D. Anguelov, P. Srinivasan, D. Koller, S. Thrun, J. Rodgers et al., SCAPE: shape completion and animation of people, Proceedings of SIGGRAPH, pp.408-416, 2005.

S. Balakrishnan, A. Rinaldo, D. Sheehy, A. Singh, and L. A. Wasserman, Minimax rates for homology inference, Journal of Machine Learning Research -Proceedings Track, vol.22, pp.64-72, 2012.

U. Bauer, A. Munk, H. Sieling, and M. Wardetzky, Persistent homology meets statistical inference -a case study: Detecting modes of one-dimensional signals, pp.1404-1214, 2014.

G. Biau, B. Cadre, D. M. Mason, and B. Pelletier, Asymptotic Normality in Density Support Estimation, Electronic Journal of Probability, vol.14, issue.0, pp.2617-2635, 2009.
DOI : 10.1214/EJP.v14-722

URL : https://hal.archives-ouvertes.fr/hal-00445700

P. Bubenik, Statistical topology using persistence landscapes, ArXiv, 2012.

P. Bubenik, T. Peter, and . Kim, A statistical approach to persistent homology. Homology, Homotopy and Applications, pp.337-362, 2007.

D. Burago, Y. Burago, and S. Ivanov, A Course in Metric Geometry, 2001.
DOI : 10.1090/gsm/033

C. Caillerie, F. Chazal, J. Dedecker, and B. Michel, Deconvolution for the Wasserstein metric and geometric inference, Electronic Journal of Statistics, vol.5, issue.0, pp.1394-1423, 2011.
DOI : 10.1214/11-EJS646

URL : https://hal.archives-ouvertes.fr/inria-00607806

G. Carlsson, Topology and data, Bulletin of the American Mathematical Society, vol.46, issue.2, pp.255-308, 2009.
DOI : 10.1090/S0273-0979-09-01249-X

F. Chazal, D. Cohen-steiner, M. Glisse, L. J. Guibas, and S. Y. Oudot, Proximity of persistence modules and their diagrams, Proceedings of the 25th annual symposium on Computational geometry, SCG '09, pp.237-246, 2009.
DOI : 10.1145/1542362.1542407

URL : https://hal.archives-ouvertes.fr/inria-00292566

F. Chazal, D. Cohen-steiner, L. J. Guibas, F. Mémoli, and S. Y. Oudot, Gromov-Hausdorff Stable Signatures for Shapes using Persistence, Computer Graphics Forum, vol.33, issue.5, pp.1393-1403, 2009.
DOI : 10.1111/j.1467-8659.2009.01516.x

URL : https://hal.archives-ouvertes.fr/hal-00772413

F. Chazal, D. Cohen-steiner, and Q. Mérigot, Geometric Inference for Probability Measures, Foundations of Computational Mathematics, vol.40, issue.2, pp.733-751, 2011.
DOI : 10.1007/s10208-011-9098-0

URL : https://hal.archives-ouvertes.fr/hal-00772444

F. Chazal, M. Vin-de-silva, S. Glisse, and . Oudot, The structure and stability of persistence modules, 2012.
DOI : 10.1007/978-3-319-42545-0

URL : https://hal.archives-ouvertes.fr/hal-01107617

F. Chazal, S. Vin-de-silva, and . Oudot, Persistence stability for geometric complexes, Geometriae Dedicata, vol.33, issue.2, 2012.
DOI : 10.1007/s10711-013-9937-z

URL : https://hal.archives-ouvertes.fr/hal-00923560

F. Chazal, L. J. Guibas, S. Y. Oudot, and P. Skraba, Persistence-based clustering in Riemannian manifolds, J. ACM, vol.60, issue.6, pp.41-42, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01094872

F. Chazal, B. T. Fasy, F. Lecci, B. Michel, A. Rinaldo et al., Robust topological inference: Distance to a measure and kernel distance, pp.1412-7197, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01232217

F. Chazal, B. T. Fasy, F. Lecci, B. Michel, A. Rinaldo et al., Subsampling methods for persistent homology ArXiv:1406, 1901.

D. Cohen-steiner, H. Edelsbrunner, and J. Harer, Stability of Persistence Diagrams, Discrete & Computational Geometry, vol.37, issue.1, pp.103-120, 2007.
DOI : 10.1007/s00454-006-1276-5

A. Cuevas, Set Estimation, pp.71-85, 2009.
DOI : 10.1093/acprof:oso/9780199232574.003.0011

A. Cuevas and R. Fraiman, A plug-in approach to support estimation. The Annals of Statistics, pp.2300-2312, 1997.

A. Cuevas and A. Rodríguez, On boundary estimation, Advances in Applied Probability, vol.21, issue.02, pp.340-354, 2004.
DOI : 10.1002/(SICI)1099-1476(19990310)22:4<301::AID-MMA42>3.0.CO;2-M

A. Cuevas, R. Fraiman, and B. Pateiro-lópez, On Statistical Properties of Sets Fulfilling Rolling-Type Conditions, Advances in Applied Probability, vol.34, issue.02, pp.311-329, 2012.
DOI : 10.1214/aos/1030741072

V. De, S. , and R. Ghrist, Homological sensor networks. Notices of the, 2007.

E. De-vito, L. Rosasco, and A. Toigo, Learning sets with separating kernels, Applied and Computational Harmonic Analysis, vol.37, issue.2, pp.185-217, 2014.
DOI : 10.1016/j.acha.2013.11.003

L. Devroye and G. L. Wise, Detection of Abnormal Behavior Via Nonparametric Estimation of the Support, SIAM Journal on Applied Mathematics, vol.38, issue.3, pp.480-488, 1980.
DOI : 10.1137/0138038

L. Dümbgen and G. Walther, Rates of convergence for random approximations of convex sets, Advances in Applied Probability, vol.28, issue.02, pp.384-393, 1996.
DOI : 10.1111/j.1365-2818.1988.tb04682.x

H. Edelsbrunner, The union of balls and its dual shape, Discrete & Computational Geometry, vol.133, issue.3-4, pp.415-440, 1995.
DOI : 10.1007/BF02574053

H. Edelsbrunner, L. John, and . Harer, Computational Topology: an Introduction, 2010.
DOI : 10.1090/mbk/069

H. Edelsbrunner, D. Letscher, and A. Zomorodian, Topological Persistence and Simplification, Discrete & Computational Geometry, vol.28, issue.4, pp.511-533, 2002.
DOI : 10.1007/s00454-002-2885-2

B. T. Fasy, F. Lecci, A. Rinaldo, L. Wasserman, S. Balakrishnan et al., Confidence sets for persistence diagrams. The Annals of Statistics, pp.2301-2339, 2014.

H. Federer, Curvature measures. Transactions of the, pp.418-491, 1959.

C. R. Genovese, M. Perone-pacifico, I. Verdinelli, and L. Wasserman, Minimax manifold estimation, Journal of Machine Learning Research, vol.13, pp.1263-1291, 2012.

C. R. Genovese, M. Perone-pacifico, I. Verdinelli, and L. Wasserman, Manifold estimation and singular deconvolution under hausdorff loss. The Annals of Statistics, pp.941-963, 2012.

A. Hatcher, Algebraic Topology, 2001.

M. Peter, A. Kasson, S. Zomorodian, N. Park, L. J. Singhal et al., Persistent voids: a new structural metric for membrane fusion, Bioinformatics, vol.23, issue.14, pp.1753-1759, 2007.

A. Petrovi?, K. , and A. B. Tsybakov, Minimax Theory of Image Reconstruction, Lecture Notes in Statistics, vol.82, 1993.

A. Petrovi?-korostelëv, L. Simar, and A. B. Tsybakov, Efficient Estimation of Monotone Boundaries, The Annals of Statistics, vol.23, issue.2, pp.476-489, 1995.
DOI : 10.1214/aos/1176324531

P. Massart, Concentration Inequalities and Model Selection Lectures from the 33rd Summer School on Probability Theory held in Saint-Flour, 2003.

A. Meister, Deconvolution Problems in Nonparametric Statistics, 2009.
DOI : 10.1007/978-3-540-87557-4

Y. Mileyko, S. Mukherjee, and J. Harer, Probability measures on the space of persistence diagrams, Inverse Problems, vol.27, issue.12, 2011.
DOI : 10.1088/0266-5611/27/12/124007

P. Niyogi, S. Smale, and S. Weinberger, Finding the Homology of Submanifolds with High Confidence from??Random??Samples, Discrete & Computational Geometry, vol.33, issue.11, pp.419-441, 2008.
DOI : 10.1007/s00454-008-9053-2

P. Niyogi, S. Smale, and S. Weinberger, A Topological View of Unsupervised Learning from Noisy Data, SIAM Journal on Computing, vol.40, issue.3, pp.646-663, 2011.
DOI : 10.1137/090762932

A. Rodríguez, Set estimation under convexity type assumptions Annales de l'Institut Henri Poincare (B) Probability and Statistics, pp.763-774, 2007.

A. Singh, C. Scott, and R. Nowak, Adaptive Hausdorff estimation of density level sets. The Annals of Statistics, pp.2760-2782, 2009.

G. Singh, F. Memoli, T. Ishkhanov, G. Sapiro, G. Carlsson et al., Topological analysis of population activity in visual cortex, Journal of Vision, vol.8, issue.8, 2008.
DOI : 10.1167/8.8.11

A. B. Tsybakov, On nonparametric estimation of density level sets. The Annals of Statistics, pp.948-969, 1997.

B. Alexandre, V. Tsybakov, and . Zaiats, Introduction to Nonparametric Estimation, 2009.

J. Wang, Geometric Structure of High-Dimensional Data and Dimensionality Reduction, 2012.
DOI : 10.1007/978-3-642-27497-8

S. Weinberger, The Complexity of Some Topological Inference Problems, Foundations of Computational Mathematics, vol.116, issue.17, pp.1277-1285, 2014.
DOI : 10.1007/s10208-013-9152-1

A. Zomorodian and G. Carlsson, Computing Persistent Homology, Discrete & Computational Geometry, vol.33, issue.2, pp.249-274, 2005.
DOI : 10.1007/s00454-004-1146-y

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.5064