-4

G. Enea, E. Bongiorno, A. Salinelli, P. Goia, and . Vieu, Contributions in infinite-dimensional statistics and related topics, 2014.

S. Boyd and L. Vandenberghe, Convex optimization, 2004.

G. Biau and R. Zenine, Online asynchronous distributed regression, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01024673

B. Cadre, -median of banach valued random variable, Statistics, vol.73, issue.4, pp.509-521, 2001.
DOI : 10.1007/BF00535005

A. Chakraborty and P. Chaudhuri, The spatial distribution in infinite dimensional spaces and related quantiles and depths. The Annals of Statistics, [CCC10] Hervé Cardot, Peggy Cénac, and Mohamed Chaouch. Stochastic approximation to the multivariate and the functional median, pp.421-428, 2010.

H. Cardot, P. Cénac, and A. Godichon-baggioni, Online estimation of the geometric median in Hilbert spaces: Nonasymptotic confidence balls, The Annals of Statistics, vol.45, issue.2, 2015.
DOI : 10.1214/16-AOS1460SUPP

URL : https://hal.archives-ouvertes.fr/hal-01555593

H. Cardot, P. Cénac, and J. Monnez, A fast and recursive algorithm for clustering large datasets with -medians, Computational Statistics & Data Analysis, vol.56, issue.6, pp.1434-1449, 2012.
DOI : 10.1016/j.csda.2011.11.019

URL : https://hal.archives-ouvertes.fr/hal-00644683

H. Cardot, P. Cénac, and P. Zitt, Recursive estimation of the conditional geometric median in Hilbert spaces, Electronic Journal of Statistics, vol.6, issue.0, pp.2535-2562, 2012.
DOI : 10.1214/12-EJS759

URL : https://hal.archives-ouvertes.fr/hal-00687762

H. Cardot, P. Cénac, and P. Zitt, Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm, Bernoulli, vol.19, issue.1, pp.18-43, 2013.
DOI : 10.3150/11-BEJ390

URL : https://hal.archives-ouvertes.fr/hal-00558481

H. Cardot and D. Degras, Online principal components analysis : which algorithm to choose ?, 2015.

Y. Chen, X. Dang, H. Peng, L. Henry, and . Bart, Outlier detection with the kernelized spatial depth function. Pattern Analysis and Machine Intelligence, IEEE Transactions on, issue.2, pp.31288-305, 2009.

C. Croux, P. Filzmoser, and M. R. Oliveira, Algorithms for projection-pursuit robust principal component analysis, pp.218-225, 2007.

H. Cardot and A. Godichon-baggioni, Fast estimation of the median covariation matrix with application to online robust principal components analysis, TEST, vol.25, issue.4, 2015.
DOI : 10.1109/TPAMI.2003.1217609

URL : https://hal.archives-ouvertes.fr/hal-01482743

J. Cupidon, D. Gilliam, R. Eubank, and F. Ruymgaart, The delta method for analytic functions of random operators with application to functional data, Bernoulli, vol.13, issue.4, pp.1179-1194, 2007.
DOI : 10.3150/07-BEJ6180

P. Chaudhuri, Multivariate Location Estimation Using Extension of $R$-Estimates Through $U$-Statistics Type Approach, The Annals of Statistics, vol.20, issue.2, pp.897-916, 1992.
DOI : 10.1214/aos/1176348662

P. Chaudhuri, On a Geometric Notion of Quantiles for Multivariate Data, Journal of the American Statistical Association, vol.24, issue.434, pp.862-872, 1996.
DOI : 10.1214/aos/1176350365

C. Croux and A. Ruiz-gazen, High breakdown estimators for principal components: the projection-pursuit approach revisited, Journal of Multivariate Analysis, vol.95, issue.1, pp.206-226, 2005.
DOI : 10.1016/j.jmva.2004.08.002

A. Cuevas, Qualitative robustness in abstract inference, Journal of Statistical Planning and Inference, vol.18, issue.3, pp.277-289, 1988.
DOI : 10.1016/0378-3758(88)90105-X

A. Cuevas, A partial overview of the theory of statistics with functional data, Journal of Statistical Planning and Inference, vol.147, pp.1-23, 2014.
DOI : 10.1016/j.jspi.2013.04.002

S. J. Devlin, R. Gnanadesikan, and J. R. Kettenring, Robust Estimation of Dispersion Matrices and Principal Components, Journal of the American Statistical Association, vol.55, issue.374, pp.354-362, 1981.
DOI : 10.1080/14786440109462720

B. Delyon and A. Juditsky, Stochastic optimization with averaging of trajectories, Stochastics and Stochastic Reports, vol.2, issue.2, pp.107-118, 1992.
DOI : 10.21236/ADA158740

B. Delyon and A. Juditsky, Accelerated Stochastic Approximation, SIAM Journal on Optimization, vol.3, issue.4, pp.868-881, 1993.
DOI : 10.1137/0803045

J. Dauxois, A. Pousse, and Y. Romain, Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference, Journal of Multivariate Analysis, vol.12, issue.1, pp.136-154, 1982.
DOI : 10.1016/0047-259X(82)90088-4

J. Dippon and J. Renz, Weighted Means in Stochastic Approximation of Minima, SIAM Journal on Control and Optimization, vol.35, issue.5, pp.1811-1827, 1997.
DOI : 10.1137/S0363012995283789

M. Duflo, Algorithmes stochastiques, 1996.

M. Duflo, Random iterative models, Applications of Mathematics, vol.34, 1997.
DOI : 10.1007/978-3-662-12880-0

M. Fischler and R. Bolles, Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography, Communications of the ACM, vol.24, issue.6, pp.381-395, 1981.
DOI : 10.1145/358669.358692

H. Fritz, P. Filzmoser, and C. Croux, A comparison of algorithms for the multivariate L 1-median, Computational Statistics, vol.43, issue.4, pp.393-410, 2012.
DOI : 10.1073/pnas.97.4.1423

F. Ferraty and P. Vieu, Nonparametric functional data analysis : theory and practice, 2006.

T. Fletcher, S. Venkatasubramanian, and S. Joshi, The geometric median on Riemannian manifolds with application to robust atlas estimation, NeuroImage, vol.45, issue.1, pp.143-152, 2009.
DOI : 10.1016/j.neuroimage.2008.10.052

A. Godichon-baggioni, Estimating the geometric median in Hilbert spaces with stochastic gradient algorithms : Lp and almost sure rates of convergence, Journal of Multivariate Analysis, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01413440

A. Godichon-baggioni and B. Portier, An averaged projected robbinsmonro algorithm for estimating the parameters of a truncated spherical distribution, 2016.

A. Sara and . Geer, Empirical Processes in M-estimation, 2000.

D. Gervini, Robust functional estimation using the median and spherical principal components, Biometrika, vol.95, issue.3, pp.587-600, 2008.
DOI : 10.1093/biomet/asn031

M. Gahbiche and M. Pelletier, On the estimation of the asymptotic covariance matrix for the averaged Robbins???Monro algorithm, Comptes Rendus de l'Académie des Sciences-Series I-Mathematics, pp.255-260, 2000.
DOI : 10.1016/S0764-4442(00)01595-0

J. B. Haldane, Note on the median of a multivariate distribution, Biometrika, vol.35, issue.3-4, pp.414-417, 1948.
DOI : 10.1093/biomet/35.3-4.414

. Ham71, R. Frank, and . Hampel, A general qualitative definition of robustness. The Annals of Mathematical Statistics, pp.1887-1896, 1971.

M. Hallin and D. Paindaveine, Semiparametrically efficient rank-based inference for shape. i. optimal rank-based tests for sphericity. The Annals of Statistics, pp.2707-2756, 2006.

P. Huber and E. Ronchetti, Robust Statistics, 2009.

M. Hubert, P. Rousseeuw, and S. Van-aelst, High-Breakdown Robust Multivariate Methods, Statistical Science, vol.23, issue.1, pp.92-119, 2008.
DOI : 10.1214/088342307000000087

R. Hyndman and S. Ullah, Robust forecasting of mortality and fertility rates: A functional data approach, Computational Statistics & Data Analysis, vol.51, issue.10, pp.4942-4956, 2007.
DOI : 10.1016/j.csda.2006.07.028

P. Huber, Robust Estimation of a Location Parameter, The Annals of Mathematical Statistics, vol.35, issue.1, pp.73-101, 1964.
DOI : 10.1214/aoms/1177703732

A. Jakubowski, Tightness criteria for random measures with application to the principle of conditioning in Hilbert spaces, Probab. Math. Statist, vol.9, issue.1, pp.95-114, 1988.

C. Bernard, S. Jiang, and . Jiang, Machine vision based inspection of oil seals, Journal of manufacturing systems, vol.17, issue.3, pp.159-166, 1998.

Y. Juditsky and . Nesterov, Deterministic and Stochastic Primal-Dual Subgradient Algorithms for Uniformly Convex Minimization, Stochastic Systems, vol.4, issue.1, pp.44-80, 2014.
DOI : 10.1287/10-SSY010

URL : https://hal.archives-ouvertes.fr/hal-00974231

I. Jolliffe, Principal Components Analysis, 2002.

J. Kemperman, The median of a finite measure on a Banach space In Statistical data analysis based on the L 1 -norm and related methods, pp.217-230, 1987.

D. Kraus and V. M. Panaretos, Dispersion operators and resistant second-order functional data analysis, Biometrika, vol.99, issue.4, pp.813-832, 2012.
DOI : 10.1093/biomet/ass037

A. Volker-krätschmer, H. Schied, and . Zähle, Qualitative and infinitesimal robustness of tail-dependent statistical functionals, Journal of Multivariate Analysis, vol.103, issue.1, pp.35-47, 2012.
DOI : 10.1016/j.jmva.2011.06.005

W. Harold and . Kuhn, A note on Fermat's problem, Mathematical programming, vol.4, issue.1, pp.98-107, 1973.

J. Harold, G. Kushner, and . Yin, Stochastic approximation and recursive algorithms and applications, 2003.

U. Landau, Estimation of a circular arc center and its radius, Computer Vision, Graphics, and Image Processing, vol.38, issue.3, pp.317-326, 1987.
DOI : 10.1016/0734-189X(87)90116-2

S. Lacoste-julien, M. Schmidt, and F. Bach, A simpler approach to obtaining an O (1/t) convergence rate for the projected stochastic subgradient method. arXiv preprint arXiv :1212, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00768187

. Lms-+-99-]-n, J. S. Locantore, D. Marron, N. Simpson, J. T. Tripoli et al., Robust principal components for functional data, Test, vol.8, pp.1-73, 1999.

J. Liu and Z. Wu, An adaptive approach for primitive shape extraction from point clouds, Optik - International Journal for Light and Electron Optics, vol.125, issue.9, pp.2000-2008, 2014.
DOI : 10.1016/j.ijleo.2013.03.176

S. Minsker, Geometric median and robust estimation in Banach spaces, Bernoulli, vol.21, issue.4, 2014.
DOI : 10.3150/14-BEJ645

R. A. Maronna, R. D. Martin, and V. J. Yohai, Theory and methods, Robust statistics. Wiley Series in Probability and Statistics, 2006.

J. Möttönen, K. Nordhausen, and H. Oja, Asymptotic theory of the spatial median In Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis : A Festschrift in honor of Professor Jana Jure? cková, IMS Collection, vol.7, pp.182-193, 2010.

A. Daniel, . Martins, J. António, A. J. Neves, and . Pinho, Real-time generic ball recognition in robocup domain, Proc. of the 3rd International Workshop on Intelligent Robotics, IROBOT, pp.37-48, 2008.

A. Mokkadem and M. Pelletier, Convergence rate and averaging of nonlinear two-time-scale stochastic approximation algorithms, The Annals of Applied Probability, vol.16, issue.3, pp.1671-1702, 2006.
DOI : 10.1214/105051606000000448

URL : https://hal.archives-ouvertes.fr/hal-00690298

[. Minsker, S. Srivastava, L. Lin, and D. Dunson, Scalable and robust bayesian inference via the median posterior, Proceedings of the 31st International Conference on Machine Learning (ICML-14), pp.1656-1664, 2014.

J. Robb and . Muirhead, Aspects of multivariate statistical theory, 2009.

A. Nemirovski, A. Juditsky, G. Lan, and A. Shapiro, Robust Stochastic Approximation Approach to Stochastic Programming, SIAM Journal on Optimization, vol.19, issue.4, pp.1574-1609, 2009.
DOI : 10.1137/070704277

URL : https://hal.archives-ouvertes.fr/hal-00976649

Y. Nesterov, A. Nemirovskii, and Y. Ye, Interior-point polynomial algorithms in convex programming, SIAM, vol.13, 1994.
DOI : 10.1137/1.9781611970791

H. Oja and A. Niinimaa, Asymptotic properties of the generalized median in the case of multivariate normality, Journal of the Royal Statistical Society. Series B (Methodological), pp.372-377, 1985.

M. Pelletier, On the almost sure asymptotic behaviour of stochastic algorithms . Stochastic processes and their applications, pp.217-244, 1998.

M. Pelletier, Asymptotic Almost Sure Efficiency of Averaged Stochastic Algorithms, SIAM Journal on Control and Optimization, vol.39, issue.1, pp.49-72, 2000.
DOI : 10.1137/S0363012998308169

V. Valentin and . Petrov, Limit theorems of probability theory. sequences of independent random variables, Oxford Studies in Probability, 1995.

I. Pinelis, Optimum bounds for the distributions of martingales in Banach spaces. The Annals of Probability, pp.1679-1706, 1994.

B. Polyak and A. Juditsky, Acceleration of Stochastic Approximation by Averaging, SIAM Journal on Control and Optimization, vol.30, issue.4, pp.838-855, 1992.
DOI : 10.1137/0330046

[. Team, R : A Language and Environment for Statistical Computing . R Foundation for Statistical Computing, 2010.

T. Rabbani, Automatic reconstruction of industrial installations using point clouds and images, Nederlandse Commissie voor Geodesie Netherlands Geodetic Commission, 2006.

P. Révész, How to apply the method of stochastic approximation in the nonparametric estimation of a regression function 1, Statistics : A Journal of Theoretical and Applied Statistics, vol.8, issue.1, pp.119-126, 1977.

H. Robbins and S. Monro, A stochastic approximation method. The annals of mathematical statistics, pp.400-407, 1951.

O. James, B. W. Ramsay, and . Silverman, Functional Data Analysis, 2005.

C. Rusu, M. Tico, P. Kuosmanen, J. Edward, and . Delp, Classical geometrical approach to circle fitting?review and new developments, Journal of Electronic Imaging, vol.12, issue.1, pp.179-193, 2003.

M. Rudelson, Recent developments in non-asymptotic theory of random matrices . Modern Aspects of Random Matrix Theory, p.83, 2014.

D. Ruppert, Efficient estimations from a slowly convergent robbins-monro process, 1988.

M. Rudelson and R. Vershynin, Non-asymptotic Theory of Random Matrices: Extreme Singular Values, Proceedings of the International Congress of Mathematicians 2010 (ICM 2010), pp.1576-1602, 2010.
DOI : 10.1142/9789814324359_0111

P. Rousseeuw and K. Van-driessen, A Fast Algorithm for the Minimum Covariance Determinant Estimator, Technometrics, vol.35, issue.3, pp.212-223, 1999.
DOI : 10.1080/01621459.1994.10476821

R. Serfling, Depth functions in nonparametric multivariate inference. DI- MACS Series in Discrete Mathematics and Theoretical Computer Science, 2006.

C. G. Small, A Survey of Multidimensional Medians, International Statistical Review / Revue Internationale de Statistique, vol.58, issue.3, pp.263-277, 1990.
DOI : 10.2307/1403809

F. Smarandache, Functional Data Analysis, Collected Papers Infinite Study, vol.1, 1996.

M. Shahid-shafiq, . Tümer, and . Güler, Marker detection and trajectory generation algorithms for a multicamera based gait analysis system, Mechatronics, vol.11, issue.4, pp.409-437, 2001.
DOI : 10.1016/S0957-4158(00)00026-X

R. Schnabel, R. Wahl, and R. Klein, Efficient ransac for pointcloud shape detection, Computer graphics forum, pp.214-226

. Trung-thien-tran, . Van-toan, D. Cao, and . Laurendeau, Extraction of cylinders and estimation of their parameters from point clouds, Computers & Graphics, vol.46, pp.345-357, 2015.
DOI : 10.1016/j.cag.2014.09.027

A. Thom, A Statistical Examination of the Megalithic Sites in Britain, Journal of the Royal Statistical Society. Series A (General), vol.118, issue.3, pp.275-295, 1955.
DOI : 10.2307/2342494

S. Taskinen, I. Koch, and H. Oja, Robustifying principal component analysis with spatial sign vectors, Statistics & Probability Letters, vol.82, issue.4, pp.765-774, 2012.
DOI : 10.1016/j.spl.2012.01.001

P. Tarrès and Y. Yao, Online Learning as Stochastic Approximation of Regularization Paths: Optimality and Almost-Sure Convergence, IEEE Transactions on Information Theory, vol.60, issue.9, pp.5716-5735, 2014.
DOI : 10.1109/TIT.2014.2332531

F. Von-hundelshausen, M. Schreiber, and R. Rojas, A Constructive Feature Detection Approach for Robotic Vision, RoboCup 2004 : Robot Soccer World Cup VIII, pp.72-83, 2005.
DOI : 10.1007/978-3-540-32256-6_6

Y. Vardi and C. Zhang, The multivariate L1-median and associated data depth, Proc. Natl. Acad. Sci. USA, pp.1423-1426, 2000.
DOI : 10.1073/pnas.97.4.1423

H. Walk, An invariance principle for the robbins-monro process in a hilbert space. Probability Theory and Related Fields, pp.135-150, 1977.

E. Weiszfeld, On the point for which the sum of the distances to n given points is minimum, Annals of Operations Research, vol.43, issue.3, pp.355-386, 1937.
DOI : 10.1007/978-3-642-56082-8_1

E. Weiszfeld, Sur le point pour lequel la somme des distances de n points donnés est minimum, Tohoku Math. J, vol.43, issue.2, pp.355-386, 1937.

A. Weber and C. Friedrich, Alfred weber's theory of the location of industries, 1929.

M. Woodroofe, Normal approximation and large deviations for the Robbins-Monro Process, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.1, issue.4, pp.329-338, 1972.
DOI : 10.1007/BF00532261

J. Weng, Y. Zhang, and W. Hwang, Candid covariance-free incremental principal component analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.25, issue.8, pp.1034-1040, 2003.
DOI : 10.1109/TPAMI.2003.1217609

L. Yang, Abstract, LMS Journal of Computation and Mathematics, vol.43, pp.461-479, 2010.
DOI : 10.1007/978-3-662-12494-9

URL : https://hal.archives-ouvertes.fr/hal-01153717

H. Zähle, A definition of qualitative robustness for general point estimators, and examples, Journal of Multivariate Analysis, vol.143, pp.12-31, 2016.
DOI : 10.1016/j.jmva.2015.08.004

]. Zhang, J. Stockel, M. Wolf, P. Cathier, G. Mclennan et al., A New Method for Spherical Object Detection and Its Application to Computer Aided Detection of Pulmonary Nodules in CT Images, Medical Image Computing and Computer-Assisted Intervention? MICCAI 2007, pp.842-849, 2007.
DOI : 10.1007/978-3-540-75757-3_102