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

J. P. Barthélemy, F. Brucker, and C. Osswald, Combinatorial optimization and hierarchical classifications

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

L. Najman, Ultrametric Watersheds, Number LNCS, vol.22, issue.2-3, pp.181-192, 2009.
DOI : 10.1007/s10851-005-4892-4

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

J. Benzécri, Analyse des données: la Taxinomie, Dunod, vol.1, 1973.

S. Johnson, Hierarchical clustering schemes, Psychometrika, vol.58, issue.4, pp.241-254, 1967.
DOI : 10.1007/BF02289588

E. Diday, Spatial classification, Discrete Applied Mathematics, vol.156, issue.8, pp.1271-1294, 2008.
DOI : 10.1016/j.dam.2007.04.031

URL : https://hal.archives-ouvertes.fr/hal-00360499

J. Serra, A Lattice Approach to Image Segmentation, Journal of Mathematical Imaging and Vision, vol.2, issue.2, pp.83-130, 2006.
DOI : 10.1007/s10851-005-3616-0

URL : https://hal.archives-ouvertes.fr/hal-00622192

C. Ronse, Partial Partitions, Partial Connections and Connective Segmentation, Journal of Mathematical Imaging and Vision, vol.25, issue.4, pp.97-105, 2008.
DOI : 10.1007/s10851-008-0090-5

T. Pavlidis, Hierarchies in structural pattern recognition, Proceedings of the IEEE, vol.67, issue.5, pp.737-744, 1979.
DOI : 10.1109/PROC.1979.11323

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

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

T. Pavlidis and . In, Structural Pattern Recognition, pp.90-123, 1977.
DOI : 10.1007/978-3-642-88304-0

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, Morphological segmentation revisited, Space, Structure and Randomness, pp.315-347, 2005.
DOI : 10.1007/0-387-29115-6_13

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

L. Najman and H. Talbot, Mathematical morphology: from theory to applications, p.9781848212152, 2010.
DOI : 10.1002/9781118600788

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

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

L. Najman, M. Couprie, and G. Bertrand, Watersheds, mosaics, and the emergence paradigm, Discrete Applied Mathematics, vol.147, issue.2-3, pp.301-324, 2005.
DOI : 10.1016/j.dam.2004.09.017

URL : https://hal.archives-ouvertes.fr/hal-00622113

J. Cousty, G. Bertrand, M. Couprie, and L. Najman, Fusion Graphs: Merging Properties and Watersheds, Journal of Mathematical Imaging and Vision, vol.147, issue.2???3, pp.87-104, 2008.
DOI : 10.1007/s10851-007-0047-0

URL : https://hal.archives-ouvertes.fr/hal-00622473

J. Cousty, L. Najman, G. Bertrand, and M. Couprie, Weighted fusion graphs: Merging properties and watersheds, Discrete Applied Mathematics, vol.156, issue.15, pp.3011-3027, 2008.
DOI : 10.1016/j.dam.2008.01.005

URL : https://hal.archives-ouvertes.fr/hal-00622473

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.31-1362, 2009.
DOI : 10.1109/TPAMI.2008.173

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

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, 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, 2010.
DOI : 10.1109/TPAMI.2010.200

R. Diestel, Graph Theory. Graduate Texts in Mathematics, 1997.

T. Kong and A. Rosenfeld, Digital Topology, Image Process, vol.48, issue.3, pp.357-393, 1989.
DOI : 10.1007/978-1-4615-1529-6_3

J. Cousty, L. Najman, and J. Serra, Some Morphological Operators in Graph Spaces, Number LNCS, vol.29, issue.10, pp.149-160, 2009.
DOI : 10.1016/j.patrec.2008.03.019

URL : https://hal.archives-ouvertes.fr/hal-00622403

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

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

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

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

M. Krasner, Espaces ultramétriques, C.R. Acad. Sci. Paris, vol.219, pp.433-435, 1944.

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

J. B. Kruskal, On the shortest spanning subtree of a graph and the traveling salesman problem, Proc. of the American Math. Soc. 7, pp.48-50, 1956.
DOI : 10.1090/S0002-9939-1956-0078686-7

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

P. Alexandroff, Diskrete Räume, Math. Sbornik, vol.2, issue.3, pp.501-518, 1937.

G. Bertrand, On critical kernels Comptes Rendus de l'Acad. des, Sciences Série Math. I, issue.345, pp.363-367, 2007.

J. Cousty, G. Bertrand, M. Couprie, and L. Najman, Collapses and Watersheds in Pseudomanifolds, Proceedings of the 13th IWCIA, pp.397-410, 2009.
DOI : 10.1007/978-3-642-10210-3_31

URL : https://hal.archives-ouvertes.fr/hal-00622419

M. Nagao, T. Matsuyama, and Y. Ikeda, Region extraction and shape analysis in aerial photographs, Computer Graphics and Image Processing, vol.10, issue.3, pp.195-223, 1979.
DOI : 10.1016/0146-664X(79)90001-7

C. Mattiussi, The finite volume, finite element, and finite difference methods as numerical methods for physical field problems, Advances in Imaging and Electron Physics, vol.113, pp.1-146, 2000.
DOI : 10.1016/S1076-5670(00)80012-9

M. Bender and M. Farach-colton, The LCA Problem Revisited, In: Latin Amer. Theor. INformatics, pp.88-94, 2000.
DOI : 10.1007/10719839_9

P. Soille and J. Grazzini, Constrained Connectivity and Transition Regions, Number LNCS, vol.42, pp.59-69, 2009.
DOI : 10.1016/j.patcog.2008.11.004

URL : https://commerce.metapress.com/content/g6h8mk8447041532/resource-secured/?target=fulltext.pdf&sid=iiot13nznlhqylrqczxwal55&sh=www.springerlink.com

J. Cousty, L. Najman, and J. Serra, Raising in watershed lattices, 2008 15th IEEE International Conference on Image Processing, pp.2196-2199, 2008.
DOI : 10.1109/ICIP.2008.4712225

URL : https://hal.archives-ouvertes.fr/hal-00622472