Characterization of Graph-Based Hierarchical Watersheds: Theory and Algorithms

Abstract

Watershed is a well established clustering and segmentation method. In this article, we aim to achieve a better theoretical understanding of the hierarchical version of the watershed operator. More precisely, we propose a characterization of hierarchical watersheds in the framework of edge-weighted graphs. The proposed characterization leads to an efficient algorithm to recognize hierarchical watersheds.

A Topological Tree of Shapes

“…These partitions can also be total. This is the case of the binary partition tree and its variants [23,27,19] and the hierarchical watershed [13,26]. Other hierarchical structures are directed acyclic graphs (DAGs), e.g.…”