C. Alì-ene, J. Audibert, M. Couprie, J. Cousty, and R. Keriven, Some links between min cuts, optimal spanning forests and watersheds, 7th international symposium on mathematical morphology ISMM'07, pp.253-264, 2007.

C. Alì-ene, J. Audibert, M. Couprie, and R. Keriven, Some links between extremum spanning forests, watersheds and min-cuts, Image and Vision Computing, p.14, 2009.

C. V. Alvino, G. B. Unal, G. Slabaugh, B. Peny, and T. Fang, Efficient segmentation based on Eikonal and diffusion equations, International Journal of Computer Mathematics, vol.84, issue.9, pp.1309-1324, 2007.
DOI : 10.1109/34.56205

A. Anandkumar, L. Tong, and A. Swami, Detection of Gauss-Markov Random Field on Nearest-Neighbor Graph, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07, 2007.
DOI : 10.1109/ICASSP.2007.366808

J. Angulo and D. Jeulin, Stochastic watershed segmentation, Proc. of the 8th International Symposium on Mathematical Morphology, pp.265-276, 2007.
URL : https://hal.archives-ouvertes.fr/hal-01104256

B. Appleton and H. Talbot, Globally minimal surfaces by continuous maximal flows, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.28, issue.1, pp.106-118, 2006.
DOI : 10.1109/TPAMI.2006.12

URL : https://hal.archives-ouvertes.fr/hal-00621983

P. A. Arbeláez and L. D. Cohen, A Metric Approach to Vector-Valued Image Segmentation, International Journal of Computer Vision, vol.133, issue.2, pp.119-126, 2006.
DOI : 10.1007/s11263-006-6857-5

R. Audigier and R. Lotufo, Uniquely-Determined Thinning of the Tie-Zone Watershed Based on Label Frequency, Journal of Mathematical Imaging and Vision, vol.13, issue.6, pp.157-173, 2007.
DOI : 10.1007/s10851-007-0780-4

X. Bai and G. Sapiro, Geodesic Matting: A Framework for Fast Interactive Image and??Video Segmentation and Matting, Proc. of ICCV'07, 2007.
DOI : 10.1007/s11263-008-0191-z

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

S. Beucher and F. Meyer, The morphological approach to segmentation: The watershed transformation, Mathematical Morphology in Image Processing, pp.433-481, 1993.

A. Bieniek and A. Moga, An efficient watershed algorithm based on connected components, Pattern Recognition, vol.33, issue.6, pp.907-916, 2000.
DOI : 10.1016/S0031-3203(99)00154-5

A. Blake, C. Rother, M. Brown, P. Perez, and P. Torr, Interactive Image Segmentation Using an Adaptive GMMRF Model, Computer Vision ? ECCV'04, pp.428-441, 2004.
DOI : 10.1007/978-3-540-24670-1_33

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.86.980

A. Blake and A. Zisserman, Visual Reconstruction, 1987.

C. Bouman and K. Sauer, A generalized Gaussian image model for edge-preserving MAP estimation, IEEE Transactions on Image Processing, vol.2, issue.3, pp.296-310, 1993.
DOI : 10.1109/83.236536

Y. Boykov and M. 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, An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision, IEEE Transactions on PAMI, vol.26, pp.359-374, 2001.

Y. Boykov and V. Kolmogorov, Computing geodesics and minimal surfaces via graph cuts, Proceedings Ninth IEEE International Conference on Computer Vision, 2003.
DOI : 10.1109/ICCV.2003.1238310

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.123.6433

E. J. Breen and R. Jones, Attribute Openings, Thinnings, and Granulometries, Computer Vision and Image Understanding, vol.64, issue.3, pp.377-389, 1996.
DOI : 10.1006/cviu.1996.0066

B. Chazelle, A minimum spanning tree algorithm with inverse-Ackermann type complexity, Journal of the ACM, vol.47, issue.6, pp.1028-1047, 2000.
DOI : 10.1145/355541.355562

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

R. R. Coifman, S. Lafon, A. B. Lee, M. Maggioni, B. Nadler et al., Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps, Proceedings of the National Academy of Sciences, vol.102, issue.21, pp.1027426-7431, 2005.
DOI : 10.1073/pnas.0500334102

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, 2002.
DOI : 10.1109/ICCV.2009.5459284

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

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

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

M. Couprie, L. Najman, and G. Bertrand, Quasi-Linear Algorithms for the Topological Watershed, Journal of Mathematical Imaging and Vision, vol.13, issue.6, pp.231-249, 2005.
DOI : 10.1007/s10851-005-4892-4

URL : https://hal.archives-ouvertes.fr/hal-00622399

J. Cousty, G. Bertrand, L. Najman, and M. Couprie, Watershed cuts, 7th international symposium on mathematical morphology (ISMM '07, pp.301-312, 2007.
DOI : 10.1007/978-3-540-79126-3_39

URL : https://hal.archives-ouvertes.fr/hal-00622036

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.311362-1374, 2009.
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

A. Criminisi, T. Sharp, and A. Blake, GeoS: Geodesic Image Segmentation, Computer Vision ? ECCV'08, pp.99-112, 2008.
DOI : 10.1007/978-3-540-88682-2_9

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.159.4329

O. Duchenne, J. Audibert, R. Keriven, J. Ponce, and F. Ségonne, Segmentation by transduction, 2008 IEEE Conference on Computer Vision and Pattern Recognition, 2008.
DOI : 10.1109/CVPR.2008.4587419

URL : https://hal.archives-ouvertes.fr/hal-00834989

A. X. Falcão, R. A. Lotufo, and G. Araujo, 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

A. X. Falcão, J. K. Udupa, S. Samarasekera, S. Sharma, B. H. Elliot 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 . De-alencar, 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

D. Geman and G. Reynolds, Constrained restoration and the recovery of discontinuities, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.3, pp.367-383, 1992.
DOI : 10.1109/34.120331

S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Transactions on PAMI, vol.6, issue.6 2, pp.721-741, 1984.

S. Geman and D. Mcclure, Statistical methods for tomographic image reconstruction, Proc. 46th Sess, pp.4-21, 1987.

T. Géraud, H. Talbot, and M. Van-droogenbroeck, Algorithms for Mathematical Morphology, Mathematical morphology: from theory to applications, pp.345-373
DOI : 10.1002/9781118600788.ch12

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

L. Grady, A Lattice-Preserving Multigrid Method for Solving the Inhomogeneous Poisson Equations Used in Image Analysis, Computer Vision ? ECCV'08, pp.252-264, 2008.
DOI : 10.1007/978-3-540-88688-4_19

L. Grady, Minimal Surfaces Extend Shortest Path Segmentation Methods to 3D, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.32, issue.2, pp.321-334, 2002.
DOI : 10.1109/TPAMI.2008.289

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

L. Grady and A. K. Sinop, Fast approximate Random Walker segmentation using eigenvector precomputation, 2008 IEEE Conference on Computer Vision and Pattern Recognition, 2008.
DOI : 10.1109/CVPR.2008.4587487

D. M. Greig, B. T. Porteous, and A. H. Seheult, Exact maximum a posteriori estimation for binary images, Journal of the Royal Statistical Society, vol.51, issue.4, pp.271-279, 1989.

L. Guigues, J. P. Cocquerez, and H. L. 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

P. Guillataud, Contribution l'analyse dendroniques des images, 1992.

P. Hanusse and P. Guillataud, Sémantique des images par analyse dendronique, 8` eme Reconnaissance des Formes et Intelligence Artificielle (RFIA), pp.577-588, 1992.

J. P. Kaufhold, Energy Formulations of Medical Image Segmentations, 2000.

P. Kohli, M. P. Kumar, and P. Torr, P3 & Beyond: Solving Energies with Higher Order Cliques, 2007 IEEE Conference on Computer Vision and Pattern Recognition, 2007.
DOI : 10.1109/CVPR.2007.383204

P. Kohli, L. Ladicky, and P. Torr, Robust higher order potentials for enforcing label consistency, 2008 IEEE Conference on Computer Vision and Pattern Recognition, 2008.
DOI : 10.1109/CVPR.2008.4587417

K. Krajsek and H. Scharr, Diffusion filtering without parameter tuning: Models and inference tools, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2010.
DOI : 10.1109/CVPR.2010.5539959

V. S. Lempitsky, S. Roth, and C. Rother, FusionFlow: Discrete-continuous optimization for optical flow estimation, 2008 IEEE Conference on Computer Vision and Pattern Recognition, p.14, 2008.
DOI : 10.1109/CVPR.2008.4587751

A. Levin, D. Lischinski, and Y. Weiss, A Closed-Form Solution to Natural Image Matting, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.30, issue.2, pp.228-242, 2008.
DOI : 10.1109/TPAMI.2007.1177

E. Levitan and G. Herman, A Maximum a Posteriori Probability Expectation Maximization Algorithm for Image Reconstruction in Emission Tomography, IEEE Transactions on Medical Imaging, vol.6, issue.3, pp.185-192, 1987.
DOI : 10.1109/TMI.1987.4307826

Y. Li and D. P. Huttenlocher, Learning for Optical Flow Using Stochastic Optimization, Proc. of ECCV, pp.379-391, 2008.
DOI : 10.1007/978-3-540-88688-4_28

Y. Li, J. Sun, C. Tang, and H. Shum, Lazy snapping, SIGGRAPH, pp.303-308, 2004.
DOI : 10.1145/1186562.1015719

P. Matas, E. Dokládalova, M. Akil, T. Grandpierre, L. Najman et al., Parallel Algorithm for Concurrent Computation of Connected Component Tree, Advanced Concepts for Intelligent Vision Systems (ACIVS'08), pp.230-241, 2008.
DOI : 10.1007/3-540-44438-6_32

URL : https://hal.archives-ouvertes.fr/hal-00622406

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 L. Najman, Segmentation, Minimum Spanning Tree and Hierarchies, Mathematical morphology: from theory to applications, chapter 9, pp.255-287, 2010.
DOI : 10.1002/9781118600788.ch9

URL : https://hal.archives-ouvertes.fr/hal-00622502

H. S. Michael, M. J. Black, and H. W. Haussecker, Image statistics and anisotropic diffusion, Proc. of ICCV, pp.840-847, 2003.

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

L. Najman, Ultrametric Watersheds, 9th international symposium on mathematical morphology (ISMM'09), pp.181-192, 2009.
DOI : 10.1007/s10851-005-4892-4

URL : https://hal.archives-ouvertes.fr/hal-00622405

L. Najman, Ultrametric Watersheds, p.14, 1887.
DOI : 10.1007/s10851-005-4892-4

URL : https://hal.archives-ouvertes.fr/hal-00622405

L. Najman and M. Couprie, Building the Component Tree in Quasi-Linear Time, IEEE Transactions on Image Processing, vol.15, issue.11, pp.3531-3539, 2006.
DOI : 10.1109/TIP.2006.877518

URL : https://hal.archives-ouvertes.fr/hal-00622110

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

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, 1996.
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

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

J. Roerdink and A. Meijster, The watershed transform: Definitions, algorithms, and parallellization strategies, Fund. Informaticae, vol.41, issue.2, pp.187-228, 2000.

C. Rother, V. Kolmogorov, and A. Blake, GrabCut " ? Interactive foreground extraction using iterated graph cuts, SIGGRAPH, pp.309-314, 2004.

P. Salembier, A. Oliveras, and L. Garrido, Antiextensive connected operators for image and sequence processing, IEEE Transactions on Image Processing, vol.7, issue.4, pp.555-570, 1998.
DOI : 10.1109/83.663500

K. G. Samuel and M. F. Tappen, Learning optimized MAP estimates in continuously-valued MRF models, 2009 IEEE Conference on Computer Vision and Pattern Recognition, 2009.
DOI : 10.1109/CVPR.2009.5206774

U. Schmidt, Q. Gao, and S. Roth, A generative perspective on MRFs in low-level vision, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2010.
DOI : 10.1109/CVPR.2010.5539844

R. Shen, I. Cheng, X. Li, and A. Basu, Stereo matching using random walks, 2008 19th International Conference on Pattern Recognition, p.14, 2008.
DOI : 10.1109/ICPR.2008.4761512

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.5427

J. Shi and J. Malik, Normalized cuts and image segmentation, IEEE Transactions on PAMI, vol.22, issue.8 2, pp.888-905, 2000.

D. Singaraju, L. Grady, A. K. Sinop, and R. Vidal, Continuous valued MRFs for image segmentation, Advances in Markov Random Fields for Vision and Image Processing, 2010.

D. Singaraju, L. Grady, and R. Vidal, P-brush: Continuous valued MRFs with normed pairwise distributions for image segmentation, 2009 IEEE Conference on Computer Vision and Pattern Recognition, 2003.
DOI : 10.1109/CVPR.2009.5206669

A. K. Sinop and L. Grady, A Seeded Image Segmentation Framework Unifying Graph Cuts And Random Walker Which Yields A New Algorithm, 2007 IEEE 11th International Conference on Computer Vision, p.14, 2007.
DOI : 10.1109/ICCV.2007.4408927

G. Strang, 1 and l ? approximation of vector fields in the plane In Nonlinear Partial Differential Equations in Applied Science, Proceedings of the U.S. -Japan Seminar, pp.273-288, 1982.

R. Szeliski, R. Zabih, D. Scharstein, O. Veksler, V. Kolmogorov et al., A Comparative Study of Energy Minimization Methods for Markov Random Fields with Smoothness-Based Priors, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.30, issue.6, pp.1068-1080, 2008.
DOI : 10.1109/TPAMI.2007.70844

M. F. Tappen, C. Liu, E. H. Adelson, and W. T. Freeman, Learning Gaussian Conditional Random Fields for Low-Level Vision, 2007 IEEE Conference on Computer Vision and Pattern Recognition, 2007.
DOI : 10.1109/CVPR.2007.382979

R. Tarjan, Efficiency of a Good But Not Linear Set Union Algorithm, Journal of the ACM, vol.22, issue.2, pp.215-225, 1975.
DOI : 10.1145/321879.321884

M. Unger, T. Pock, D. Cremers, and H. Bischof, TVSeg - Interactive Total Variation Based Image Segmentation, Procedings of the British Machine Vision Conference 2008, 2008.
DOI : 10.5244/C.22.40

S. Vicente, V. Kolmogorov, and C. Rother, Graph cut based image segmentation with connectivity priors, 2008 IEEE Conference on Computer Vision and Pattern Recognition, 2008.
DOI : 10.1109/CVPR.2008.4587440

L. Vincent, Morphological grayscale reconstruction in image analysis: applications and efficient algorithms, IEEE Transactions on Image Processing, vol.2, issue.2, pp.176-201, 1993.
DOI : 10.1109/83.217222

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

M. H. Wilkinson, H. Gao, W. H. Hesselink, J. Jonker, and A. Meijster, Concurrent Computation of Attribute Filters on Shared Memory Parallel Machines, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.30, issue.10, pp.1800-1813, 2008.
DOI : 10.1109/TPAMI.2007.70836