Playing with Kruskal: algorithms for morphological trees in edge-weighted graphs

Laurent Najman (1) , Jean Cousty (1) , Benjamin Perret (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

The goal of this paper is to provide linear or quasi-linear algorithms for producing some of the various trees used in mathematical morphology, in particular the trees corresponding to hierarchies of watershed cuts and hierarchies of constrained connectivity. A specific binary tree, corresponding to an ordered version of the edges of the minimum spanning tree, is the key structure in this study, and is computed thanks to variations around Kruskal algorithm for minimum spanning tree.

Mots clés: Algorithms; Morphological trees; constrained connectivity; watershed cuts; hierarchies

Domaines: Algorithme et structure de données [cs.DS]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Laurent Najman, Jean Cousty, Benjamin Perret. Playing with Kruskal: algorithms for morphological trees in edge-weighted graphs. International Symposium on Mathematical Morphology, May 2013, Uppsala, Sweden. pp.135-146. ⟨hal-00798621⟩