Playing with Kruskal: algorithms for flat and hierarchical watershed cuts

In the framework of edge-weighted graphs, watersheds have proven to be linked to well-known optimization problems, as Minimum Spanning Tree, which allowed the design of efficient algorithms for computing (hierarchical) watershed segmentations. In the present article, after reviewing the literature related to watershed segmentation, we present a detailed end-to-end pipeline of algorithms to compute (hierarchical) watershed segmentations, starting from the computation of graph-based image representations, up to the computation of connected components of the final (hierarchical) segmentation. We consider the several variations of watersheds, including their supervised and unsupervised versions, and the various ways of computing seeds, to name a few. For the first time, we bring together all these watershed notions and algorithms in a compact and understandable way. We aim at providing a reference for those interested in employing and reimplementing the watershed segmentation framework for their task at hand.