Abstract
Image segmentation in mathematical morphology is essentially based on one method: the watershed of a gradient image from a set of markers. We show that this watershed can be obtained from the neighbourhood graph of the initial image. The result of the segmentation is then a minimum spanning forest of the neighbourhood graph. Powerful interactive and very fast segmentation methods are derived
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References
Beucher S., Lantuéjoul C., Use of watersheds in contour detection, Int. Workshop on Image Processing, CCETT/IRISA, Rennes, France, Sept. 79.
Beucher S., Segmentation d’images et Morphologie Mathématique, Thèse Ecole des Mines de Paris, 1990
Grimaud M. La géodésie numérique en Morphologie Mathématique, Thèse de l’Ecole des Mines de Paris, décembre 1990
Gondran M., Minoux M., Graphes et algorithmes, Eyrolles, Paris, 1979, chapitre 4: Arbres et arborescences.
Hanusse P., Guillataud P., Sémantique des images par analyse dendronique, Actes du 8ème Congres AFCET, Lyon-Villeurbanne, France, 1991, pp. 577–598.
Hu T.C., The maximum capacity route problem, Operations Research 9, 1961, pp. 898–900.
Kruskal J.B., On the shortest spanning subtree of a graph and the traveling salesman problem, Proc. Am. Math. Soc., 71, 1956, pp. 48–50.
Meyer F., Un algorithme optimal de ligne de partage des eaux, Actes du 8ème Congres AFCET, Lyon-Villeurbanne, France, 1991, pp. 847–859.
Meyer F., Beucher S., Morphological segmentation, JVCIR, Vol.11, N1, pp. 21–46, 1990.
Meyer F., Integrals, gradients and watershed lines, in “Mathematical Morphology and its applications to Signal Processing”, Symposium held in Barcelona, May 1993, pp. 70–75
Meyer F., Arbre des minima et dynamique, Note interne CMM, juillet 1993.
Najman L. and Schmitt M., Definition and some properties of the watershed of a continuous function, in “Mathematical Morphology and its applications to Signal Processing”, Symposium held in Barcelona, May 1993, pp. 75–81
Prim R.C., Shortest connection networks and some generalizations, Bell Syst. Techn. J., 36, 1957, p. 1389.
Vincent L., Graphs and Mathematical Morphology, Signal Processing, Vol. 16, No. 4, April 1989, pp. 365–389.
Yao A.C.C., An O(IEI log log IVI)algorithm for finding minimum spanning trees, Info. Processing Letters, 4., 1975, pp. 21–25.
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© 1994 Springer Science+Business Media Dordrecht
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Meyer, F. (1994). Minimum Spanning Forests for Morphological Segmentation. In: Serra, J., Soille, P. (eds) Mathematical Morphology and Its Applications to Image Processing. Computational Imaging and Vision, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1040-2_11
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DOI: https://doi.org/10.1007/978-94-011-1040-2_11
Publisher Name: Springer, Dordrecht
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