R. Adams and L. Bischof, Seeded region growing, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.16, issue.6, pp.641-647, 1994.
DOI : 10.1109/34.295913

B. Appleton, Globally minimal contours and surfaces for image segmentation, 2004.

B. Appleton and C. Sun, Circular shortest paths by branch and bound, Pattern Recognition, vol.36, issue.11, pp.2513-2520, 2003.
DOI : 10.1016/S0031-3203(03)00122-5

URL : http://espace.library.uq.edu.au/view/UQ:9743/BABCSP.pdf

B. Appleton and H. Talbot, Globally Optimal Geodesic Active Contours, Journal of Mathematical Imaging and Vision, vol.7, issue.3, pp.67-86, 2005.
DOI : 10.1007/s10851-005-4968-1

URL : https://hal.archives-ouvertes.fr/hal-00621985

R. Ardon and L. Cohen, Fast Constrained Surface Extraction by Minimal Paths, International Journal of Computer Vision, vol.8, issue.2, pp.127-136, 2006.
DOI : 10.1007/s11263-006-6850-z

S. Beucher and C. Lantuéjoul, Use of watersheds in contour detection, International Workshop on Image Processing. CCETT/IRISA, 1979.

Y. Boykov and V. Kolmogorov, An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.26, issue.9, pp.1124-1137, 2004.
DOI : 10.1109/TPAMI.2004.60

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

J. Canny, A computational approach to edge detection, IEEE Trans. Pattern Anal. Mach. Intell, vol.8, issue.6, pp.679-698, 1986.

V. Caselles, R. Kimmel, and G. Sapiro, Geodesic active contours, Proceedings of IEEE International Conference on Computer Vision, pp.61-79, 1997.
DOI : 10.1109/ICCV.1995.466871

A. Chambolle, An algorithm for total variation minimization and applications, J. Math. Imaging Vis, vol.20, issue.12, pp.89-97, 2004.

T. Chan and X. Bresson, Continuous convex relaxation methods for image processing Keynote talk, Proceedings of ICIP 2010, 2010.

T. Chan and L. Vese, Active contours without edges, IEEE Transactions on Image Processing, vol.10, issue.2, pp.266-277, 2001.
DOI : 10.1109/83.902291

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1828

L. D. Cohen and R. Kimmel, Global minimum for active contour models: a minimal path approach, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.57-78, 1997.
DOI : 10.1109/CVPR.1996.517144

C. Couprie, L. Grady, L. Najman, and H. Talbot, Power watersheds: A new image segmentation framework extending graph cuts, random walker and optimal spanning forest, 2009 IEEE 12th International Conference on Computer Vision, pp.731-738, 2009.
DOI : 10.1109/ICCV.2009.5459284

URL : https://hal.archives-ouvertes.fr/hal-00622409

C. Couprie, L. Grady, L. Najman, and H. Talbot, Power Watershed: A Unifying Graph-Based Optimization Framework, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.33, issue.7, pp.1384-1399, 2011.
DOI : 10.1109/TPAMI.2010.200

C. Couprie, L. Grady, H. Talbot, and L. Najman, Anisotropic diffusion using power watersheds, 2010 IEEE International Conference on Image Processing, pp.4153-4156, 2010.
DOI : 10.1109/ICIP.2010.5653896

URL : https://hal.archives-ouvertes.fr/hal-00744091

C. Couprie, L. Grady, H. Talbot, and L. Najman, Combinatorial Continuous Maximum Flow, SIAM Journal on Imaging Sciences, vol.4, issue.3, 2010.
DOI : 10.1137/100799186

J. Cousty, G. Bertrand, L. Najman, and M. Couprie, Watershed Cuts: Minimum Spanning Forests and the Drop of Water Principle, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.31, issue.8, pp.1362-1374, 2008.
DOI : 10.1109/TPAMI.2008.173

URL : https://hal.archives-ouvertes.fr/hal-00622410

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. Cserti, Application of the lattice Green???s function for calculating the resistance of an infinite network of resistors, American Journal of Physics, vol.68, issue.10, p.896, 2000.
DOI : 10.1119/1.1285881

X. Daragon, M. Couprie, and G. Bertrand, Marching Chains algorithm for Alexandroff-Khalimsky spaces, Vision Geometry XI, pp.51-62, 2002.
DOI : 10.1117/12.453595

URL : https://hal.archives-ouvertes.fr/hal-00622041

E. Dougherty and R. Lotufo, Hands-on Morphological Image Processing, 2003.
DOI : 10.1117/3.501104

P. Doyle and J. Snell, Random Walks and Electric Networks, Carus Mathematical Monographs, vol.22, p.52, 1984.
DOI : 10.5948/UPO9781614440222

S. Geman and D. Geman, Stochastic relaxation, gibbs distributions, and the bayesian restoration of images, PAMI, vol.6, pp.721-741, 1984.

A. Goldberg and R. Tarjan, A new approach to the maximum-flow problem, Journal of the ACM, vol.35, issue.4, pp.921-940, 1988.
DOI : 10.1145/48014.61051

R. Goldenberg, R. Kimmel, E. Rivlin, and M. Rudzsky, Fast geodesic active contours, IEEE Transactions on Image Processing, vol.10, issue.10, pp.1467-1475, 2001.
DOI : 10.1109/83.951533

L. Grady, Multilabel Random Walker Image Segmentation Using Prior Models, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05), pp.763-770239, 2005.
DOI : 10.1109/CVPR.2005.239

L. Grady, Computing exact discrete minimal surfaces: Extending and solving the shortest path problem in 3D with application to segmentation In: Computer Vision and Pattern Recognition, IEEE Computer Society Conference IEEE, vol.1, pp.69-78, 2006.

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

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.375.3389

L. Grady and G. Funka-lea, Multi-label Image Segmentation for Medical Applications Based on Graph-Theoretic Electrical Potentials, Computer Vision and Mathematical Methods in Medical and Biomedical Image Analysis, pp.230-245, 2004.
DOI : 10.1007/978-3-540-27816-0_20

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.91.4365

L. Grady and J. Polimeni, Discrete Calculus: Applied Analysis on Graphs for Computational Science, 2010.
DOI : 10.1007/978-1-84996-290-2

L. Grady and E. Schwartz, Isoperimetric graph partitioning for image segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.28, issue.3, pp.469-475, 2006.
DOI : 10.1109/TPAMI.2006.57

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.68.5597

L. Guigues, J. Cocquerez, and H. Le-men, Scale-Sets Image Analysis, International Journal of Computer Vision, vol.20, issue.6, pp.289-317, 2006.
DOI : 10.1007/s11263-005-6299-0

URL : https://hal.archives-ouvertes.fr/hal-00705364

S. Horowitz and T. Pavlidis, Picture segmentation by a directed split-and-merge procedure, Proceedings of the Second International Joint Conference on Pattern Recognition, p.433, 1974.

S. Kakutani, Markov processes and the Dirichlet problem, Proceedings of the Japan Academy, pp.227-233, 1945.

M. Kass, A. Witkin, and D. Terzopoulos, Snakes: Active contour models, International Journal of Computer Vision, vol.5, issue.6035, pp.321-331, 1988.
DOI : 10.1007/BF00133570

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.124.5318

E. Khalimsky, R. Kopperman, and P. 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

URL : http://doi.org/10.1016/0166-8641(90)90031-v

J. J. Kruskal, On the shortest spanning subtree of a graph and the travelling salesman problem, Proc. AMS, vol.7, issue.1, 1956.

A. Levinshtein, A. Stere, K. Kutulakos, D. Fleet, S. Dickinson et al., Turbopixels: Fast superpixels using geometric flows. Pattern Anal, Mach. Intell. IEEE Trans, issue.12, pp.31-2290, 2009.
DOI : 10.1109/tpami.2009.96

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.161.240

R. Malladi, J. Sethian, and B. Vemuri, Shape modeling with front propagation: a level set approach, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.17, issue.2, pp.158-175, 1995.
DOI : 10.1109/34.368173

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.131.6656

D. Marr and E. Hildreth, Theory of Edge Detection, Proceedings of the Royal Society B: Biological Sciences, vol.207, issue.1167, pp.187-217, 1980.
DOI : 10.1098/rspb.1980.0020

S. W. Menzies, K. A. Crotty, C. Ingvar, and W. H. Mccarthy, An Atlas of Surface Microscopy of Pigmented Skin Lesions, 1996.

F. Meyer, Topographic distance and watershed lines. Signal Process, pp.113-125, 1994.

F. Meyer and S. Beucher, Morphological segmentation, Journal of Visual Communication and Image Representation, vol.1, issue.1, pp.21-46, 1990.
DOI : 10.1016/1047-3203(90)90014-M

E. Mortensen and W. Barrett, Interactive Segmentation with Intelligent Scissors, Graphical Models and Image Processing, vol.60, issue.5, pp.349-384, 1998.
DOI : 10.1006/gmip.1998.0480

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.89.2987

D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, vol.3, issue.5, pp.577-685, 1989.
DOI : 10.1002/cpa.3160420503

URL : http://nrs.harvard.edu/urn-3:HUL.InstRepos:3637121

L. Najman, On the Equivalence Between Hierarchical Segmentations and??Ultrametric Watersheds, Journal of Mathematical Imaging and Vision, vol.113, issue.3, pp.231-247, 2011.
DOI : 10.1007/s10851-011-0259-1

URL : https://hal.archives-ouvertes.fr/hal-00419373

L. Najman and M. Schmitt, Geodesic saliency of watershed contours and hierarchical segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, issue.12, pp.1163-1173, 2002.
DOI : 10.1109/34.546254

URL : https://hal.archives-ouvertes.fr/hal-00622128

L. Najman and H. Talbot, Mathematical Morphology: From theory to applications, 2010.
DOI : 10.1002/9781118600788

URL : https://hal.archives-ouvertes.fr/hal-00622479

S. Osher and J. 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.
DOI : 10.1016/0021-9991(88)90002-2

N. Otsu, A Threshold Selection Method from Gray-Level Histograms, IEEE Transactions on Systems, Man, and Cybernetics, vol.9, issue.1, pp.285-296, 1975.
DOI : 10.1109/TSMC.1979.4310076

N. Paragios and R. Deriche, Geodesic active contours and level sets for the detection and tracking of moving objects, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.22, issue.3, pp.266-280, 2002.
DOI : 10.1109/34.841758

N. Paragios and R. Deriche, Geodesic active regions and level set methods for supervised texture segmentation, International Journal of Computer Vision, vol.46, issue.3, pp.223-247, 2002.
DOI : 10.1023/A:1014080923068

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.2737

D. Pham, C. Xu, and J. Prince, Current methods in medical image segmentation1, Biomed. Eng, vol.2, issue.1, p.315, 2000.
DOI : 10.1146/annurev.bioeng.2.1.315

T. Pock, D. Cremers, H. Bischof, and A. Chambolle, An algorithm for minimizing the Mumford-Shah functional, 2009 IEEE 12th International Conference on Computer Vision, pp.1133-1140, 2009.
DOI : 10.1109/ICCV.2009.5459348

R. Prim, Shortest Connection Networks And Some Generalizations, Bell System Technical Journal, vol.36, issue.6, pp.1389-1401, 1957.
DOI : 10.1002/j.1538-7305.1957.tb01515.x

L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, pp.259-2680167, 1992.
DOI : 10.1016/0167-2789(92)90242-F

C. Sagiv, N. Sochen, and Y. Zeevi, Integrated active contours for texture segmentation, IEEE Transactions on Image Processing, vol.15, issue.6, pp.1633-1646, 2006.
DOI : 10.1109/TIP.2006.871133

J. Sethian, Level set methods and fast marching methods, 1999.

P. Soille, Constrained connectivity for hierarchical image partitioning and simplification, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.30, issue.7, pp.1132-1145, 2008.
DOI : 10.1109/TPAMI.2007.70817

URL : http://publications.jrc.ec.europa.eu/repository/handle/JRC36392

J. Stawiaski, E. Decencì-ere, F. Bidault, G. J. Banon, and J. Barrera, Computing approximate geodesics and minimal surfaces using watershed and graph cuts, Proceedings of the 8th International Symposium on Mathematical Morphology, pp.349-360, 2007.

G. Strang, Maximal flow through a domain, Mathematical Programming, vol.19, issue.2, pp.123-143, 1983.
DOI : 10.1007/BF02592050

O. Veksler, Efficient graph-based energy minimization, 1999.

L. Vincent and P. Soille, Watersheds in digital spaces: an efficient algorithm based on immersion simulations, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.13, issue.6, pp.583-598, 1991.
DOI : 10.1109/34.87344

J. Weickert, B. Romeny, and M. Viergever, Efficient and reliable schemes for nonlinear diffusion filtering. Image Process, IEEE Trans, vol.7, issue.3, pp.398-410, 2002.

S. Zhu and A. Yuille, Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation. Pattern Anal, Mach. Intell. IEEE Trans, vol.18, issue.9, pp.884-900, 2002.