Morphology on graphs and minimum spanning trees

Fernand Meyer (1) , Jean Stawiaski (1)

1 CMM - Centre de Morphologie Mathématique

This paper revisits the construction of watershed and waterfall hierarchies through a thorough analysis of Boruvka's algorithms for constructing minimum spanning trees of edge weighted graphs. In the case where the watershed of a node weighted graph is to be constructed, we propose a distribution of weights on the edges, so that the waterfall extraction on the edge weighted graph becomes equivalent with the watershed extraction on the node weighted graph.

Mots clés: Adjunctions on graphs; Edge-weighted graph; Minimum spanning tree; Minimum spanning trees; Waterfall; Watershed extraction; Weighted graph; Edge detection; Image processing; Imaging systems; Landforms; Mathematical morphology; Watersheds; Graph theory

Domaines: Mathématiques [math]; Mathématiques appliquées

Fernand Meyer, Jean Stawiaski. Morphology on graphs and minimum spanning trees. 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing, ISMM 2009, Aug 2009, Groningen, Netherlands. pp.161-170, ⟨10.1007/978-3-642-03613-2_15⟩. ⟨hal-00834386⟩