G. Matheron, Random sets and integral geometry, 1975.

J. Serra, Image analysis and mathematical morphology, 1982.

J. Serra and E. , Image analysis and mathematical morphology, Theoretical advances, 1988.

L. Vincent, Graphs and mathematical morphology, Signal Processing, vol.16, issue.4, pp.365-388, 1989.
DOI : 10.1016/0165-1684(89)90031-5

H. Heijmans and L. Vincent, Graph morphology in image analysis, " in Mathematical morphology in image processing, pp.171-203, 1993.

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

F. Meyer and R. Lerallut, Morphological Operators for Flooding, Leveling and Filtering Images Using Graphs, Graph-based Representations in Pattern Recognition (GbRPR'07), pp.158-167, 2007.
DOI : 10.1007/978-3-540-72903-7_15

F. Meyer and J. Angulo, Micro-viscous morphological operators, Mathematical Morphology and its Application to Signal and Image Processing, pp.165-176, 2007.

V. Ta, A. Elmoataz, and O. Lézoray, Partial Difference Equations over Graphs: Morphological Processing of Arbitrary Discrete Data, Computer Vision -ECCV 2008, ser. Lecture Notes in Computer Science, pp.668-680, 2008.
DOI : 10.1007/978-3-540-88690-7_50
URL : https://hal.archives-ouvertes.fr/hal-00333390

J. Cousty, L. Najman, and J. Serra, Some Morphological Operators in Graph Spaces, International Symposium on Mathematical Morphology 2009, ser, pp.149-160, 2009.
DOI : 10.1016/j.patrec.2008.03.019
URL : https://hal.archives-ouvertes.fr/hal-00622403

I. Bloch and A. Bretto, Mathematical morphology on hypergraphs: Preliminary definitions and results, " in Discrete Geometry for Computer Imagery, ser. Lecture Notes in Computer Science, I. Debled-Rennesson, pp.429-440, 2011.

F. Dias, J. Cousty, and L. Najman, Some morphological operators on simplicial complexes spaces, DGCI 2011, ser, pp.441-452, 2011.

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, 2009.
DOI : 10.1109/TPAMI.2008.173
URL : https://hal.archives-ouvertes.fr/hal-00622410

J. Cousty and L. Najman, Incremental Algorithm for Hierarchical Minimum Spanning Forests and Saliency of Watershed Cuts, ISMM 2011, ser, pp.272-283, 2011.
DOI : 10.1007/978-3-642-21569-8_24
URL : https://hal.archives-ouvertes.fr/hal-00622505

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

P. Soille, Morphological Image Analysis, 1999.

M. Nesetril and N. , Otakar Boruvka on Minimum Spanning Tree problem: Translation of both the 1926 papers, comments, history, DMATH: Discrete Mathematics, vol.233, 2001.

G. Choquet, ´ etude de certains réseaux de routes, Comptes-rendus de l'Acad. des Sciences, pp.310-313, 1938.

C. Zahn, Graph-theoretical methods for detecting and descibing Gestalt clusters, IEEE Transactions on Computers, vol.20, issue.1, pp.99-112, 1971.

O. J. Morris, M. D. Lee, and A. G. Constantinides, Graph theory for image analysis: an approach based on the shortest spanning tree, IEE Proceedings F Communications, Radar and Signal Processing, vol.133, issue.2, pp.146-152, 1986.
DOI : 10.1049/ip-f-1.1986.0025

F. Meyer, Minimum Spanning Forests for Morphological Segmentation, Procs. of the second international conference on Mathematical Morphology and its Applications to Image Processing, pp.77-84, 1994.
DOI : 10.1007/978-94-011-1040-2_11

P. Felzenszwalb and D. Huttenlocher, Efficient Graph-Based Image Segmentation, International Journal of Computer Vision, vol.59, issue.2, pp.167-181, 2004.
DOI : 10.1023/B:VISI.0000022288.19776.77

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

G. Birkhoff, Lattice Theory, ser, 1995.

C. Ronse and J. Serra, Algebric foundations of morphology, pp.35-79, 2010.

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
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.9460

C. Ronse, Set-theoretical algebraic approaches to connectivity in continuous or digital spaces, pp.41-58, 1998.

U. Braga-neto and J. Goutsias, Connectivity on Complete Lattices: New Results, Computer Vision and Image Understanding, vol.85, issue.1, pp.22-53, 2002.
DOI : 10.1006/cviu.2002.0961

G. K. Ouzounis and M. H. Wilkinson, Mask-Based Second-Generation Connectivity and Attribute Filters, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.29, issue.6, pp.990-1004, 2007.
DOI : 10.1109/TPAMI.2007.1045

R. K. Gabriel and R. R. Sokal, A New Statistical Approach to Geographic Variation Analysis, Systematic Zoology, vol.18, issue.3, pp.259-278, 1969.
DOI : 10.2307/2412323

P. Salembier, A. Oliveras, and L. Garrido, Anti-extensive connected operators for image and sequence processing, IEEE TIP, vol.7, issue.4, pp.555-570, 1998.

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

P. Salembier and L. Garrido, Binary partition tree as an efficient representation for image processing, segmentation, and information retrieval, IEEE Transactions on Image Processing, vol.9, issue.4, pp.561-576, 2000.
DOI : 10.1109/83.841934

V. Caselles and P. Monasse, Geometric Description of Images as Topographic Maps, ser. Lecture Notes in Computer Science, 1984.

P. Salembier, Connected operators based on region-tree pruning strategies, Proceedings 15th International Conference on Pattern Recognition. ICPR-2000, pp.179-198, 2010.
DOI : 10.1109/ICPR.2000.903561
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.299

J. Benzécri and L. , Analyse des données: la Taxinomie. Dunod, 1973.

B. Leclerc, Description combinatoire des ultramétriques, Mathématique et sciences humaines, vol.73, pp.5-37, 1981.

J. Gower and G. Ross, Minimum Spanning Trees and Single Linkage Cluster Analysis, Applied Statistics, vol.18, issue.1, pp.54-64, 1969.
DOI : 10.2307/2346439

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

S. Beucher and F. Meyer, The morphological approach to segmentation: the watershed transformation, " in Mathematical morphology in image processing, ser, Optical Engineering, vol.34, pp.433-481, 1993.

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

J. B. Roerdink and A. Meijster, The watershed transform: Definitions, algorithms and parallelization strategies, Fundamenta Informaticae, vol.41, issue.12, pp.187-228, 2001.

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

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

F. Meyer, Topographic distance and watershed lines, Signal Processing, vol.38, issue.1, pp.113-125, 1994.
DOI : 10.1016/0165-1684(94)90060-4

P. Soille and C. Gratin, An Efficient Algorithm for Drainage Network Extraction on DEMs, Journal of Visual Communication and Image Representation, vol.5, issue.2, pp.181-189, 1994.
DOI : 10.1006/jvci.1994.1017

S. Philipp-foliguet, M. Jordan, L. Najman, and J. Cousty, Artwork 3D model database indexing and classification, Pattern Recognition, vol.44, issue.3, pp.588-597, 2011.
DOI : 10.1016/j.patcog.2010.09.016
URL : https://hal.archives-ouvertes.fr/hal-00538470

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

P. J. Basser, J. Mattiello, and D. Lebihan, MR diffusion tensor spectroscopy and imaging, Biophysical Journal, vol.66, issue.1, pp.259-267, 1994.
DOI : 10.1016/S0006-3495(94)80775-1
URL : https://hal.archives-ouvertes.fr/hal-00349721

V. Arsigny, P. Fillard, X. Pennec, and N. Ayache, Log-Euclidean metrics for fast and simple calculus on diffusion tensors, Magnetic Resonance in Medicine, vol.52, issue.2, pp.411-421, 2006.
DOI : 10.1002/mrm.20965
URL : https://hal.archives-ouvertes.fr/inria-00502678

J. Cousty, L. Najman, M. Couprie, S. Clément-guinaudeau, T. Goissen et al., Segmentation of 4D cardiac MRI: Automated method based on spatio-temporal watershed cuts, Image and Vision Computing, vol.28, issue.8, pp.1229-1243, 2010.
DOI : 10.1016/j.imavis.2010.01.001
URL : https://hal.archives-ouvertes.fr/hal-00622482

F. Meyer, The Dynamics of Minima and Contours, Mathematical Morphology and its Applications to Image and Signal Processing, pp.329-336, 1996.
DOI : 10.1007/978-1-4613-0469-2_38

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. Guigues, J. P. Cocquerez, and H. L. Men, Scale-sets image analysis, pp.289-317, 2006.
DOI : 10.1109/icip.2003.1246612
URL : https://hal.archives-ouvertes.fr/hal-00705364

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

F. Meyer and L. Najman, Segmentation, minimum spanning tree and hierarchies, " in Mathematical Morphology: from theory to application, pp.229-261, 2010.

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

C. Alì-ene, J. Audibert, M. Couprie, and R. Keriven, Some links between extremum spanning forests, watersheds and min-cuts, Image and Vision Computing, vol.28, issue.10, pp.1460-1471, 2010.
DOI : 10.1016/j.imavis.2009.06.017

C. Vachier and F. Meyer, Extinction value: a new measurement of persistence, IEEE Workshop on Nonlinear Signal and Image Processing, pp.254-257, 1995.

G. Bertrand, On the dynamics, Image and Vision Computing, vol.25, issue.4, pp.447-454, 2007.
DOI : 10.1016/j.imavis.2006.04.017
URL : https://hal.archives-ouvertes.fr/hal-00621988

S. Beucher, Watershed, Hierarchical Segmentation and Waterfall Algorithm, Mathematical Morphology and its Applications to Image Processing, pp.69-76, 1994.
DOI : 10.1007/978-94-011-1040-2_10

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

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, 2007.
DOI : 10.1109/ICCV.2007.4408927

G. Peyre, M. Pechaud, R. Keriven, and L. Cohen, Geodesic Methods in Computer Vision and Graphics, Foundations and Trends?? in Computer Graphics and Vision, vol.5, issue.3-4, pp.197-397, 2010.
DOI : 10.1561/0600000029
URL : https://hal.archives-ouvertes.fr/hal-00528999

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

C. Couprie, X. Bresson, L. Najman, H. Talbot, and L. Grady, Surface Reconstruction Using Power Watershed, ISMM 2011, ser, pp.381-392, 2011.
DOI : 10.1007/978-3-642-21569-8_33
URL : https://hal.archives-ouvertes.fr/hal-00622504

C. Couprie, L. Grady, L. Najman, and H. Talbot, 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

T. Goldstein, X. Bresson, and S. Osher, Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction, UCLA, Computational and Applied Mathematics Reports, 2009.
DOI : 10.1007/s10915-009-9331-z

J. Ye, X. Bresson, T. Goldstein, and S. Osher, A fast variational method for surface reconstruction from sets of scattered points, UCLA, Computational and Applied Mathematics Reports, 2010.

V. Lempitsky and Y. Boykov, Global Optimization for Shape Fitting, 2007 IEEE Conference on Computer Vision and Pattern Recognition, 2007.
DOI : 10.1109/CVPR.2007.383293

R. Levillain, T. Géraud, and L. Najman, Why and How to Design a Generic and Efficient Image Processing Framework: The Case of the Milena Library, 17th International Conference on Image Processing, pp.1941-1944, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00622480