Issue No. 08 - August (2009 vol. 31)
Jean Cousty , Université Paris-Est, ESIEE, and INRIA Sophia Antipolis, France
Gilles Bertrand , Université Paris-Est, ESIEE, France
Laurent Najman , Université Paris-Est, ESIEE, France
Michel Couprie , Université Paris-Est, ESIEE, France
We study the watersheds in edge-weighted graphs. We define the watershed cuts following the intuitive idea of drops of water flowing on a topographic surface. We first establish the consistency of these watersheds: They can be equivalently defined by their "catchment basins” (through a steepest descent property) or by the "dividing lines” separating these catchment basins (through the drop of water principle). Then, we prove, through an equivalence theorem, their optimality in terms of minimum spanning forests. Afterward, we introduce a linear-time algorithm to compute them. To the best of our knowledge, similar properties are not verified in other frameworks and the proposed algorithm is the most efficient existing algorithm, both in theory and in practice. Finally, the defined concepts are illustrated in image segmentation, leading to the conclusion that the proposed approach improves, on the tested images, the quality of watershed-based segmentations.
Watershed, minimum spanning forest, minimum spanning tree, graph, mathematical morphology, image segmentation.
L. Najman, M. Couprie, G. Bertrand and J. Cousty, "Watershed Cuts: Minimum Spanning Forests and the Drop of Water Principle," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 31, no. , pp. 1362-1374, 2008.