Watersheds on weighted graphs

Abstract : The watershed is an efficient and versatile segmentation tool, as it partitions the images into disjoint catchment basins. We study the watershed on node or edge weighted graphs. We do not aim at constructing a partition of the nodes but consider the catchment zones, i.e. the attraction zone of a drop of water. Often, such zones largely overlap. In a first part we show how to derive from a node or edge weighted graph a ooding graph with the same trajectories of a drop of water, whether one considers its node weights alone or its edge weights alone. In a second part we show how to reduce the number of possible trajectories of a drop of water in order to generate watershed partitions. This is the long version, with proofs, of a paper published with the same title "Watersheds on weighted graphs" in Pattern Recognition Letters, Volume 47, October, 2014.
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Pattern Recognition Letters, Elsevier, 2014, 47, pp.72-79. 〈10.1016/j.patrec.2014.02.018〉
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Fernand Meyer. Watersheds on weighted graphs. Pattern Recognition Letters, Elsevier, 2014, 47, pp.72-79. 〈10.1016/j.patrec.2014.02.018〉. 〈hal-01111752〉

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