I. N. In and . Chapter, we give a global overview of the state of the art of skeletonization in the digital topology framework (also called, sometimes, voxel framework), at the time when this thesis was written. We talk about skeleton computation, skeleton analysis and preservation of the visual aspect (medial axes

Y. Anguy, D. Bernard, and R. Ehrlich, The local change of scale method for modelling flow in natural porous media (I): Numerical tools, Advances in Water Resources, vol.17, issue.6, pp.337-351, 1994.
DOI : 10.1016/0309-1708(94)90010-8

D. Attali, J. Boissonnat, and H. Edelsbrunner, Stability and computation of the medial axis ? a state-of-the-art report, Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration, pp.1-19, 2009.

N. Ahuja and J. Chuang, Shape representation using a generalized potential field model, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.19, issue.2, pp.169-176, 1997.
DOI : 10.1109/34.574801

D. Attali and J. Lachaud, Constructing iso-surfaces satisfying the Delaunay constraint. Application to the skeleton computation, Proceedings 10th International Conference on Image Analysis and Processing, pp.382-387, 1999.
DOI : 10.1109/ICIAP.1999.797625

D. Attali and J. Lachaud, Delaunay conforming iso-surface, skeleton??extraction and noise removal, Computational Geometry, vol.19, issue.2-3, pp.175-189, 2001.
DOI : 10.1016/S0925-7721(01)00019-0
URL : http://doi.org/10.1016/s0925-7721(01)00019-0

D. Attali and A. Montanvert, Modelling noise for a better simplification of skeletons, ICIP 1996: Proceedings of the 3rd IEEE International Conference on Image Processing (ICIP), pp.13-16, 1996.

D. Attali and A. Montanvert, Computing and Simplifying 2D and 3D Continuous Skeletons, Computer Vision and Image Understanding, vol.67, issue.3, pp.261-273, 1997.
DOI : 10.1006/cviu.1997.0536

C. Arcelli, Pattern thinning by contour tracing, Computer Graphics and Image Processing, vol.17, issue.2, pp.130-144, 1981.
DOI : 10.1016/0146-664X(81)90021-6

C. Arcelli, G. S. , and D. Baja, Medial Lines and Figure Analysis, ICPR 1980: Proceedings of the 5th International Conference on Pattern Recognition, pp.1016-1018, 1980.

C. Arcelli, G. S. , and D. Baja, A thinning algorithm based on prominence detection, Pattern Recognition, vol.13, issue.3, pp.225-235, 1981.
DOI : 10.1016/0031-3203(81)90099-6

W. Habib-abdulla, A. O. Saleh, and A. H. Morad, A preprocessing algorithm for hand-written character recognition, Pattern Recognition Letters, vol.7, issue.1, pp.13-18, 1984.
DOI : 10.1016/0167-8655(88)90039-6

J. W. Brandt and V. R. Algazi, Continuous skeleton computation by Voronoi diagram, CVGIP: Image Understanding, vol.55, issue.3, pp.329-338, 1992.
DOI : 10.1016/1049-9660(92)90030-7

G. Bertrand and Z. Aktouf, A 3D thinning algorithm using subfields, SPIE Proceedings of Conference on Vision Geometry III, pp.113-124, 1994.

[. Bertrand and M. Couprie, Three-dimensional parallel thinning algorithms based on critical kernels

F. Nivando, B. , and M. Couprie, Réduction d'anisotropie des squelettes en niveaux de gris, RFIA 2002: Proceedings of 13ème Congrès Francophone de Reconnaissance des Formes et Intelligence Artificielle, pp.819-828, 2002.

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

G. Bertrand, M. Couprie, and N. Passat, A note on 3-D simple points and simple-equivalence, Information Processing Letters, vol.109, issue.13, pp.700-704, 2009.
DOI : 10.1016/j.ipl.2009.03.002
URL : https://hal.archives-ouvertes.fr/hal-00622395

R. [. Brain, J. H. Duda, and . Munson, Graphical data processing research study and experimental investigation, 1965.

J. Bear, Dynamics of Fluids in Porous Media, Soil Science, vol.120, issue.2, 1972.
DOI : 10.1097/00010694-197508000-00022

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

G. Bertrand, A parallel thinning algorithm for medial surfaces, Pattern Recognition Letters, vol.16, issue.9, pp.979-986, 1995.
DOI : 10.1016/0167-8655(95)00034-E
URL : https://hal.archives-ouvertes.fr/hal-00621995

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

G. Bertrand, Sufficient conditions for 3D parallel thinning algorithms, SPIE Proceedings of Conference on Vision Geometry IV, volume 2573 of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, pp.52-60, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00621998

G. Bertrand, A Boolean characterization of three-dimensional simple points, Pattern Recognition Letters, vol.17, issue.2, pp.115-124, 1996.
DOI : 10.1016/0167-8655(95)00100-X
URL : https://hal.archives-ouvertes.fr/hal-00621994

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

M. Beun, A flexible method for automatic reading of hand written numerals, 1973.

R. Bing, Some aspects of the topology of 3-manifolds related to the Poincaré Conjecture, Lectures on Modern Mathematics II, pp.93-128, 1964.

H. Blum, An Associative Machine for Dealing with the Visual Field and Some of Its Biological Implications, Biological Prototypes and Synthetic Systems, pp.244-260, 1962.
DOI : 10.1007/978-1-4684-1716-6_34

H. Blum, A transformation for extracting new descriptors of shape, Models for the Perception of Speech and Visual Form, pp.362-380, 1967.

S. Beucher and F. Meyer, The morphological approach of segmentation: the watershed transformation, Mathematical Morphology in Image Processing, pp.433-481

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

M. Thierry, A. Bernard, and . Manzanera, Improved Low Complexity Fully Parallel Thinning Algorithm, ICIAP 1999: Proceedings of the 10th International Conference on Image Analysis and Processing, 1999.

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

R. Benjamin, C. Michel, and N. Vincent, Generic Initialization for Motion Capture from 3D Shape, Image Analysis and Recognition, pp.306-315, 2010.

G. Borgefors, I. Nyström, G. S. , and D. Baja, Computing skeletons in three dimensions, Pattern Recognition, vol.32, issue.7, pp.1225-1236, 1999.
DOI : 10.1016/S0031-3203(98)00082-X

D. Bernard, L. Nielsen, P. Salvo, and . Cloetens, Permeability assessment by 3D interdendritic flow simulations on microtomography mappings of Al-Cu alloys. Materials Science and Engineering: A, Structural materials : properties, microstructure and processing, pp.112-120, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00022098

A. Bonnassie, F. Peyrin, and D. Attali, Shape description of three-dimensional images based on medial axis, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205), pp.931-934, 2001.
DOI : 10.1109/ICIP.2001.958277

G. Borgefors, I. Ragnemalm, G. S. , and D. Baja, The Euclidean distance transform: finding the local maxima and reconstructing the shape, SCIA 1991: Proceedings of the 7th Scandinavian Conference on Image Analysis, pp.974-981, 1991.

D. Bernard and G. L. Vignoles, Numerical study of the coupled evolution of microgeometry and transport properties of simple 3D porous media, Computational Methods for Fluid Flow and Transport in Porous Media, Theory and Applications of Transport in Porous Media, pp.217-226, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00327608

Y. Boykov, O. Veksler, and R. Zabih, Fast approximate energy minimization via graph cuts, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.23, issue.11, pp.1222-1239, 2001.
DOI : 10.1109/34.969114
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.6806

]. L. Cal65 and . Calabi, A study of the skeleton of plane figures, 1965.

M. Couprie and G. Bertrand, Topological Grayscale Watershed Transformation, Proceedings of SPIE : Vision Geometry V, pp.136-146, 1997.
DOI : 10.1117/12.292778
URL : https://hal.archives-ouvertes.fr/hal-00622030

M. Couprie and G. Bertrand, New Characterizations of Simple Points, Minimal Non-simple Sets and P-Simple Points in 2D, 3D and 4D Discrete Spaces, DGCI 2008 : Proceedings of the 14th IAPR International Conference on Discrete Geometry for Computer Imagery, pp.105-116, 2008.
DOI : 10.1007/978-3-540-79126-3_11
URL : https://hal.archives-ouvertes.fr/hal-00622026

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

M. Couprie, F. N. Bezerra, and G. Bertrand, Topological operators for grayscale image processing, Journal of Electronic Imaging, vol.10, issue.4, pp.1003-1015, 2001.
DOI : 10.1117/1.1408316
URL : https://hal.archives-ouvertes.fr/hal-00622474

J. Chaussard, G. Bertrand, and M. Couprie, Characterizing and Detecting Toric Loops in n-Dimensional Discrete Toric Spaces, DGCI 2008 : Proceedings of the 14th IAPR International Conference on Discrete Geometry for Computer Imagery, pp.129-140, 2008.
DOI : 10.1007/978-3-540-79126-3_13
URL : https://hal.archives-ouvertes.fr/hal-00622024

J. Chaussard, G. Bertrand, and M. Couprie, Characterization and Detection of Toric Loops in n-Dimensional Discrete Toric Spaces, Journal of Mathematical Imaging and Vision, vol.1, issue.7, pp.111-124, 2010.
DOI : 10.1007/s10851-009-0175-9
URL : https://hal.archives-ouvertes.fr/hal-00622425

J. Cousty, G. Bertrand, L. Najman, and M. Couprie, Watershed Cuts: Thinnings, Shortest Path Forests, and Topological Watersheds, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.32, issue.5, pp.925-939, 2010.
DOI : 10.1109/TPAMI.2009.71
URL : https://hal.archives-ouvertes.fr/hal-00729346

J. Chaussard and M. Couprie, Surface Thinning in 3D Cubical Complexes, IWCIA 2009: Proceedings of the 13th International Workshop on Combinatorial Image Analysis, pp.135-148, 2009.
DOI : 10.1007/978-3-642-10210-3_11
URL : https://hal.archives-ouvertes.fr/hal-00622486

F. Chazal, D. Cohen-steiner, and A. Lieutier, Normal cone approximation and offset shape isotopy, Computational Geometry, vol.42, issue.6-7, pp.566-581, 2009.
DOI : 10.1016/j.comgeo.2008.12.002
URL : https://hal.archives-ouvertes.fr/inria-00124825

J. Chaussard, M. Couprie, and H. Talbot, A Discrete ??-Medial Axis, DGCI 2009 : Proceedings of the 15th IAPR International Conference on Discrete Geometry for Computer Imagery, pp.421-433, 2009.
DOI : 10.1007/BFb0038202
URL : https://hal.archives-ouvertes.fr/hal-00622407

J. Chaussard, M. Couprie, and H. Talbot, Robust skeletonization using the discrete lambda-medial axis, Pattern Recognition Letters, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00622523

M. Couprie, D. Coeurjolly, and R. Zrour, Discrete bisector function and Euclidean skeleton in 2D and 3D, Image and Vision Computing, vol.25, issue.10, pp.1543-1556, 2007.
DOI : 10.1016/j.imavis.2006.06.020
URL : https://hal.archives-ouvertes.fr/hal-00180616

Y. Chen and W. Hsu, A modified fast parallel algorithm for thinning digital patterns, Pattern Recognition Letters, vol.7, issue.2, pp.99-106, 1988.
DOI : 10.1016/0167-8655(88)90124-9

Y. Chen and W. Hsu, Systematic approach for designing 2-subcycle and pseudo 1-subcycle parallel thinning algorithms, Pattern Recognition, vol.22, issue.3, pp.267-282, 1989.
DOI : 10.1016/0031-3203(89)90075-7

Y. Chen, Comments on "A systematic approach for designing 2-subcycle and pseudo 1-subcycle parallel thinning algorithms, Pattern Recognition, vol.25, issue.12, pp.1545-1546, 1992.

Y. Chang and X. Li, Adaptive image region-growing, IEEE Transactions on Image Processing, vol.3, issue.6, pp.868-872, 1994.
DOI : 10.1109/83.336259

B. Curless and M. Levoy, A volumetric method for building complex models from range images, Proceedings of the 23rd annual conference on Computer graphics and interactive techniques , SIGGRAPH '96, pp.303-312, 1996.
DOI : 10.1145/237170.237269

F. Chazal and A. Lieutier, The ?????-medial axis???, Graphical Models, vol.67, issue.4, pp.304-331, 2005.
DOI : 10.1016/j.gmod.2005.01.002

D. Coeurjolly and A. Montanvert, Optimal Separable Algorithms to Compute the Reverse Euclidean Distance Transformation and Discrete Medial Axis in Arbitrary Dimension, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.29, issue.3, pp.437-485, 2007.
DOI : 10.1109/TPAMI.2007.54
URL : https://hal.archives-ouvertes.fr/hal-00148621

D. Coeurjolly, d-Dimensional Reverse Euclidean Distance Transformation and Euclidean Medial Axis Extraction in Optimal Time, 2003.
DOI : 10.1007/978-3-540-39966-7_31
URL : https://hal.archives-ouvertes.fr/hal-00185186

[. Combaret, Modèles de réseaux, pores, et calculs de perméabilité

M. Couprie, Note on fifteen 2D parallel thinning algorithms An alternate smoothing and stripping algorithm for thinning digital binary patterns, Signal Processing, vol.11, issue.3, pp.207-222, 1986.

R. T. Chin, D. L. Hong-khoon-wan, R. D. Strover, and . Iverson, A one-pass thinning algorithm and its parallel implementation, Computer Vision, Graphics, and Image Processing, vol.40, issue.1, pp.30-40, 1987.
DOI : 10.1016/0734-189X(87)90054-5

X. Daragon and M. Couprie, Segmentation topologique du neo-cortex cérébral depuis des données IRM, RFIA 2002: Proceedings of 13ème Congrès Francophone de Reconnaissance des Formes et Intelligence Artificielle, pp.809-818, 2002.

A. Dupas, G. Damiand, and J. Lachaud, Multi-Label Simple Points Definition for 3D??Images Digital Deformable Model, DGCI 2009 : Proceedings of the 15th IAPR International Conference on Discrete Geometry for Computer Imagery, pp.156-167, 2009.
DOI : 10.1023/A:1020874308076
URL : https://hal.archives-ouvertes.fr/hal-00413691

S. Edward and . Deutsch, Thinning algorithms on rectangular, hexagonal, and triangular arrays, Communications of the ACM, vol.15, issue.9, pp.827-837, 1972.

M. and A. K. Jain, A modified Hausdorff distance for object matching, ICPR 1994: Proceedings of the 12th International Conference on Pattern Recognition, pp.566-568, 1994.

P. Dokládal, C. Lohou, L. Perroton, and G. Bertrand, Liver Blood Vessels Extraction by a 3-D Topological Approach, MICCAI 1999: Proceedings of the 2nd International Conference on Medical Image Computing and Computer-Assisted Intervention, pp.1679-1698, 1999.
DOI : 10.1007/10704282_11

E. R. Davies and A. P. Plummer, Thinning algorithms: A critique and a new methodology, Pattern Recognition, vol.14, issue.1-6, pp.53-63, 1981.
DOI : 10.1016/0031-3203(81)90045-5

U. Eckhardt, A note on Rutovitz' method for parallel thinning, Pattern Recognition Letters, vol.8, issue.1, pp.35-38, 1988.
DOI : 10.1016/0167-8655(88)90021-9

M. Eden, A two-dimensional growth process, Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probabilities, pp.223-239, 1961.

U. Eckhardt and G. Maderlechner, INVARIANT THINNING, International Journal of Pattern Recognition and Artificial Intelligence, vol.07, issue.05, pp.1115-1144, 1993.
DOI : 10.1142/S021800149300056X

L. Euler, Solutio problematis ad geometriam situs pertinentis. Commentarii Academiae Scientiarum Imperialis Petropolitanae, pp.128-140

T. Faucon, E. Decencière, and C. Magneron, Application of Surface Topological Segmentation to Seismic Imaging, DGCI 2006 : Proceedings of the 13th IAPR International Conference on Discrete Geometry for Computer Imagery, pp.506-517, 2006.
DOI : 10.1007/11907350_43

A. Fabijaå?dskafabijaå?-fabijaå?dska, M. Janaszewski, M. M. Postolski, and L. Babout, Airway Tree Segmentation from CT Scans Using Gradient-Guided 3D Region Growing, CIARP 2009: Proceedings of the 14th Iberoamerican Conference on Pattern Recognition, pp.247-254, 2009.

]. Fouard, G. Malandain, S. Prohaska, M. Westerhoff, F. Cassot et al., Skeletonization by blocks for large 3D datasets: application to brain microcirculation, 2004 2nd IEEE International Symposium on Biomedical Imaging: Macro to Nano (IEEE Cat No. 04EX821), pp.89-92, 2004.
DOI : 10.1109/ISBI.2004.1398481

[. Fan, G. Zeng, M. Body, and M. Hacid, Seeded region growing: an extensive and comparative study, Pattern Recognition Letters, vol.26, issue.8, pp.1139-1156, 2005.
DOI : 10.1016/j.patrec.2004.10.010

W. Gong and G. Bertrand, A simple parallel 3D thinning algorithm, [1990] Proceedings. 10th International Conference on Pattern Recognition, pp.188-190, 1990.
DOI : 10.1109/ICPR.1990.118087

Y. Ge and J. M. Fitzpatrick, On the generation of skeletons from discrete Euclidean distance maps, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, issue.11, pp.1055-1066, 1996.

Z. Guo and R. W. Hall, Parallel thinning with two-subiteration algorithms, Communications of the ACM, vol.32, issue.3, pp.359-373, 1989.
DOI : 10.1145/62065.62074

Z. Guo and R. W. Hall, Fast fully parallel thinning algorithms, CVGIP: Image Understanding, vol.55, issue.3, pp.317-328, 1992.
DOI : 10.1016/1049-9660(92)90029-3

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 and B. B. Kimia, A formal classification of 3d medial axis points and their local geometry, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.26, issue.2, pp.238-51, 2004.
DOI : 10.1109/TPAMI.2004.1262192

R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, Computers in Physics, vol.3, issue.5, 1994.
DOI : 10.1063/1.4822863

G. Gallus and P. W. Neurath, Improved computer chromosome analysis incorporating preprocessing and boundary analysis, Physics in Medicine and Biology, vol.15, issue.3, 1970.
DOI : 10.1088/0031-9155/15/3/004

J. E. Marcel and . Golay, Hexagonal Parallel Pattern Transformations, IEEE Transactions on Computers, vol.18, issue.8, pp.733-740, 1969.

L. Grady, Random Walks for Image Segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.28, issue.11, pp.1768-1783, 2006.
DOI : 10.1109/TPAMI.2006.233

A. [. Govindan and . Shivaprasad, A pattern adaptive thinning algorithm, Pattern Recognition, vol.20, issue.6, pp.623-637, 1987.
DOI : 10.1016/0031-3203(87)90032-X

R. W. Hall, Fast parallel thinning algorithms: parallel speed and connectivity preservation, Communications of the ACM, vol.32, issue.1, pp.124-131, 1989.
DOI : 10.1145/63238.63248

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
URL : http://doi.org/10.1016/0166-8641(92)90015-r

R. W. Hall, Optimally small operator supports for fully parallel thinning algorithms, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.15, issue.8, pp.828-833, 1993.
DOI : 10.1109/34.236245

A. Hatcher, Algebraic topology, 2002.

]. C. Hil69 and . Hilditch, Linear Skeletons From Square Cupboards, Machine Intelligence, vol.403, 1969.

C. J. Hilditch, Comparison of thinning algorithms on a parallel processor, Image and Vision Computing, vol.1, issue.3, pp.115-132, 1983.
DOI : 10.1016/0262-8856(83)90063-X

T. Hirata, A unified linear-time algorithm for computing distance maps, Information Processing Letters, vol.58, issue.3, pp.129-133, 1996.
DOI : 10.1016/0020-0190(96)00049-X

L. Steven, T. Horowitz, and . Pavlidis, Picture Segmentation by a Tree Traversal Algorithm, Journal of the ACM, vol.23, issue.2, pp.368-388, 1976.

H. Wim, J. B. Hesselink, and . Roerdink, Euclidean Skeletons of Digital Image and Volume Data in Linear Time by the Integer Medial Axis Transform, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.30, issue.12, pp.2204-2217, 2008.

C. M. Holt, A. Stewart, M. Clint, and R. H. Perrott, An improved parallel thinning algorithm, Communications of the ACM, vol.30, issue.2, pp.156-160, 1987.
DOI : 10.1145/12527.12531

J. Hulin, Axe Médian Discret : Propriétés Arithmétiques et Algorithmes, 2009.

B. Hopkins and R. Wilson, The truth about Königsberg, Leonhard Euler: Life, Work and Legacy of Studies in the History and Philosophy of Mathematics, pp.409-420, 2007.

M. I. Izutsdkiver, Algorithm for the initial processing of an ensemble of symbols in the recognition process. Automation and Remote Control, pp.1292-1298, 1974.

G. Jennane, C. Aufort, M. Benhamou, Y. Ceylan, O. Özbay et al., A New Method for 3D Thinning of Hybrid Shaped Porous Media Using Artificial Intelligence. Application to Trabecular Bone, Journal of Medical Systems, vol.32, issue.7, pp.1-14, 2010.
DOI : 10.1007/s10916-010-9495-y
URL : https://hal.archives-ouvertes.fr/hal-00657652

T. Ju, M. L. Baker, and W. Chiu, Computing a family of skeletons of volumetric models for shape description, Computer-Aided Design, vol.39, issue.5, pp.352-360, 2007.
DOI : 10.1016/j.cad.2007.02.006

B. Jang and R. T. Chin, One-pass parallel thinning: analysis, properties, and quantitative evaluation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.11, pp.1129-1140, 1992.
DOI : 10.1109/34.166630

B. Jang and R. T. Chin, RECONSTRUCTABLE PARALLEL THINNING, International Journal of Pattern Recognition and Artificial Intelligence, vol.07, issue.05, pp.1145-1181, 1993.
DOI : 10.1142/S0218001493000571

M. Janaszewski, M. Couprie, and L. Babout, Hole filling in 3D volumetric objects, Pattern Recognition, vol.43, issue.10, pp.3548-3559, 2010.
DOI : 10.1016/j.patcog.2010.04.015
URL : https://hal.archives-ouvertes.fr/hal-00622484

[. Kong and C. Gau, Minimal Non-simple Sets in 4-Dimensional Binary Images with (8,80)-Adjacency, IWCIA 2004: Proceedings of the 10th International Workshop on Combinatorial Image Analysis, pp.318-333, 2004.
DOI : 10.1007/978-3-540-30503-3_24

K. Kedem and D. Keret, A fast algorithm for skeletonizing lines by midline technique, ICSC 1988: Proceedings of the 1st International Computer Science Conference, pp.731-735, 1988.

G. Klette, Voxels and Junctions in 3D skeletons, IWCIA 2006: Proceedings of the 11th International Workshop on Combinatorial Image Analysis, pp.34-44, 2006.

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

P. Kardos, G. Németh, and K. Palágyi, An Order???Independent Sequential Thinning Algorithm, IWCIA 2009: Proceedings of the 13th International Workshop on Combinatorial Image Analysis, pp.162-175, 2009.
DOI : 10.1007/978-3-642-10210-3_13
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.204.5348

]. T. Kon89 and . Kong, A digital fundamental group. Computers and Graphics, pp.159-166, 1989.

]. T. Kon93 and . Kong, Problem of determining whether a parallel reduction operator for n-dimensional binary images always preserves topology, SPIE Proceedings of Conference on Vision Geometry II, volume 2060 of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, pp.69-77, 1993.

]. T. Kon95 and . Kong, On Topology Preservation in 2-D and 3-D Thinning, International Journal of Pattern Recognition and Artificial Intelligence, vol.9, pp.813-844, 1995.

]. T. Kon97 and . Kong, Topology-Preserving Deletion of 1's from 2-, 3-and 4-Dimensional Binary Images, DGCI 1997 : Proceedings of the 7th IAPR International Conference on Discrete Geometry for Computer Imagery, pp.3-18, 1997.

[. Kong and A. Rosenfeld, Digital topology: introduction and survey, Computer Vision, Graphics, and Image Processing, pp.357-393, 1989.
DOI : 10.1016/0734-189x(89)90127-8

[. Kong, A. W. Roscoe, and A. Rosenfeld, Concepts of digital topology, Topology and its Applications, vol.46, issue.3, pp.219-262, 1992.
DOI : 10.1016/0166-8641(92)90016-S

R. Kimmel, D. Shaked, N. Kiryati, and A. M. Bruckstein, Skeletonization via Distance Maps and Level Sets, Computer Vision and Image Understanding, vol.62, issue.3, pp.382-391, 1995.
DOI : 10.1006/cviu.1995.1062
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.7008

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. Thomas, R. Lee, and . Cowan, A Stochastic Tesselation of Digital Space, ISMM 1994: Proceedings of the 2nd International Symposium on Mathematical Morphology, pp.218-224, 1994.

L. Lui, E. W. Chambers, D. Letscher, and T. Ju, A simple and robust thinning algorithm on cell complexes, Computer Graphics Forum (Proceedings of Pacific Graphics 2010), 2010.

A. Lieutier, Any open bounded subset of R n has the same homotopy type as its medial axis, Proceedings of the 8th ACM Symposium on Solid Modeling Applications, pp.65-75, 2003.

J. Benedikt, L. Ta-chih-lee, R. L. Kashyap, and C. Chu, Vorstudien zur Topologie Building Skeleton Models via 3-D Medial Surface Axis Thinning Algorithms, Vandenhoeck und Ruprecht CVGIP: Graphical Models and Image Processing, issue.6, pp.56462-478, 1847.

L. Lam, S. Lee, and C. Y. Suen, Thinning methodologies-a comprehensive survey, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.9, pp.869-885, 1992.
DOI : 10.1109/34.161346
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.323.9365

C. Lohou, Contribution à l'analyse topologique des images : Étude d'algorithmes de squelettisation pour images 2D et 3D selon une approche topologie digitale ou topologie discrète, 2001.

C. Lohou, Detection of the non-topology preservation of Ma???s 3D surface-thinning algorithm, by the use of P-simple points, Pattern Recognition Letters, vol.29, issue.6, pp.822-827, 2008.
DOI : 10.1016/j.patrec.2008.01.002

C. Lohou, Detection of the non-topology preservation of Ma and Sonka???s algorithm, by the use of P-simple points, Computer Vision and Image Understanding, vol.114, issue.3, pp.384-399, 2010.
DOI : 10.1016/j.cviu.2009.10.003

J. Lachaud and A. Vialard, Discrete Deformable Boundaries for the Segmentation of Multidimensional Images, Visual Form 2001 : Proceedings of the 4th International Workshop on Visual Form, pp.542-551, 2001.
DOI : 10.1007/3-540-45129-3_50
URL : https://hal.archives-ouvertes.fr/hal-00308203

P. [. Lü, -. Shen, and . Wang, A comment on ???a fast parallel algorithm for thinning digital patterns???, Communications of the ACM, vol.29, issue.3, pp.239-242, 1986.
DOI : 10.1145/5666.5670

C. Ma, On topology preservation in 3D thinning, CVGIP: Image Understanding, vol.59, issue.3, pp.328-339, 1994.
DOI : 10.1006/ciun.1994.1023

C. Ma, A 3D fully parallel thinning algorithm for generating medial faces, Pattern Recognition Letters, vol.16, issue.1, pp.83-87, 1995.

C. Ma, 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

R. Malgouyres, Homotopy in two-dimensional digital images, Theoretical Computer Science, vol.230, issue.1-2, pp.221-233, 2000.
DOI : 10.1016/S0304-3975(98)00347-8

R. Malgouyres, COMPUTING THE FUNDAMENTAL GROUP IN DIGITAL SPACES, International Journal of Pattern Recognition and Artificial Intelligence, vol.15, issue.07, pp.1053-1074, 2001.
DOI : 10.1142/S0218001401001325

M. Andreï-andreyevich, Insolubility of the problem of homeomorphy, Proceedings of the International Congress of Mathematics of 1958, pp.300-306, 1960.

G. Matheron, Examples of topological properties of skeletons, pp.217-238, 1988.

C. R. and F. Maunder, Algebraic Topology, 1996.

G. Malandain and G. Bertrand, Fast characterization of 3D simple points The Hague, The Netherlands, ICPR 1992: Proceedings of the 11th International Conference on Pattern Recognition, pp.232-235, 1992.

G. Malandain, G. Bertrand, and N. Ayache, Topological segmentation of discrete surfaces, International Journal of Computer Vision, vol.17, issue.6, pp.183-197, 1993.
DOI : 10.1007/BF01420736
URL : https://hal.archives-ouvertes.fr/inria-00615557

J. Mukherjee, P. P. Das, and B. N. Chatterji, On connectivity issues of ESPTA, Pattern Recognition Letters, vol.11, issue.9, pp.643-648, 1990.
DOI : 10.1016/0167-8655(90)90018-W

Y. Menguy, Optimisation quadratique et géométrique de problèmes de dosimétrie inverse, 1996.

F. Meyer, Cytologie quantitative et morphologie mathématique, 1979.

R. Malgouyres and A. R. Francés, Determining Whether a Simplicial 3-Complex Collapses to a 1-Complex Is NP-Complete, DGCI 2008 : Proceedings of the 14th IAPR International Conference on
DOI : 10.1007/978-3-540-79126-3_17

G. Malandain, S. Fernández, and . Vidal, Euclidean skeletons, Image and Vision Computing, vol.16, issue.5, pp.317-327, 1998.
DOI : 10.1016/S0262-8856(97)00074-7
URL : https://hal.archives-ouvertes.fr/inria-00615037

P. Mrazek and M. Navara, Consistent Positive Directional Splitting of Anisotropic Diffusion, Computer Vision Winter Workshop, 2001.

D. George and M. , Three-dimensional simple points: serial erosion, parallel thinning and skeletonization, 1981.

R. Calvin, . Jr, R. Maurer, V. V. Qi, and . Raghavan, A Linear Time Algorithm for Computing Exact Euclidean Distance Transforms of Binary Images in Arbitrary Dimensions, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.25, issue.2, pp.265-270, 2003.

A. Meijster, J. B. Roerdink, and W. H. Hesselink, A General Algorithm for Computing Distance Transforms in Linear Time, pp.331-340, 2000.
DOI : 10.1007/0-306-47025-X_36

C. Ma and M. Sonka, A Fully Parallel 3D Thinning Algorithm and Its Applications, Computer Vision and Image Understanding, vol.64, issue.3, pp.420-433, 1996.
DOI : 10.1006/cviu.1996.0069

S. N. Ivaturi, J. K. Murthy, and . Udupa, A Search Algorithm for Skeletonization of Thick Patterns, Computer Graphics and Image Processing, vol.3, issue.3, pp.246-259, 1974.

C. Ma, S. Wan, and J. 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.

G. Németh, P. Kardos, and K. Palágyi, Topology Preserving 2-Subfield 3D Thinning Algorithms, Signal Processing, Pattern Recognition and Applications, pp.310-316
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, pp.316-325, 2010.
DOI : 10.1007/978-3-642-13772-3_32

G. Németh and K. Palágyi, Parallel Thinning Algorithms Based on Ronse's Sufficient Conditions for Topology Preservation, Progress in Combinatorial Image Analysis, pp.183-194, 2009.

N. Jean-naccache and R. Shinghal, SPTA: A proposed algorithm for thinning binary patterns, IEEE Transactions on Systems, Man, and Cybernetics, vol.14, issue.3, pp.409-418, 1984.
DOI : 10.1109/TSMC.1984.6313233

G. Nsk-+-97-]-martin-näf, R. Székely, M. E. Kikinis, O. Shenton, and . Kübler, 3d Voronoi skeletons and their usage for the characterization and recognition of 3D organ shape, Computer Vision and Image Understanding, vol.66, issue.2, pp.147-161, 1997.

L. Robert, O. Ogniewicz, and . Kübler, Hierarchic Voronoi skeletons, Pattern Recognition, vol.28, issue.33, pp.343-359, 1995.

J. Stanley, N. Osher, and . Paragios, Geometric Level Set Methods in Imaging,Vision,and Graphics, 2003.

J. Stanley, J. A. Osher, and . Sethian, Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988.

K. Palágyi, A 3-subiteration 3D thinning algorithm for extracting medial surfaces, Pattern Recognition Letters, vol.23, issue.6, pp.663-675, 2002.
DOI : 10.1016/S0167-8655(01)00142-8

K. Palágyi, A 3???Subiteration Surface???Thinning Algorithm, CAIP 2007: Proceedings of the 12th International Conference on Computer Analysis of Images and Patterns, CAIP'07, pp.628-635, 2007.
DOI : 10.1007/978-3-540-74272-2_78

K. Palágyi, A Subiteration-Based Surface-Thinning Algorithm with a Period of Three, Pattern Recognition, pp.294-303, 2007.
DOI : 10.1007/978-3-540-74936-3_30

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

T. Pavlidis, A thinning algorithm for discrete binary images, Computer Graphics and Image Processing, vol.13, issue.2, pp.142-157, 1980.
DOI : 10.1016/S0146-664X(80)80037-2

T. Pavlidis, A Flexible Parallel Thinning Algorithm, Proceedings of the IEEE Computer Society Conference on Pattern Recognition and Image Processing, pp.162-167, 1981.

T. Pavlidis, An asynchronous thinning algorithm, Computer Graphics and Image Processing, vol.20, issue.2, pp.133-157, 1982.
DOI : 10.1016/0146-664X(82)90041-7

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

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

K. Palágyi and A. Kuba, A Parallel 3D 12-Subiteration Thinning Algorithm, Graphical Models and Image Processing, vol.61, issue.4, pp.199-221, 1999.
DOI : 10.1006/gmip.1999.0498

K. Palágyi and A. Kuba, Directional 3D Thinning Using 8 Subiterations, Discrete Geometry for Computer Imagery, pp.325-336, 1999.
DOI : 10.1007/3-540-49126-0_25

T. Pavlidis and Y. Liow, Integrating region growing and edge detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.12, issue.3, pp.225-233, 1990.
DOI : 10.1109/34.49050

E. Plougonven, Lien entre la microstructure des matériaux poreux et leur perméabilité : mise en évidence des paramètres géométriques et topologiques influant sur les propriétés de transport par analyses d'images microtomographiques, 2009.

P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.12, issue.7, pp.629-639, 1990.
DOI : 10.1109/34.56205

H. Poincaré, Analysis Situs Journal de l'École Polytechnique, 2ème série, pp.1-121

K. Palágyi, J. Tschirren, E. A. Hoffman, and M. Sonka, Quantitative analysis of pulmonary airway tree structures, Computers in Biology and Medicine, vol.36, issue.9, pp.974-996, 2006.
DOI : 10.1016/j.compbiomed.2005.05.004

C. Pudney, Distance-Ordered Homotopic Thinning: A Skeletonization Algorithm for 3D Digital Images, Computer Vision and Image Understanding, vol.72, issue.3, pp.404-413, 1998.
DOI : 10.1006/cviu.1998.0680

S. Riazanoff, B. Cervelle, and J. Chorowicz, Parametrisable skeletonization of binary and multi-level images, Pattern Recognition Letters, vol.11, issue.1, pp.25-33, 1990.
DOI : 10.1016/0167-8655(90)90052-4

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

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, 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

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

A. Rosenfeld, Digital topology. The American Mathematical Monthly, pp.621-630, 1979.

A. Rosenfeld, Three-dimensional digital topology, Information and Control, vol.50, issue.2, pp.119-127, 1981.
DOI : 10.1016/S0019-9958(81)90177-7

V. Ranwez and P. Soille, Order independent homotopic thinning for binary and grey tone anchored skeletons, Pattern Recognition Letters, vol.23, issue.6, pp.687-702, 2002.
DOI : 10.1016/S0167-8655(01)00146-5

É. Rémy and É. Thiel, Medial axis for chamfer distances: computing look-up tables and neighbourhoods in 2D or 3D, Pattern Recognition Letters, vol.23, issue.6, pp.649-661, 2002.
DOI : 10.1016/S0167-8655(01)00141-6

M. Rumpf and A. Telea, A continuous skeletonization method based on level sets, VisSym 2002: Proceedings of the Symposium on Data Visualisation, p.151, 2002.

É. Rémy and É. Thiel, Look-Up Tables for Medial Axis on Squared Euclidean Distance Transform, DGCI 2003 : Proceedings of the 11th IAPR International Conference on Discrete Geometry for Computer Imagery, pp.224-235, 2003.
DOI : 10.1007/978-3-540-39966-7_21

É. Rémy and É. Thiel, Exact medial axis with euclidean distance, Image and Vision Computing, vol.23, issue.2, pp.167-175, 2005.
DOI : 10.1016/j.imavis.2004.06.007

D. Reniers and A. Telea, Segmenting Simplified Surface Skeletons, DGCI 2008 : Proceedings of the 14th IAPR International Conference on Discrete Geometry for Computer Imagery, pp.262-274, 2008.
DOI : 10.1007/978-3-540-79126-3_24
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.109.780

D. Rutovitz, Pattern Recognition, Journal of the Royal Statistical Society. Series A (General), vol.129, issue.4, pp.504-530, 1966.
DOI : 10.2307/2982255

M. Samozino, M. Alexa, P. Alliez, and M. Yvinec, Reconstruction with Voronoi Centered Radial Basis Functions, SGP 2006: Proceedings of the 4th Symposium on Geometry Processing (SGP'06), pp.51-60, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00116651

K. Siddiqi, S. Bouix, A. Tannenbaum, and S. W. Zucker, The Hamilton-Jacobi skeleton, Proceedings of the Seventh IEEE International Conference on Computer Vision, pp.828-834, 1999.
DOI : 10.1109/ICCV.1999.790307

P. Kumar, S. , and B. Baran-chaudhuri, Detection of 3-D Simple Points for Topology Preserving Transformations with Application to Thinning, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.16, issue.10, pp.1028-1032, 1994.

. Punam-kumar-saha, B. Bidyut-baran-chaudhuri, D. D. Chanda, and . 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

. Punam-kumar-saha, D. Bidyut-baran-chaudhuri, and . Majumder, A new shape preserving parallel thinning algorithm for 3D digital images, Pattern Recognition, vol.30, issue.12, pp.1939-1955, 1997.
DOI : 10.1016/S0031-3203(97)00016-2

A. Vital-saúde, M. Couprie, R. , and A. Lotufo, Exact Euclidean Medial Axis in Higher Resolution, DGCI 2006 : Proceedings of the 13th IAPR International Conference on Discrete Geometry for Computer Imagery, pp.605-616, 2006.
DOI : 10.1007/11907350_51

A. E. Scheidegger, The Physics of Flow Through Porous Media, Soil Science, vol.86, issue.6, 1974.
DOI : 10.1097/00010694-195812000-00015

D. Sharvit, J. Chan, H. Tek, and B. B. Kimia, Symmetry-Based Indexing of Image Databases, Journal of Visual Communication and Image Representation, vol.9, issue.4, pp.366-380, 1998.
DOI : 10.1006/jvci.1998.0396

J. Serra, Image Analysis and Mathematical Morphology, 1982.

M. Schmitt and J. Mattioli, Morphologie mathématique. Collection logique mathématiques informatique, 1993.

P. Soille, Morphological Image Analysis, 1999.

J. H. and S. Azuela, An Improved Parallel Algorithm for Thinning Digital Patterns, Pattern Recognition Letters, vol.10, pp.77-80, 1989.

R. Stefanelli and A. Rosenfeld, Some Parallel Thinning Algorithms for Digital Pictures, Journal of the ACM, vol.18, issue.2, pp.255-264, 1971.
DOI : 10.1145/321637.321646

G. Linda, G. C. Shapiro, and . Stockman, Computer Vision, 2001.

G. Sanniti, D. Baja, and É. Thiel, Skeletonization algorithm running on path-based distance maps, Image and Vision Computing, vol.14, issue.1, pp.47-57, 1996.

J. Stillwell, Classical Topology and Combinatorial Group Theory, 1980.

R. Strand, A Classification of Centres of Maximal Balls in ???3, SCIA 2005: Proceedings of the 14th Scandinavian Conference on Image Analysis, pp.1057-1065, 2005.
DOI : 10.1007/11499145_107

S. N. Srihari and J. K. Udupa, Understanding the bin of parts, Proceedings of the International Conference on Cybernetics and Society, pp.44-49, 1979.

Y. Frank, W. Shih, and . Wong, Fully Parallel Thinning With Tolerance To Boundary Noise, Pattern Recognition, vol.27, issue.12, pp.1677-1695, 1994.

]. H. Tam78 and . Tamura, A Comparison of Line Thinning Algorithms from Digital Geometry Viewpoint, ICPR 1978: Proceedings of the 4th International Conference on Pattern Recognition, pp.715-719, 1978.

M. Tancer, T. , and K. S. Fu, d-collapsibility is NP-complete for, Electronic Notes in Discrete Mathematics, vol.34, issue.174, pp.53-57315, 1981.
DOI : 10.1016/j.endm.2009.07.009

Y. F. Tsao and K. S. Fu, Parallel Thinning Operations for Digital Binary Images, Pattern Recognition and Image Processing, pp.150-155, 1981.

J. Toriwaki and K. Mori, Distance Transformation and Skeletonization of 3D Pictures and Their Applications to Medical Images, Digital and Image Geometry, pp.412-428, 2001.
DOI : 10.1007/3-540-45576-0_25

[. Tankyevych, H. Talbot, P. Dokládal, and N. Passat, Direction-adaptive grey-level morphology. application to 3D vascular brain imaging, 2009 16th IEEE International Conference on Image Processing (ICIP), pp.2237-2240, 2009.
DOI : 10.1109/ICIP.2009.5414356
URL : https://hal.archives-ouvertes.fr/hal-00622439

H. Talbot and L. M. Vincent, Euclidean skeletons and conditional bisectors, VCIP 1992: Proceedings of the International Conference on Visual Communications and Image Processing, pp.862-876, 1992.

L. Gérard, O. Vignoles, A. Coindreau, D. Ahmadi, and . Bernard, Assessment of geometrical and transport properties of a fibrous C/C composite preform as digitized by X-ray computerized microtomography: Part II. Heat and gas transport properties, Journal of Materials Research, vol.22, issue.6, pp.1537-1550, 2007.

M. Luc and . Vincent, Efficient computation of various types of skeletons, Proceedings of SPIE : Medical Imaging V: Image Processing, pp.297-311, 1991.

T. Wang and A. Basu, A note on ???A fully parallel 3D thinning algorithm and its applications???, Pattern Recognition Letters, vol.28, issue.4, pp.501-506, 2007.
DOI : 10.1016/j.patrec.2006.09.004

E. Welzl, Smallest enclosing disks (balls and ellipsoids), Lecture Notes in Computer Science, vol.555, pp.359-370, 1991.
DOI : 10.1007/BFb0038202
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.1450

P. Shen-pei-wang, L. W. Hui, and T. Fleming, Further improved fast parallel thinning algorithm for digital patterns, Computer Vision, Image Processing and Communications -Systems and Applications, pp.37-40, 1986.

Z. Wu and R. Leahy, An optimal graph theoretic approach to data clustering: theory and its application to image segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.15, issue.11, pp.1101-1113, 1993.
DOI : 10.1109/34.244673

R. Wu and W. Tsai, A new one-pass parallel thinning algorithm for binary images, Pattern Recognition Letters, vol.13, issue.10, pp.715-723, 1992.
DOI : 10.1016/0167-8655(92)90101-5

W. Xie, R. P. Thompson, and R. Perucchio, A topology-preserving parallel 3D thinning algorithm for extracting the curve skeleton, Pattern Recognition, vol.36, issue.7, pp.1529-1544, 2003.
DOI : 10.1016/S0031-3203(02)00348-5

S. Yokoi, J. Toriwaki, and T. Fukumura, An Analysis of Topological Properties of Digitized Binary Pictures Using Local Features, Computer Graphics and Image Processing, vol.4, issue.1, pp.63-73, 1975.
DOI : 10.1016/0146-664X(75)90022-2

C. T. Zahn, Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters, IEEE Transactions on Computers, vol.20, issue.1, pp.68-86, 1971.
DOI : 10.1109/T-C.1971.223083
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.6859

H. Zhao, T. F. Chan, B. Merriman, and S. J. Osher, A Variational Level Set Approach to Multiphase Motion, Journal of Computational Physics, vol.127, issue.1, 1996.
DOI : 10.1006/jcph.1996.0167
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.3048

T. Y. Zhang and C. Y. Suen, A fast parallel algorithm for thinning digital patterns, Communications of the ACM, vol.27, issue.3, pp.236-239, 1984.
DOI : 10.1145/357994.358023