Ultrametric watersheds: a bijection theorem for hierarchical edge-segmentation

Abstract. We study hierachical segmentation in the framework of edgeweighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical edgesegmentations. We end this paper by showing how the proposed framework allows to see constrained connectivity as a classical watershed-based morphological scheme, which provides an efficient algorithm to compute the whole hierarchy.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Laurent Najman
• Keywords: CORR 2010, Education, Hierachical Segmentation, Topological Watersheds, Ultrametric Watersheds