Watershed Cuts: Thinnings, Shortest Path Forests, and Topological Watersheds

Authors:
Jean Cousty;Gilles Bertrand;Laurent Najman;Michel Couprie
Affiliations:
Université Paris-Est, Equipe A3SI, ESIEE, Paris and INRIA Sophia Antipolis, France;Université Paris-Est, Equipe A3SI, ESIEE, Paris;Université Paris-Est, Equipe A3SI, ESIEE, Paris;Université Paris-Est, Equipe A3SI, ESIEE, Paris
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
2010

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Abstract

We recently introduced 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 several morphological region merging methods are (implicitly) based. We also establish the links and differences between watershed cuts, minimum spanning forests, shortest path forests, and topological watersheds. Finally, we present illustrations of the proposed framework to the segmentation of artwork surfaces and diffusion tensor images.