. Fig, Results of medial axis extraction in 2D: The first row presents the input binary shapes, the second row shows the Sk sets

A. Rosenfeld and J. L. Pfaltz, Sequential Operations in Digital Picture Processing, J. ACM, vol.13, issue.4, pp.471-494, 1966.

A. Rosenfeld and J. L. Pfalz, Distance functions on digital pictures, Pattern Recognition, vol.1, issue.1, pp.33-61, 1968.
DOI : 10.1016/0031-3203(68)90013-7

G. Borgefors, Distance transformations in digital images, Computer Vision, Graphics, and Image Processing, vol.34, issue.3, pp.344-371, 1986.
DOI : 10.1016/S0734-189X(86)80047-0

E. Remy and E. Thiel, Optimizing 3D Chamfer Masks with Norm Constraints, Proc. Int'l Workshop Combinatorial Image Analysis, pp.39-56, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01502947

C. Fouard and G. Malandain, 3-D chamfer distances and norms in anisotropic grids, Image and Vision Computing, vol.23, issue.2, pp.143-158, 2005.
DOI : 10.1016/j.imavis.2004.06.009

URL : https://hal.archives-ouvertes.fr/hal-00308886

J. Mukherjee, P. P. Das, M. A. Kumarb, and B. N. Chatterjib, On approximating Euclidean metrics by digital distances in 2D and 3D, Pattern Recognition Letters, vol.21, issue.6-7, pp.6-7, 2000.
DOI : 10.1016/S0167-8655(00)00022-2

B. Nagy, A Comparison Among Distances Based on Neighborhood Sequences in Regular Grids, Proc. 14th Scandinavian Conf. Image Analysis, pp.1027-1036, 2005.
DOI : 10.1007/11499145_104

P. Danielsson, Euclidean distance mapping, Computer Graphics and Image Processing, vol.14, issue.3, pp.227-248, 1980.
DOI : 10.1016/0146-664X(80)90054-4

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.322.7605

I. Ragnemalm, Contour Processing Distance Transforms, pp.204-211, 1990.

J. C. Mullikin, The vector distance transform in two and three dimensions, CVGIP: Graphical Models and Image Processing, vol.54, issue.6, pp.526-535, 1992.
DOI : 10.1016/1049-9652(92)90072-6

O. Cuisenaire and B. Macq, Fast Euclidean Distance Transformation by Propagation Using Multiple Neighborhoods, Computer Vision and Image Understanding, vol.76, issue.2, pp.163-172, 1999.
DOI : 10.1006/cviu.1999.0783

H. Breu, J. Gil, D. Kirkpatrick, and M. Werman, Linear time Euclidean distance transform algorithms, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.17, issue.5, pp.529-533, 1995.
DOI : 10.1109/34.391389

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.7352

C. Gotsman and M. Lindenbaum, Euclidean Voronoi labelling on the multidimensional grid, Pattern Recognition Letters, vol.16, issue.4, pp.409-415, 1995.
DOI : 10.1016/0167-8655(94)00112-G

W. Guan and S. Ma, A list-processing approach to compute Voronoi diagrams and the Euclidean distance transform, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.20, issue.7, pp.757-761, 1998.
DOI : 10.1109/34.689306

C. R. Maurer, R. Qi, and V. 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.
DOI : 10.1109/TPAMI.2003.1177156

T. Saito and J. I. Toriwaki, New algorithms for euclidean distance transformation of an n-dimensional digitized picture with applications, Pattern Recognition, vol.27, issue.11, pp.1551-1565, 1994.
DOI : 10.1016/0031-3203(94)90133-3

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

A. Meijster, J. Roerdink, and W. H. Hesselink, A General Algorithm for Computing Distance Transforms in Linear Time, Math. Morphology and Its Applications to Image and Signal Processing, pp.331-340, 2000.
DOI : 10.1007/0-306-47025-X_36

H. Blum, A Transformation for Extracting Descriptors of Shape Models for the Perception of Speech and Visual Forms, pp.362-380, 1967.

U. Montanari, Continuous Skeletons from Digitized Images, Journal of the ACM, vol.16, issue.4, pp.534-549, 1969.
DOI : 10.1145/321541.321543

P. Giblin and B. B. Kimia, On the local form and transitions of symmetry sets, medial axes, and shocks, Proceedings of the Seventh IEEE International Conference on Computer Vision, pp.1-3, 2003.
DOI : 10.1109/ICCV.1999.791246

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.238-251, 2004.
DOI : 10.1109/TPAMI.2004.1262192

D. Attali and A. Montanvert, Computing and Simplifying 2D and 3D Continuous Skeletons, Computer Vision and Image Understanding, vol.67, issue.3, pp.161-273, 1997.
DOI : 10.1006/cviu.1997.0536

F. F. Leymarie and M. D. Levine, Simulating the grassfire transform using an active contour model, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.1, pp.56-75, 1992.
DOI : 10.1109/34.107013

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.381-391, 1995.
DOI : 10.1006/cviu.1995.1062

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.7008

K. Siddiqi, S. Bouix, A. Tannenbaum, and S. 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

J. H. Chuang, C. H. Tsai, and M. C. Ko, Skeletonization of Three- Dimensional Object Using Generalized Potential Field, IEEE Trans. Pattern Analysis and Machine Intelligence, vol.22, issue.11, pp.1241-1251, 2000.

R. Klette, A. Rosenfeld, and D. Geometry, Geometric Methods for Digital Picture Analysis, series in computer graphics and geometric modeling, 2004.

G. S. Di-baja, Well-Shaped, Stable, and Reversible Skeletons from the (3,4)-Distance Transform, Journal of Visual Communication and Image Representation, vol.5, issue.1, pp.107-115, 1994.
DOI : 10.1006/jvci.1994.1010

E. Remy and E. 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

URL : https://hal.archives-ouvertes.fr/hal-01494689

I. Ragnemalm, The Euclidean Distance Transform, Linkö ping, Sweden, 1993.

Y. Ge and J. M. Fitzpatrick, On the Generation of Skeletons from Discrete Euclidean Distance Maps, IEEE Trans. Pattern Analysis and Machine Intelligence, vol.18, issue.11, pp.1055-1066, 1996.

T. Saito and J. Toriwaki, Reverse Distance Transformation and Skeletons Based upon the Euclidean Metric for n-Dimensionnal Digital Pictures, IECE Trans. Information & Systems, vol.77, issue.9, pp.1005-1016, 1994.

E. Remy and E. 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

URL : https://hal.archives-ouvertes.fr/hal-01502823

G. Borgefors and I. Nyströ-m, Efficient shape representation by minimizing the set of centres of maximal discs/spheres, Pattern Recognition Letters, vol.18, issue.5, pp.465-472, 1997.
DOI : 10.1016/S0167-8655(97)00027-5

F. Nilsson and P. Danielsson, Finding the Minimal Set of Maximum Disks for Binary Objects, Graphical Models and Image Processing, vol.59, issue.1, pp.55-60, 1997.
DOI : 10.1006/gmip.1996.0412

D. Attali, G. S. Di-baja, and E. Thiel, Pruning Discrete and Semiocontinuous Skeletons, Proc. Eighth Int'l Conf. Image Analysis and Processing, pp.488-493, 1995.
DOI : 10.1007/3-540-60298-4_303

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

F. P. Preparata and M. I. Shamos, Computational Geometry: An Introduction, 1985.
DOI : 10.1007/978-1-4612-1098-6

D. Coeurjolly, Algorithmique et Géométrie Discrète pour la Caractérisation des Courbes et des Surfaces, 2002.

W. H. Hesselink, M. Visser, and J. B. Roerdink, Euclidean Skeletons of 3D Data Sets in Linear Time by the Integer Medial Axis Transform, Math. Morphology: 40 Years On (Proc. Seventh Int'l Symp. Math. Morphology), C. Ronse, L. Najman, and E. Decencière, pp.259-268, 2005.
DOI : 10.1007/1-4020-3443-1_23

F. Aurenhammer, Power Diagrams: Properties, Algorithms and Applications, SIAM Journal on Computing, vol.16, issue.1, pp.78-96, 1987.
DOI : 10.1137/0216006

J. D. Boissonnat, A. Cerezo, O. Devillers, J. Duquesne, and M. Yvinec, An algorithm for constructing the convex hull of a set of spheres in dimension d, Computational Geometry, vol.6, issue.2, pp.123-130, 1996.
DOI : 10.1016/0925-7721(95)00024-0

URL : https://hal.archives-ouvertes.fr/hal-01179732

N. Amenta, S. Choi, and R. K. Kolluri, The power crust, unions of balls, and the medial axis transform, Computational Geometry, vol.19, issue.2-3, pp.127-153, 2001.
DOI : 10.1016/S0925-7721(01)00017-7