J. Maxwell, On Hills and Dales, Philosophical Magazine, vol.440, pp.421-427, 1870.
DOI : 10.1017/CBO9780511710377.018

C. Jordan, Nouvelles observations sur les lignes de fa??tesfa??tes et de thalweg, Comptes Rendus des Séances de l'Académie des Sciences, pp.1023-1025

H. Digabel and C. Lantuéjoul, Iterative algorithms, Proc. 2nd European Symp. Quantitative Analysis of Microstructures in Material Science, pp.85-89, 1978.

S. Beucher and C. Lantuéjoul, Use of watersheds in contour detection, Procs. of the International Workshop on Image Processing Real-Time Edge and Motion Detection/Estimation, 1979.

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

F. Meyer, Un algorithme optimal de ligne de partage des eaux, Procs. of 8` eme Congrès AFCET, pp.847-859, 1991.

L. Najman and M. Schmitt, Watershed of a continuous function, Signal Processing, vol.38, issue.1, pp.68-86, 1993.
DOI : 10.1016/0165-1684(94)90059-0
URL : https://hal.archives-ouvertes.fr/hal-00622129

F. Lemonnier, Architecturé electronique dédiée aux algorithmes rapides de segmentation basés sur la morphologie mathématique, 1996.

M. Couprie and G. Bertrand, Topological grayscale watershed transform, Procs. of SPIE Vision Geometry V, pp.136-146, 1997.

A. Meijster and J. Roerdink, A disjoint set algorithm for the watershed transform, Procs. of Eusipco : European signal processing conference, pp.1669-1672, 1998.

A. Bieniek and A. Moga, A connected component approach to the watershed segmentation, Mathematical Morphology and its Applications to Image and Signal Processing, procs. ISMM'98, pp.215-222, 1998.

S. Stoev, Rafsi -a fast watershed algorithm based on rainfalling simulation, Proceedings of 8-th International Conference on Computer Graphics, Visualization, and Interactive Digital Media, 2000.

J. Cousty, M. Couprie, L. Najman, and G. Bertrand, Weighted fusion graphs: Merging properties and watersheds, Discrete Applied Mathematics, vol.156, issue.15, 2008.
DOI : 10.1016/j.dam.2008.01.005
URL : https://hal.archives-ouvertes.fr/hal-00622473

S. Available, F. Beucher, and . Meyer, The morphological approach to segmentation: the watershed transformation, Mathematical Morphology in Image Processing, pp.443-481, 1993.

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

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

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

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

J. K. Udupa and S. Samarsekara, Fuzzy Connectedness and Object Definition: Theory, Algorithms, and Applications in Image Segmentation, Graphical Models and Image Processing, vol.58, issue.3, pp.246-261, 1996.
DOI : 10.1006/gmip.1996.0021

J. K. Udupa, P. K. Saha, and R. A. Lotufo, Relative fuzzy connectedness and object definition: theory, algorithms, and applications in image segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, issue.11, pp.1485-1500, 2002.
DOI : 10.1109/TPAMI.2002.1046162

Y. Zhuge, J. K. Udupa, and P. K. Saha, Vectorial scale-based fuzzy-connected image segmentation, Computer Vision and Image Understanding, vol.101, issue.3, pp.177-193, 2006.
DOI : 10.1016/j.cviu.2005.07.009

R. Englert and W. Kropatsch, Image structure from monotonic dual graph, AGTIVE'99, pp.297-308, 2000.

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

A. X. Falcão, J. Stolfi, R. De-alencar, and . 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

R. Lotufo and A. Falcão, The Ordered Queue and the Optimality of the Watershed Approaches, Procs. of the 5th International Symposium on Mathematical Morphology, pp.341-350, 2000.
DOI : 10.1007/0-306-47025-X_37

J. Cousty, G. Bertrand, L. Najman, and M. Couprie, Watershed cuts, procs. ISMM, pp.301-312, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00622036

T. Kong and A. Rosenfeld, Digital topology: Introduction and survey, Computer Vision, Graphics, and Image Processing, vol.48, issue.3, pp.357-393, 1989.
DOI : 10.1016/0734-189X(89)90147-3

E. Dahlhaus, D. Johnson, C. Papadimitriou, P. Seymour, and M. Yannakakis, Complexity of multiway cuts, Procs. of the 24th Annual ACM Symposium on the Theory of Computing, pp.241-251, 1992.

C. Alì-ene, J. Audibert, M. Couprie, J. Cousty, and R. Keriven, Some links between min-cuts, optimal spanning forests and watersheds, procs. ISMM, pp.253-264, 2007.

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

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

J. Cousty, Lignes de partage des eaux discrètes : théorie et applicationà application`applicationà la segmentation d'images cardiaques, 2007.

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

R. L. Graham and P. Hell, On the History of the Minimum Spanning Tree Problem, IEEE Annals of the History of Computing, vol.7, issue.1, pp.43-57, 1985.
DOI : 10.1109/MAHC.1985.10011

J. Nesetril, E. Milková, and H. Nesetrilová, Otakar Bor??vka on minimum spanning tree problem Translation of both the 1926 papers, comments, history, Discrete Mathematics, vol.233, issue.1-3, pp.3-36, 2001.
DOI : 10.1016/S0012-365X(00)00224-7

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

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

M. Thorup, On RAM Priority Queues, Procs. of the 7th ACM-SIAM Symposium on Discrete Algorithms, pp.59-67, 1996.
DOI : 10.1137/S0097539795288246

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

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.sub- mitted, 2008.
DOI : 10.1109/TPAMI.2009.71
URL : https://hal.archives-ouvertes.fr/hal-00729346

M. Grimaud, New measure of contrast: dynamics, " in Image algebra and morphological image processing III, pp.292-305, 1992.

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

R. Duda and P. Hart, Pattern Classification and Scene Analysis, 1973.

R. Deriche, Using Canny's criteria to derive a recursively implemented optimal edge detector, International Journal of Computer Vision, vol.1, issue.2, pp.167-187, 1987.
DOI : 10.1007/BF00123164

P. Soille, Morphological Image Analysis, 1999.

P. K. Saha, J. K. Udupa, and D. Odhner, Scale-Based Fuzzy Connected Image Segmentation: Theory, Algorithms, and Validation, Computer Vision and Image Understanding, vol.77, issue.2, pp.145-174, 2000.
DOI : 10.1006/cviu.1999.0813

F. Meyer and L. Najman, Morphologie mathématique 1 : approches déterministes, ser. Traité IC2, série signal et image, ch. Segmentation, arbre de poids minimum et hiérarchies, pp.201-232, 2008.

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

J. Cousty, G. Bertrand, L. Najman, and M. Couprie, On Watershed Cuts and Thinnings, Discrete Geometry for Computer Imagery, pp.434-445, 2008.
DOI : 10.1007/978-3-540-79126-3_39
URL : https://hal.archives-ouvertes.fr/hal-00622037

J. Serra, Image Analysis and Mathematical Morphology, II: Theoretical Advances, 1988.

J. Serra and L. Vincent, An overview of morphological filtering, Circuits Systems Signal Process, vol.11, issue.1, pp.48-107, 1992.

E. 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

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

J. Cousty, L. Najman, G. Bertrand, and M. Couprie, Minimum spanning tree by watershed

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

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