On morphological hierarchical representations for image processing and spatial data clustering

Pierre Soille (1) , Laurent Najman (2)

1 IPSC - JRC Institute for the Protection and Security of the Citizen [Ispra]
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing.

Domaines: Mathématique discrète [cs.DM]; Algorithme et structure de données [cs.DS]; Traitement des images [eess.IV]

Pierre Soille, Laurent Najman. On morphological hierarchical representations for image processing and spatial data clustering. Workshop on APPLICATIONS OF DISCRETE GEOMETRY AND MATHEMATICAL MORPHOLOGY, Aug 2010, Istanbul, Turkey. pp.43-67, ⟨10.1007/978-3-642-32313-3_4⟩. ⟨hal-00733251⟩