Playing with Kruskal: algorithms for flat and hierarchical watershed cuts

2026-10-07

AI Summary

This study addresses the fragmented conceptualization and inconsistent implementation standards of existing watershed segmentation algorithms, which hinder research reproducibility and application efficiency. To overcome these limitations, this work presents the first compact integration of diverse watershed theories and algorithms. By leveraging weighted graphs, Kruskal-based minimum spanning trees, and connected component analysis, it constructs an end-to-end segmentation pipeline encompassing both supervised and unsupervised paradigms alongside multiple seed computation variants. The primary contribution lies in establishing a clear, unified implementation standard that serves as a highly reproducible framework guide for watershed segmentation. Ultimately, this systematic consolidation significantly enhances both the theoretical understanding and the engineering implementation efficiency of watershed algorithms within the field.

Abstract

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.

Problem

• watershed segmentation
• edge-weighted graphs
• hierarchical watershed
• minimum spanning tree
• image segmentation

Innovation

• Watershed segmentation
• Hierarchical watershed
• Minimum Spanning Tree
• End-to-end pipeline
• Edge-weighted graphs