CVMar 7, 2013
Watersheds on edge or node weighted graphs "par l'exemple"
arXiv:1303.1829v12 citations
Originality Synthesis-oriented
AI Analysis
This clarifies foundational concepts in graph theory and image processing, but it is incremental as it builds on existing watershed definitions.
The paper demonstrates that watersheds defined on edge-weighted and node-weighted graphs are equivalent, showing that for any edge-weighted graph there exists a node-weighted graph with identical minima and catchment basins, and vice versa.
Watersheds have been defined both for node and edge weighted graphs. We show that they are identical: for each edge (resp.\ node) weighted graph exists a node (resp. edge) weighted graph with the same minima and catchment basin.