Abstract : We recently introduced the watershed cuts, a notion of watershed in edge-weighted graphs. In this paper, our main contribution is a thinning paradigm from which we derive three algorithmic watershed cut strategies: the first one is well suited to parallel implementations, the second one leads to a flexible linear-time sequential implementation whereas the third one links the watershed cuts and the popular flooding algorithms. We state that watershed cuts preserve a notion of contrast, called connection value, on which are (implicitly) ased several morphological region merging methods. We also establish the links and differences between watershed cuts, minimum spanning forests, shortest-path forests and topological watersheds. Finally, we present illsutrations of the proposed framework to the segmentation of artwork surfaces and diffusion tensor images.