On the Probabilities of Hierarchical Watersheds

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11564)


Hierarchical watersheds are obtained by iteratively merging the regions of a watershed segmentation. In the watershed segmentation of an image, each region contains exactly one (local) minimum of the original image. Therefore, the construction of a hierarchical watershed of any image I can be guided by a total order \(\prec \) on the set of minima of I. The regions that contain the least minima according to the order \(\prec \) are the first regions to be merged in the hierarchy. In fact, given any image I, for any hierarchical watershed \(\mathcal {H}\) of I, there exists more than one total order on the set of minima of I which could be used to obtain \(\mathcal {H}.\) In this article, we define the probability of a hierarchical watershed \(\mathcal {H}\) as the probability of \(\mathcal {H}\) to be the hierarchical watershed of I for an arbitrary total order on the set of minima of I. We introduce an efficient method to obtain the probability of hierarchical watersheds and we provide a characterization of the most probable hierarchical watersheds.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Université Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEMNoisy-le-GrandFrance

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