On watershed cuts and thinnings

Abstract

We recently introduced the watershed cuts, a notion of watershed in edge-weighted graphs. In this paper, we propose a new thinning paradigm to compute them. More precisely, we introduce a new transformation, called border thinning, that lowers the values of edges that match a simple local configuration until idempotence and prove the equivalence between the cuts obtained by this transformation and the watershed cuts of a map. We discuss the possibility of parallel algorithms based on this transformation and give a sequential implementation that runs in linear time whatever the range of the input map. © 2008 Springer-Verlag Berlin Heidelberg.