J. Mangin, V. Frouin, I. Bloch, J. Régis, and J. , From 3D magnetic resonance images to structural representations of the cortex topography using topology preserving deformations, Journal of Mathematical Imaging and Vision, vol.44, issue.6, pp.297-318, 1995.
DOI : 10.1007/BF01250286

S. Faisan, N. Passat, V. Noblet, R. Chabrier, and C. Meyer, Topology Preserving Warping of Binary Images: Application to Atlas-Based Skull Segmentation, MICCAI'08 Proceedings, Part I, pp.211-218, 2008.
DOI : 10.1007/978-3-540-85988-8_26

N. Cornea, D. Silver, X. Yuan, and R. Balasubramanian, Computing hierarchical curve-skeletons of 3D objects, The Visual Computer, vol.14, issue.11, pp.945-955, 2005.
DOI : 10.1007/s00371-005-0308-0

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

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

E. R. Davies and A. P. Plummer, Thinning algorithms: A critique and a new methodology, Pattern Recognition, vol.14, issue.1-6, pp.1-6
DOI : 10.1016/0031-3203(81)90045-5

N. Passat, M. Couprie, and G. Bertrand, Minimal Simple Pairs in the 3-D Cubic Grid, Journal of Mathematical Imaging and Vision, vol.17, issue.1, pp.239-249, 2008.
DOI : 10.1007/s10851-008-0099-9

URL : https://hal.archives-ouvertes.fr/hal-00622368

A. Rosenfeld, Connectivity in Digital Pictures, Journal of the ACM, vol.17, issue.1, pp.146-160, 1970.
DOI : 10.1145/321556.321570

A. Rosenfeld, Arcs and Curves in Digital Pictures, Journal of the ACM, vol.20, issue.1, pp.81-87, 1973.
DOI : 10.1145/321738.321745

C. Ronse, A topological characterization of thinning, Theoretical Computer Science, vol.43, issue.1, pp.31-41, 1986.
DOI : 10.1016/0304-3975(86)90164-7

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

T. Y. Kong, R. Litherland, and A. Rosenfeld, Problems in the topology of binary digital images, Open Problems in Topology, pp.377-385, 1990.

V. A. Kovalesky, 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, Topology-preserving deletion of 1's from 2-, 3- and 4-dimensional binary images, Discrete Geometry for Computer Imagery -DGCI'97, 7th International Workshop, Proceedings, pp.3-18, 1997.
DOI : 10.1007/BFb0024826

G. Bertrand, On critical kernels, Comptes Rendus de l'Académie des Sciences, Série Mathématiques, vol.1, issue.345, pp.363-367, 2007.

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

N. Passat and L. Mazo, An introduction to simple sets, Pattern Recognition Letters, vol.30, issue.15, pp.1366-1377, 2009.
DOI : 10.1016/j.patrec.2009.07.008

G. Bertrand, On Topological Watersheds, Journal of Mathematical Imaging and Vision, vol.34, issue.6, pp.217-230, 2005.
DOI : 10.1007/s10851-005-4891-5

URL : https://hal.archives-ouvertes.fr/hal-00622398

T. Y. Kong, Minimal non-deletable sets and minimal non-codeletable sets in binary images, Theoretical Computer Science, vol.406, issue.1-2, pp.97-118, 2008.
DOI : 10.1016/j.tcs.2008.02.001

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

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.

C. R. Maunder, Algebraic topology, 1996.

L. Mazo and N. Passat, On 2-dimensional simple sets in n-dimensional cubic grids, Discrete & Computational Geometry (In press

R. Malgouyres and A. Lenoir, Topology Preservation Within Digital Surfaces, Graphical Models, vol.62, issue.2, pp.71-84, 2000.
DOI : 10.1006/gmod.1999.0517

URL : https://hal.archives-ouvertes.fr/hal-01318725