D. Attali, A. Lieutier, and D. Salinas, Vietoris???Rips complexes also provide topologically correct reconstructions of sampled shapes, Computational Geometry, vol.46, issue.4, pp.448-465, 2012.
DOI : 10.1016/j.comgeo.2012.02.009

URL : https://hal.archives-ouvertes.fr/hal-00579864

I. N. Bernstein, I. M. Gelfand, and V. A. Ponomarev, COXETER FUNCTORS AND GABRIEL'S THEOREM, Russian Mathematical Surveys, vol.28, issue.2, pp.17-32, 1973.
DOI : 10.1070/RM1973v028n02ABEH001526

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

D. Burago, Y. Burago, and S. Ivanov, A Course in Metric Geometry, Graduate Studies in Mathematics, vol.33, 2001.
DOI : 10.1090/gsm/033

G. Carlsson, Topology and data. Bulletin of the, pp.255-308, 2009.

G. Carlsson and V. Silva, Zigzag Persistence, Foundations of Computational Mathematics, vol.33, issue.2, pp.367-405, 2010.
DOI : 10.1007/s10208-010-9066-0

URL : http://dx.doi.org/10.1007/s10208-010-9066-0

G. Carlsson, T. Ishkhanov, V. De-silva, and A. Zomorodian, On the Local Behavior of Spaces of Natural Images, International Journal of Computer Vision, vol.265, issue.4, pp.1-12, 2008.
DOI : 10.1007/s11263-007-0056-x

F. Chazal and D. Cohen-steiner, Geometric inference, Tesselations in the Sciences, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00772444

F. Chazal, D. Cohen-steiner, and A. Lieutier, A Sampling Theory for Compact Sets in Euclidean Space, Discrete & Computational Geometry, vol.18, issue.3, pp.461-479, 2009.
DOI : 10.1007/s00454-009-9144-8

URL : https://hal.archives-ouvertes.fr/hal-00864493

F. Chazal, L. J. Guibas, S. Y. Oudot, and P. Skraba, Scalar Field Analysis over Point Cloud Data, Discrete & Computational Geometry, vol.33, issue.2, pp.743-775, 2011.
DOI : 10.1007/s00454-011-9360-x

URL : https://hal.archives-ouvertes.fr/hal-00772430

F. Chazal and S. Y. Oudot, Towards persistence-based reconstruction in euclidean spaces, Proceedings of the twenty-fourth annual symposium on Computational geometry , SCG '08, pp.232-241, 2008.
DOI : 10.1145/1377676.1377719

URL : https://hal.archives-ouvertes.fr/inria-00197543

V. Silva, A weak characterisation of the Delaunay triangulation, Geometriae Dedicata, vol.33, issue.2, pp.39-64, 2008.
DOI : 10.1007/s10711-008-9261-1

V. De-silva and G. Carlsson, Topological estimation using witness complexes, IEEE Symposium on Point-based Graphic, pp.157-166, 2004.

V. De-silva and R. Ghrist, Coverage in sensor networks via persistent homology, Algebraic & Geometric Topology, vol.7, issue.1, pp.339-358, 2007.
DOI : 10.2140/agt.2007.7.339

T. K. Dey, F. Fan, and Y. Wang, Graph induced complex on point data, Proc. 29th Annual Symposium on Computational Geometry, pp.107-116, 2013.

K. Tamal, F. Dey, Y. Fan, and . Wang, Computing topological persistence for simplicial maps, Proc. 30th Annual Symposium on Computational Geometry, 2014.

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

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

P. Gabriel, Unzerlegbare Darstellungen I, manuscripta mathematica, vol.8, issue.1, pp.71-103, 1972.
DOI : 10.2307/1969899

URL : http://www.digizeitschriften.de/download/PPN365956996_0006/PPN365956996_0006___log9.pdf

L. J. Guibas and S. Y. Oudot, Reconstruction Using Witness Complexes, Discrete & Computational Geometry, vol.33, issue.2, pp.325-356, 2008.
DOI : 10.1007/s00454-008-9094-6

URL : https://hal.archives-ouvertes.fr/hal-00488434

A. Hatcher, Algebraic Topology, 2001.

J. Hausmann, On the Vietoris-Rips complexes and a cohomology theory for metric spaces. Prospects in topology, Ann. of Math. Stud, vol.138, pp.175-188, 1995.

B. Hudson, G. Miller, S. Y. Oudot, and D. Sheehy, Topological inference via meshing, Proceedings of the 2010 annual symposium on Computational geometry, SoCG '10, pp.277-286, 2010.
DOI : 10.1145/1810959.1811006

URL : https://hal.archives-ouvertes.fr/inria-00436891

M. Kashiwara and P. Schapira, Categories and Sheaves, volume 332 of Grundlehren der mathematischen Wissenschaften, 2006.

J. Latschev, Vietoris-Rips complexes of metric spaces near a closed Riemannian manifold, Archiv der Mathematik, vol.77, issue.6, pp.522-528, 2001.
DOI : 10.1007/PL00000526

A. B. Lee, K. S. Pedersen, and D. Mumford, The nonlinear statistics of high-contrast patches in natural images, International Journal of Computer Vision, vol.54, issue.1/2, pp.83-103, 2003.
DOI : 10.1023/A:1023705401078

D. R. Sheehy, Linear-size approximations to the vietoris-rips filtration, Proc. ACM Symposium on Computational Geometry, pp.239-248, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01111878

J. H. Van-hateren, A. Van, and . Schaaff, Independent component filters of natural images compared with simple cells in primary visual cortex, Proceedings of the Royal Society B: Biological Sciences, vol.265, issue.1394, pp.359-366, 1997.
DOI : 10.1098/rspb.1998.0303

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=