C. Alì-ene, J. Audibert, M. Couprie, J. Cousty, and R. Keriven, Some links between min-cuts, optimal spanning forests and watersheds, Proceedings of the The 8th International Symposium on Mathematical Morphology, pp.253-264, 2007.

R. Audigier and R. A. Lotufo, Watershed by image foresting transform, tie-zone, and theoretical relationships with other watershed definitions, Proceedings of the The 8th International Symposium on Mathematical Morphology, pp.277-288, 2007.

R. Beare, Regularized seeded region growing, Proceedings of the The 6th International Symposium on Mathematical Morphology, pp.91-99, 2002.

J. Beaulieu and M. Goldberg, Hierarchy in picture segmentation: a stepwise optimization approach, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.11, issue.2, 1989.
DOI : 10.1109/34.16711

I. Ben-dan and E. Shenhav, Liver tumor segmentation in ct images using probabilistic., Workshop on 3D Segmentation in the Clinic: A Grand Challenge II. Liver Tumor Segmentation Challenge, 2008.

C. Berge, Théorie des graphes et ses applications, 1958.

J. Besag, Statistical analysis of dirty pictures*, Journal of Applied Statistics, vol.6, issue.5-6, pp.259-302, 1974.
DOI : 10.1016/0031-3203(83)90012-2

S. Beucher, Watershed, hierarchical segmentation and waterfall algorithm, Mathematical Morphology and its applications to signal processing, Proceedings ISMM'94), pp.69-76, 1994.

S. Beucher and C. Lantuéjoul, Use of watershed in contour detection, International workshop on image processing, real time edge and motion detection/estimation, 1979.

Y. Boykov and M. P. Jolly, Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001, pp.105-112, 2001.
DOI : 10.1109/ICCV.2001.937505

Y. Boykov and V. Kolmogorov, Computing geodesics and minimal surfaces via graph cuts, Proceedings Ninth IEEE International Conference on Computer Vision, pp.26-33, 2003.
DOI : 10.1109/ICCV.2003.1238310
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.123.6433

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

Y. Boykov, O. Veksler, and R. Zabih, Markov random fields with efficient approximations, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231), pp.648-655, 1998.
DOI : 10.1109/CVPR.1998.698673

M. Bruglieri, F. Maffioli, and M. Ehrgott, Cardinality constrained minimum cut problems: complexity and algorithms, Discrete Applied Mathematics, vol.137, issue.3, pp.311-341, 2004.
DOI : 10.1016/S0166-218X(03)00358-5
URL : http://doi.org/10.1016/s0166-218x(03)00358-5

V. Caselles, R. Kimmel, and G. Sapiro, Geodesic active contours, Proceedings of IEEE International Conference on Computer Vision, pp.694-699
DOI : 10.1109/ICCV.1995.466871
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.2196

V. Caselles, R. Kimmel, G. Sapiro, and C. Sbert, Minimal surfaces: A three dimensional segmentation approach, Technion EE Pub, p.973, 1995.

A. Choudhary, N. Moretto, F. Pizzorni-ferrarese, and G. Zamboni, An entropy based multithresholding method for semi-automatic segmentation of liver tumors, Workshop on 3D Segmentation in the Clinic: A Grand Challenge II. Liver Tumor Segmentation Challenge, 2008.

T. Cormen, C. Leiserson, and R. Rivest, Introduction to algorithms, 1990.

J. Crespo, R. Schafer, J. Serra, C. Gratin, and F. Meyer, The flat zone approach: A general low-level region merging segmentation method, Signal Processing, vol.62, issue.1, pp.37-60, 1997.
DOI : 10.1016/S0165-1684(97)00114-X

E. Dahlhaus, D. S. Johnson, C. H. Papadimitriou, P. Seymour, and M. Yannakakis, The Complexity of Multiterminal Cuts, SIAM Journal on Computing, vol.23, issue.4, pp.864-894, 1994.
DOI : 10.1137/S0097539792225297

G. B. Dantzig, Maximization of a linear function of variables subject to linear inequalities, Activity of production and allocation, pp.359-373, 1951.

G. B. Dantzig and D. R. Fulkerson, 12. On the Max-Flow Min-Cut Theorem of Networks, pp.215-221, 1956.
DOI : 10.1515/9781400881987-013

E. W. Dijkstra, A note on two problems in connexion with graphs, Numerische Mathematik, vol.4, issue.1, pp.269-271, 1959.
DOI : 10.1007/BF01386390

E. A. Dinic, Algorithm for solution of a problem of maximum flow in a network with power estimation, Soviet Math. Doklady, vol.11, pp.1277-1280, 1970.

J. Edmonds and R. M. Karp, Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems, Journal of the ACM, vol.19, issue.2, pp.248-264, 1972.
DOI : 10.1145/321694.321699

A. N. Evans and X. U. Liu, A morphological gradient approach to color edge detection, IEEE Transactions on Image Processing, vol.15, issue.6, pp.1454-1463, 2006.
DOI : 10.1109/TIP.2005.864164

A. X. Falcão, J. K. Udupa, S. Samarasekera, S. Sharma, B. E. Hirsch et al., User-Steered Image Segmentation Paradigms: Live Wire and Live Lane, Graphical Models and Image Processing, vol.60, issue.4, pp.233-260, 1998.
DOI : 10.1006/gmip.1998.0475

A. X. Falcao, J. Stolfi, and R. Lotufo, The image foresting transform: theory, algorithms, and applications, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.26, issue.1, pp.19-29, 2004.
DOI : 10.1109/TPAMI.2004.1261076

J. 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

F. Ford and D. Fulkerson, A simplex algorithm finding maximal networks flows and an application to the hitchock problem, Rand Report Rand Corporation, 1955.

D. Freedman and P. Drineas, Energy minimization via graph cuts: Settling what is possible, D. Freedman and P. Drineas. Energy minimization via graph cuts: Settling what is possible, Proc. IEEE Conf. Com (b) (c), pp.939-946, 2005.
DOI : 10.1109/cvpr.2005.143
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.1348

S. Gaubert, Two lectures on max-plus algebra, Proceedings of the 26th Spring School on Theoretical Computer Science and Automatic Control, 1998.

S. Geman and D. Geman, Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.6, issue.6, pp.721-741, 1984.
DOI : 10.1109/TPAMI.1984.4767596

B. Glocker, N. Komodakis, N. Paragios, G. Tziritas, and N. Navab, Inter and Intra-modal Deformable Registration: Continuous Deformations Meet Efficient Optimal Linear Programming, Proceedings of the 20th International Conference on Information Processing in Medical Imaging, 2008.
DOI : 10.1007/978-3-540-73273-0_34

A. Goldberg and R. Tarjan, A new approach to the maximum-flow problem, pp.921-940, 1988.

L. Grady, Computing Exact Discrete Minimal Surfaces: Extending and Solving the Shortest Path Problem in 3D with Application to Segmentation, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Volume 1 (CVPR'06), pp.69-78, 2006.
DOI : 10.1109/CVPR.2006.82

L. Grady and E. L. Schwartz, Isoperimetric Partitioning: A New Algorithm for Graph Partitioning, SIAM Journal on Scientific Computing, vol.27, issue.6, pp.1844-1866, 2006.
DOI : 10.1137/040609008

L. Grady and A. K. Sinop, A seeded image segmentation framework unifying graph cuts and random walker which yields a new algorithm, Proceedings of the 11th International Conference on Computer Vision, 2007.

D. M. Greig, B. T. Porteous, and A. H. Seheult, Exact maximum a posteriori estimation for binary images, Royal Journal of Statistics, Soc. B, vol.51, issue.2, pp.271-279, 1989.

O. Grygorash, Y. Zhou, and Z. Jorgensen, Minimum Spanning Tree Based Clustering Algorithms, 2006 18th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'06), pp.73-81, 2006.
DOI : 10.1109/ICTAI.2006.83

Y. Hame, Liver tumor segmentation using implicit surface evolution., Workshop on 3D Segmentation in the Clinic: A Grand Challenge II. Liver Tumor Segmentation Challenge, 2008.

W. R. Hamilton, Account of the icosian game, Proceedings of the Royal Irish Academy, vol.6, pp.415-416

T. C. Hu, Letter to the Editor???The Maximum Capacity Route Problem, Operations Research, vol.9, issue.6, pp.898-900, 1961.
DOI : 10.1287/opre.9.6.898

H. Ishikawa, Exact optimization for markov random fields with convex priors, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.25, issue.10, pp.1333-1336, 2003.
DOI : 10.1109/TPAMI.2003.1233908

E. Ising, Beitrag zur Theorie des Ferromagnetismus, Zeitschrift f??r Physik, vol.6, issue.4, pp.235-258, 1925.
DOI : 10.1007/BF02980577

T. N. Janakiraman, Image Segmentation Based on Minimal Spanning Tree and Cycles, International Conference on Computational Intelligence and Multimedia Applications (ICCIMA 2007), pp.215-219, 2007.
DOI : 10.1109/ICCIMA.2007.54

I. H. Jermyn and H. Ishikawa, Globally optimal regions and boundaries as minimum ratio weight cycles, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.23, issue.10, pp.1075-1088, 2001.
DOI : 10.1109/34.954599
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.100.7360

D. Karger, P. Klein, C. Stein, M. Thorup, and N. Young, Rounding algorithms for a geometric embedding of minimum multiway cut, pp.99-668, 1999.

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

R. Kindermann and J. L. Snell, Markov random fields and their applications, 1980.
DOI : 10.1090/conm/001

V. Kolmogorov and R. Zabih, What energy functions can be minimized via graph cuts?, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.26, issue.2, pp.147-159, 2004.
DOI : 10.1109/TPAMI.2004.1262177

B. Korte and J. Vygen, Combinatorial optimization. theory and algorithms, 2005.

A. H. Land and A. G. Doig, An Automatic Method of Solving Discrete Programming Problems, Econometrica, vol.28, issue.3, pp.497-520, 1960.
DOI : 10.2307/1910129

Y. Li, S. Hara, and K. Shimura, A machine learning approach for locating boundaries of liver tumors in ct images, Proceedings of the 18th International Conference on Pattern Recognition, pp.400-403, 2006.

Y. Li, J. Sun, C. Tang, and H. Shum, Lazy snapping, ACM Transactions on Graphics, vol.23, issue.3, pp.303-308, 2004.
DOI : 10.1145/1015706.1015719

R. Lotufo and A. Falcao, The Ordered Queue and the Optimality of the Watershed Approaches, Proceedings of the International Symposium on Mathematical Morphology, pp.341-350, 2000.
DOI : 10.1007/0-306-47025-X_37

R. Lu, P. Marziliano, and C. H. Thng, Liver tumor volume estimation by semi-automatic segmentation method, Proceedings of the 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference, pp.3297-3299, 2005.

B. Marcotegui, P. Correia, F. Marqués, R. Mech, R. Rosa et al., A video object generator tool allowing friendly user interaction, IEEE International Conference on Image Processing, 1999.

C. E. Mathieu and I. E. Magnin, On the choice of the first level on graph pyramids, Journal of Mathematical Imaging and Vision, vol.138, issue.No. 4, pp.85-96, 1996.
DOI : 10.1007/BF00127376

J. Mcqueen, Some methods for classification and analysis of multivariate observations, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, pp.281-297, 1967.

F. Meyer, Minimal spanning forests for morphological segmentation, ISMM'94, Mathematical Morphology and its applications to Signal Processing, pp.77-84, 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

F. Meyer and C. Vachier, Image segmentation based on viscous flooding simulation, Proceedings of The 6th International Symposium on Mathematical Morphology, pp.69-77, 2002.

M. Mohri, Semiring frameworks and algorithms for shortest-distance problems, Journal of Automata , Languages and Combinatorics, vol.7, pp.321-350

J. Moltz, L. Bornemann, V. Dicken, and H. Peitgen, Segmentation of liver metastases in ct scans by adaptive thresholding and morphological processing, Workshop on 3D Segmentation in the Clinic: A Grand Challenge II. Liver Tumor Segmentation Challenge, 2008.

E. N. Mortensen and W. A. 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

L. Najman and M. Schmitt, Watershed of a continuous function, Signal Processing, vol.38, issue.1, pp.99-112, 1994.
DOI : 10.1016/0165-1684(94)90059-0
URL : https://hal.archives-ouvertes.fr/hal-00622129

S. Osher and R. Fedkiw, Level set methods and dynamic implicit surfaces
DOI : 10.1115/1.1760520
URL : http://dx.doi.org/10.1016/s0898-1221(03)90179-9

M. Pardàs, Segmentacì on morfológica de secuencias de imàgenes: Aplicación a la codificación, 1995.

T. Popa, L. Ibanez, E. Levy, A. White, J. Bruno et al., Tumor volume measurement and volume measurement comparison plug-ins for VolView using ITK, Medical Imaging 2006: Visualization, Image-Guided Procedures, and Display, pp.6141-395, 2006.
DOI : 10.1117/12.655213

F. A. Potra and S. J. Wright, Interior-point methods, Journal of Computational and Applied Mathematics, vol.124, issue.1-2, pp.281-302, 2000.
DOI : 10.1016/S0377-0427(00)00433-7

F. Preteux, On a distance function approach for gray-level mathematical morphology, Mathematical Morphology in Image Processing, pp.323-349, 1993.

Y. Qi, W. Xiong, W. Leow, Q. Tian, J. Zhou et al., Semi-automatic segmentation of liver tumors from ct scans using bayesian rule-based 3d region growing, Workshop on 3D Segmentation in the Clinic: A Grand Challenge II. Liver Tumor Segmentation Challenge, 2008.

J. B. Roerdink and A. Meijster, The watershed transform: Definitions, algorithms and parallelization strategies, Fundamenta Informatica, pp.41-187, 2001.

P. Salembier and J. Serra, Flat zones filtering, connected operators, and filters by reconstruction, IEEE Transactions on Image Processing, vol.4, issue.8, pp.1153-1160, 1995.
DOI : 10.1109/83.403422

G. Schmidt, G. Binnig, M. Kietzmann, and J. Kim, Cognition network technology for a fully automated 3d segmentation of liver tumors, Workshop on 3D Segmentation in the Clinic: A Grand Challenge II. Liver Tumor Segmentation Challenge, 2008.

J. Serra, Image analysis and mathematical morphology -volume i, 1982.

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

J. Shi, S. Belongie, T. Leung, and J. Malik, Image and video segmentation: the normalized cut framework, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269), pp.943-947, 1998.
DOI : 10.1109/ICIP.1998.723676

A. Shimizu, T. Narihira, D. Furukawa, H. Kobatake, S. Nawano et al., Ensemble segmentation using adaboost with application to liver lesion extraction from a ct volume, Workshop on 3D Segmentation in the Clinic: A Grand Challenge II. Liver Tumor Segmentation Challenge, 2008.

D. Smeets, B. Stijnen, D. Loeckx, B. De-dobbelaer, and P. Suetens, Segmentation of liver metastases using a level set method with spiral-scanning technique and supervised fuzzy pixel classification., Workshop on 3D Segmentation in the Clinic: A Grand Challenge II. Liver Tumor Segmentation Challenge, 2008.

T. S. Sørensen, G. F. Greil, O. K. Hansen, and J. Mosegaard, Surgical simulation - a new tool to evaluate surgical incisions in congenital heart disease?, Interactive CardioVascular and Thoracic Surgery, vol.5, issue.5, pp.536-539, 2006.
DOI : 10.1510/icvts.2006.132316

T. S. Sørensen, J. Stawiaski, and J. Mosegaard, Virtual open heart surgery, ACM SIGGRAPH 2006 Emerging technologies on , SIGGRAPH '06, pp.445-452, 2007.
DOI : 10.1145/1179133.1179169

S. Sarkar and P. Soundararajan, Supervised learning of large perceptual organization: graph spectral partitioning and learning automata, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.22, issue.5, pp.504-525, 2000.
DOI : 10.1109/34.857006

J. Stawiaski, F. Bidault, E. Decencì-ere, T. Girinsky, C. Le-pchoux et al., Analyse dimages ct 4d : ApplicationàApplicationà la segmentation des poumons, Journée française de Radiologie, 2007.

J. Stawiaski, F. Bidault, E. Decencì-ere, T. Girinsky, C. Le-péchoux et al., Segmentation interactive dimages médicales par hiérarchie de partitions, 2006.

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

J. Stawiaski, E. Decencì, and F. Bidault, Interactive liver tumor segmentation using graph cuts and watershed, Workshop on 3D Segmentation in the Clinic: A Grand Challenge II. Liver Tumor Segmentation Challenge, 2008.

J. Stawiaski, E. Decencì, and F. Bidault, Spatio-temporal segmentation of 4d ct images., The European Consortium For Mathematics In Industry, 2008.

J. Stawiaski, E. Decencì, and D. Jeulin, Interactive segmentation of microstructures, Workshop on 3D image analysis and modelling of microstructures, ITWM Fraunhofer, 2007.

J. Stawiaski, J. Mosegaard, and T. S. Sørensen, Virtual open heart surgery: Segmentation, Proceedings of Medicine Meets Virtual Reality 15, Stud Health Technol Inform, vol.125, pp.448-50, 2007.

J. Stawiaski, T. S. Sørensen, E. Decencì, and F. Bidault, Combining morphological and graph based methods for multi-label segmentation, Workshop on interaction in medical image analysis and visualisation, MICCAI, 2007.

J. J. Sylvester, Chemistry and Algebra, Nature, vol.17, issue.432, p.284, 1878.
DOI : 10.1038/017284a0

Y. Taieb, O. Eliassaf, M. Freiman, L. Joskowicz, and J. Sosna, An iterative bayesian approach for liver analysis: tumors validation study., Workshop on 3D Segmentation in the Clinic: A Grand Challenge II. Liver Tumor Segmentation Challenge, 2008.

K. Tsuda and G. Ratsch, Image reconstruction by linear programming, IEEE Transactions on Image Processing, vol.14, issue.6, pp.737-744, 2005.
DOI : 10.1109/TIP.2005.846029
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.150.3616

P. Tylsky, G. Bonniaud, E. Decencì-ere, J. Stawiaski, D. Lefkopoulos et al., /sup 18/F-FDG PET images segmentation using morphological watershed: a phantom study, 2006 IEEE Nuclear Science Symposium Conference Record, 2006.
DOI : 10.1109/NSSMIC.2006.354319

O. Veksler, Image segmentation by nested cuts, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662), pp.339-344, 2000.
DOI : 10.1109/CVPR.2000.855838
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.8283

L. Vincent, Algorithmes morphologiquesàmorphologiquesà base de files d'attente et de lacets. extension aux graphes, 1990.

W. E. Lorensen and H. E. Cline, Marching cubes: A high resolution 3d surface construction algorithm, Computer Graphics (Proceedings of SIGGRAPH '87), pp.163-169, 1987.

D. Wong, J. Liu, F. Yin, Q. Tian, W. Xiong et al., A semi-automated method for liver tumor segmentation based on 2d region growing., Workshop on 3D Segmentation in the Clinic: A Grand Challenge II. Liver Tumor Segmentation Challenge, 2008.

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

F. Zanoguera, B. Marcotegui, and F. Meyer, A tool-box for interactive image segmentation based on nested partitions, IEEE International Conference on Image Processing, 1999.

J. Zhou, W. Xiong, Q. Tian, Y. Qi, J. Liu et al., Semi-automatic segmentation of 3d liver tumors from ct scans using voxel classification and propagational learning, Workshop on 3D Segmentation in the Clinic: A Grand Challenge II. Liver Tumor Segmentation Challenge, 2008.