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Some links between min-cuts, optimal spanning forests and watersheds

Summary: Some links between min-cuts, optimal
spanning forests and watersheds
Cédric Allène1,2, Jean-Yves Audibert1, Michel Couprie2,
Jean Cousty2 and Renaud Keriven1
1 CERTIS, Ecole des Ponts, Champs-sur-Marne, France
2 Université Paris-Est, LABINFO-IGM, UMR CNRS 8049, A2SI-ESIEE, France
Abstract Dierent optimal structures: minimum cuts, minimum spanning
forests and shortest-path forests, have been used as the basis for
powerful image segmentation procedures. The well-known notion
of watershed also falls into this category. In this paper, we present
some new results about the links which exist between these dier-
ent approaches. Especially, we show that min-cuts coincide with
watersheds for some particular weight functions.
Keywords: min-cuts, spanning forests, watersheds, shortest-path forests.
Min-cuts (graph cuts) and watersheds are two popular tools for image seg-
mentation, which can both be expressed in the framework of graphs and are
well suited to computer implementations. Informally, a cut in a graph is a


Source: Audibert, Jean-Yves - Département d'Informatique, École Normale Supérieure


Collections: Computer Technologies and Information Sciences