On watershed cuts and thinnings

Authors:
Jean Cousty;Gilles Bertrand;Laurent Najman;Michel Couprie
Affiliations:
Université Paris-Est, LABINFO, IGM, UMR, CNRS, A2SI, ESIEE, France;Université Paris-Est, LABINFO, IGM, UMR, CNRS, A2SI, ESIEE, France;Université Paris-Est, LABINFO, IGM, UMR, CNRS, A2SI, ESIEE, France;Université Paris-Est, LABINFO, IGM, UMR, CNRS, A2SI, ESIEE, France
Venue:
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Year:
2008

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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.