Watersheding hierarchies

International audienceThe computation of hierarchies of partitions from the watershed transform is a well-established segmentation technique in mathematical morphology. In this article, we introduce the watersheding operator , which maps any hierarchy into a hierarchical watershed. The hierarchical watersheds are the only hierarchies that remain unchanged under the action of this operator. After defining the watersheding operator , we present its main properties, namely its relation with extinction values and sequences of minima of weighted graphs. Finally, we discuss practical applications of the watersheding operator