G. Bertrand, On P-simple points Comptes Rendus de l'Académie des Sciences, Série Math., I, issue.321, pp.1077-1084, 1995.

G. Bertrand, Sufficient conditions for 3D parallel thinning algorithms, SPIE Vision Geometry IV, pp.52-60, 1995.
DOI : 10.1117/12.216440
URL : https://hal.archives-ouvertes.fr/hal-00621998

G. Bertrand, On critical kernels Comptes Rendus de l'Académie des Sciences, pp.363-367, 2007.

G. Bertrand and M. Couprie, A New 3D Parallel Thinning Scheme Based on Critical Kernels, Discrete Geometry for Computer Imagery, pp.580-591, 2006.
DOI : 10.1007/11907350_49
URL : https://hal.archives-ouvertes.fr/hal-00622000

G. Bertrand and M. Couprie, Two-Dimensional Parallel Thinning Algorithms Based on Critical Kernels, Journal of Mathematical Imaging and Vision, vol.13, issue.2, pp.35-56, 2008.
DOI : 10.1007/s10851-007-0063-0

R. H. Bing, Some aspects of the topology of 3- manifolds related to the Poincaré conjecture. Lectures on modern mathematics, II, pp.93-128, 1964.

J. Burguet and R. Malgouyres, Strong thinning and polyhedric approximation of the surface of a voxel object, Discrete Applied Mathematics, vol.125, issue.1, pp.93-114, 2003.
DOI : 10.1016/S0166-218X(02)00226-3

M. Marshall and . Cohen, A Course in Simple Homotopy Theory, 1973.

M. Couprie, Note on fifteen 2d parallel thinning algorithms, Internal Report, pp.2006-2007, 2006.

M. Couprie and G. Bertrand, New Characterizations of Simple Points in 2D, 3D, and 4D Discrete Spaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.31, issue.4, pp.637-648, 2009.
DOI : 10.1109/TPAMI.2008.117
URL : https://hal.archives-ouvertes.fr/hal-00622393

C. Gau and T. Y. Kong, Minimal non-simple sets in 4D binary images, Graphical Models, vol.65, issue.1-3, pp.112-130, 2003.
DOI : 10.1016/S1524-0703(03)00010-9

P. Giblin, Graphs, Surfaces and Homology, 1981.
DOI : 10.1017/CBO9780511779534

R. W. Hall, Tests for connectivity preservation for parallel reduction operators, Topology and its Applications, vol.46, issue.3, pp.199-217, 1992.
DOI : 10.1016/0166-8641(92)90015-R

T. Kaczynski, K. Mischaikow, and M. Mrozek, Computational Homology, 2004.
DOI : 10.1007/b97315

E. Khalimsky, R. Kopperman, and P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topology and its Applications, vol.36, issue.1, pp.1-17, 1990.
DOI : 10.1016/0166-8641(90)90031-V

T. Y. Kong, ON TOPOLOGY PRESERVATION IN 2-D AND 3-D THINNING, International Journal of Pattern Recognition and Artificial Intelligence, vol.09, issue.05, pp.813-844, 1995.
DOI : 10.1142/S0218001495000341

T. Y. Kong, Topology-preserving deletion of 1's from 2-, 3- and 4-dimensional binary images, Discrete Geometry for Computer Imagery, pp.3-18, 1997.
DOI : 10.1007/BFb0024826

T. Y. Kong, Minimal Non-simple and Minimal Non-cosimple Sets in Binary Images on Cell Complexes, Discrete Geometry for Computer Imagery, pp.169-188, 2006.
DOI : 10.1007/11907350_15

T. Y. Kong, C. Kong, and . Gau, Minimal non-deletable sets and minimal non-codeletable sets in binary images, International Workshop on Combinatorial Image Analysis, pp.97-118, 2004.
DOI : 10.1016/j.tcs.2008.02.001

T. Y. Kong and A. Rosenfeld, Digital Topology, pp.357-393, 1989.
DOI : 10.1007/978-1-4615-1529-6_3

T. Y. Kong, Problem of determining whether a parallel reduction operator for n -dimensional binary images always preserves topology, Vision Geometry II, pp.69-77, 1993.
DOI : 10.1117/12.165013

T. Y. Kong, R. Litherland, and A. Rosenfeld, Problems in the topology of binary digital images, Open problems in topology, pp.376-385, 1990.

V. A. Kovalevsky, Finite topology as applied to image analysis. Computer Vision, Graphics and Image Processing, pp.141-161, 1989.

C. Lohou and G. Bertrand, A 3D 12-subiteration thinning algorithm based on P-simple points, Discrete Applied Mathematics, vol.139, issue.1-3, pp.171-195, 2004.
DOI : 10.1016/j.dam.2002.11.002
URL : https://hal.archives-ouvertes.fr/hal-00622096

C. Lohou and G. Bertrand, A 3D 6-subiteration curve thinning algorithm based on P-simple points, Discrete Applied Mathematics, vol.151, issue.1-3, pp.198-228, 2005.
DOI : 10.1016/j.dam.2005.02.030
URL : https://hal.archives-ouvertes.fr/hal-00622095

C. M. Ma, On Topology Preservation in 3D Thinning, Computer Vision and Image Understanding, vol.59, issue.3, pp.328-339, 1994.
DOI : 10.1006/cviu.1994.1027

A. Manzanera, T. M. Bernard, F. Prêteux, and B. Longuet, <bold>n</bold>-dimensional skeletonization: a unified mathematical framework, Journal of Electronic Imaging, vol.11, issue.1, pp.25-37, 2002.
DOI : 10.1117/1.1426080

C. R. Maunder, Algebraic topology, 1996.

C. Ronse, Minimal test patterns for connectivity preservation in parallel thinning algorithms for binary digital images, Discrete Applied Mathematics, vol.21, issue.1, pp.67-79, 1988.
DOI : 10.1016/0166-218X(88)90034-0

A. Rosenfeld, A characterization of parallel thinning algorithms, Information and Control, vol.29, issue.3, pp.286-291, 1975.
DOI : 10.1016/S0019-9958(75)90448-9

J. H. Whitehead, Simplicial spaces, nuclei and mgroups, Proceedings of the London Mathematical Society, pp.243-327, 1939.
DOI : 10.1112/plms/s2-45.1.243
URL : http://plms.oxfordjournals.org/cgi/content/short/s2-45/1/243

E. C. Zeeman, On the dunce hat, Topology, vol.2, issue.4, pp.341-358, 1964.
DOI : 10.1016/0040-9383(63)90014-4