Abstract
The 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.
This research is partly funded by the Bézout Labex, funded by ANR, reference ANR-10-LABX-58.
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The proofs of the lemmas, properties and theorem presented in this article can be found in [10].
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Santana Maia, D., Cousty, J., Najman, L., Perret, B. (2019). Watersheding Hierarchies. In: Burgeth, B., Kleefeld, A., Naegel, B., Passat, N., Perret, B. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2019. Lecture Notes in Computer Science(), vol 11564. Springer, Cham. https://doi.org/10.1007/978-3-030-20867-7_10
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