On morphological hierarchical representations for image processing and spatial data clustering
Pierre Soille, Laurent Najman · 2010
Abstract. Hierarchical data representations in the context of classifi-cation and data clustering were put forward during the fifties. Recently, hierarchical image representations have gained renewed interest for seg-mentation 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 mathemat-ical 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 satisfied. 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.