Characterization of graph-based hierarchical watersheds: theory and algorithms

Deise Santana Maia (1) , Jean Cousty (1) , Laurent Najman (1) , Benjamin Perret (2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection

We propose a characterization of hierarchical watersheds built in the framework of edge-weighted graphs. Based on the notion of binary partition hierarchy by altitude ordering, we provide sufficient and necessary conditions for a hierarchy to be a hierarchical watershed. Those conditions are further used to design an efficient algorithm to recognize hierarchical watersheds. Furthermore, as an immediate application of our theoretical results, we present experiments with the combinations of hierarchical watersheds studied in [15]. Namely, we test if combinations of hierarchical watersheds are hierarchical watersheds themselves.

Domaines: Traitement des images [eess.IV]

Deise Santana Maia, Jean Cousty, Laurent Najman, Benjamin Perret. Characterization of graph-based hierarchical watersheds: theory and algorithms. 2019. ⟨hal-02280023v1⟩