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

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

G. Bertrand, On critical kernels Comptes Rendus de l, Académie des Sciences, Série Math. I, issue.345, pp.363-367, 2007.

G. Bertrand and M. Couprie, On Parallel Thinning Algorithms: Minimal Non-simple Sets, P-simple Points and Critical Kernels, Journal of Mathematical Imaging and Vision, vol.2, issue.2, pp.23-35, 2009.
DOI : 10.1007/b97315

URL : https://hal.archives-ouvertes.fr/hal-00731784

A. Manzanera, T. 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. Lohou and G. Bertrand, Two symmetrical thinning algorithms for 3D binary images, based on -simple points, Pattern Recognition, vol.40, issue.8, pp.2301-2314, 2007.
DOI : 10.1016/j.patcog.2006.12.032

URL : https://hal.archives-ouvertes.fr/hal-00622094

K. Palágyi, A 3D fully parallel surface-thinning algorithm, Theoretical Computer Science, vol.406, issue.1-2, pp.119-135, 2008.
DOI : 10.1016/j.tcs.2008.06.041

Y. Tsao and K. Fu, A parallel thinning algorithm for 3-D pictures, Computer Graphics and Image Processing, vol.17, issue.4, pp.315-331, 1981.
DOI : 10.1016/0146-664X(81)90011-3

Y. Tsao and K. Fu, A 3D parallel skeletonwise thinning algorithm pictures, Proceedings PRIP 82: IEEE Computer Society Conference on Pattern Recognition and Image Processing, pp.678-683, 1982.

K. Palágyi and A. Kuba, A 3D 6-subiteration thinning algorithm for extracting medial lines, Pattern Recognition Letters, vol.19, issue.7, pp.613-627, 1998.
DOI : 10.1016/S0167-8655(98)00031-2

C. M. Ma and S. Y. Wan, Parallel Thinning Algorithms on 3D (18, 6) Binary Images, Computer Vision and Image Understanding, vol.80, issue.3, pp.364-378, 2000.
DOI : 10.1006/cviu.2000.0879

C. M. Ma, S. Y. Wan, and J. D. Lee, Three-dimensional topology preserving reduction on the 4-subfields, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, issue.12, pp.1594-1605, 2002.

C. Ma, S. Wan, and H. Chang, Extracting medial curves on 3D images, Pattern Recognition Letters, vol.23, issue.8, pp.895-904, 2002.
DOI : 10.1016/S0167-8655(01)00162-3

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

G. Németh, P. Kardos, and K. Palágyi, Topology Preserving 2-Subfield 3D Thinning Algorithms, Signal Processing, Pattern Recognition and Applications, pp.311-316, 2010.
DOI : 10.2316/P.2010.678-090

G. Németh, P. Kardos, and K. Palágyi, Topology Preserving 3D Thinning Algorithms Using Four and Eight Subfields, Image Analysis and Recognition. Lecture Notes in Computer Science, vol.6111, pp.316-325, 2010.
DOI : 10.1007/978-3-642-13772-3_32

G. Bertrand and M. Couprie, Powerful Parallel and Symmetric 3D Thinning Schemes Based on Critical Kernels, Journal of Mathematical Imaging and Vision, vol.2, issue.2, pp.134-148, 2014.
DOI : 10.1016/0040-9383(63)90014-4

URL : https://hal.archives-ouvertes.fr/hal-00828450

L. Liu, E. W. Chambers, D. Letscher, and T. Ju, A simple and robust thinning algorithm on cell complexes, Computer Graphics Forum, vol.13, issue.4, pp.2253-2260, 2010.
DOI : 10.1111/j.1467-8659.2010.01814.x

G. Bertrand and M. Couprie, Isthmus based parallel and symmetric 3D thinning algorithms, Graphical Models, vol.80, pp.1-15, 2015.
DOI : 10.1016/j.gmod.2015.05.001

URL : https://hal.archives-ouvertes.fr/hal-01217936

M. Couprie and G. Bertrand, Asymmetric parallel 3D thinning scheme and algorithms based on isthmuses, Pattern Recognition Letters, vol.76, pp.22-31, 2016.
DOI : 10.1016/j.patrec.2015.03.014

URL : https://hal.archives-ouvertes.fr/hal-01104691

V. Kovalevsky, Finite topology as applied to image analysis, Computer Vision, Graphics, and Image Processing, vol.46, issue.2, pp.141-161, 1989.
DOI : 10.1016/0734-189X(89)90165-5

T. Y. Kong and A. Rosenfeld, Digital topology: Introduction and survey, Computer Vision, Graphics, and Image Processing, vol.48, issue.3, pp.357-393, 1989.
DOI : 10.1016/0734-189X(89)90147-3

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

G. Bertrand, New Notions for Discrete Topology, Lecture Notes in Computer Science, vol.1568, pp.218-228, 1999.
DOI : 10.1007/3-540-49126-0_17

URL : https://hal.archives-ouvertes.fr/hal-00621992

G. Bertrand and G. Malandain, A new characterization of three-dimensional simple points, Pattern Recognition Letters, vol.15, issue.2, pp.169-175, 1994.
DOI : 10.1016/0167-8655(94)90046-9

URL : https://hal.archives-ouvertes.fr/inria-00615050

G. Bertrand, Simple points, topological numbers and geodesic neighborhoods in cubic grids, Pattern Recognition Letters, vol.15, issue.10, pp.1003-1011, 1994.
DOI : 10.1016/0167-8655(94)90032-9

URL : https://hal.archives-ouvertes.fr/hal-00621999

P. Saha, B. Chaudhuri, B. Chanda, and D. Dutta-majumder, Topology preservation in 3D digital space, Pattern Recognition, vol.27, issue.2, pp.295-300, 1994.
DOI : 10.1016/0031-3203(94)90060-4

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

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

J. Whitehead, -Groups, Proceedings of the London Mathematical Society, vol.2, issue.1, pp.243-327, 1939.
DOI : 10.1112/plms/s2-45.1.243

URL : https://hal.archives-ouvertes.fr/hal-00304554

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 : 10.1145/321637.321646

H. Blum, A transformation for extracting new descriptors of shape: Models for the perception of speech and visual form, pp.382-380, 1967.

A. Lieutier, Any open bounded subset of has the same homotopy type as its medial axis, Computer-Aided Design, vol.36, issue.11, pp.1029-1046, 2004.
DOI : 10.1016/j.cad.2004.01.011

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

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

R. Malgouyres and A. Francés, Determining Whether a Simplicial 3-Complex Collapses to a 1-Complex Is NP-Complete, Proceedings Discrete Geometry for Computer Imagery, pp.177-188, 2008.
DOI : 10.1007/978-3-540-79126-3_17

D. Shaked and A. M. Bruckstein, Pruning Medial Axes, Computer Vision and Image Understanding, vol.69, issue.2, pp.156-169, 1998.
DOI : 10.1006/cviu.1997.0598

J. Chaussard, Topological tools for discrete shape analysis, 2010.
URL : https://hal.archives-ouvertes.fr/tel-00587411

M. Thorup, Equivalence between priority queues and sorting, Proceedings 43rd Symposium on Foundations of Computer Science. FOCS '02, pp.125-134, 2002.