On morphological hierarchical representations for image processing and spatial data clustering

TL;DR

This paper surveys hierarchical image representations in mathematical morphology, focusing on constrained connectivity and ultrametric watersheds, and demonstrates their application in remote sensing data clustering.

Contribution

It details recent paradigms for hierarchical image representation using constrained connectivity and ultrametric watersheds within mathematical morphology, highlighting practical applications.

Findings

Ultrametric watersheds provide a generic scheme for hierarchical clustering.

Constrained connectivity allows for tailored hierarchical segmentation.

Applications in remote sensing demonstrate practical utility.

Abstract

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.