Abstract
The watershed is an efficient and versatile segmentation tool, as it partitions the images into disjoint catchment basins. We study the watershed on node or edge weighted graphs. We do not aim at constructing a partition of the nodes but consider the catchment zones, i.e., the attraction zones of a drop of water. Often, such zones largely overlap. In a first part, we show how to derive from a node or edge weighted graph a flooding graph with the same trajectories of a drop of water, whether one considers its node weights alone or its edge weights alone. In a second part we show how to reduce the number of possible trajectories of a drop of water in order to generate watershed partitions.
Highlights
Catchment basins and watershed lines are topographical notions
Criterion 4 A node p belongs to a regional minimum if no ‡ooding path with origin p leads to a lower node
Criterion 8 A node p belongs to a regional minimum if no ‡ooding path with origin p contains an edge which is lower than the edges inside the minimum
Summary
Catchment basins and watershed lines are topographical notions. A catchment basin is the attraction domain of a regional minimum: a drop of water falling everywhere within this domain glides towards this minimum. Shortest paths algorithm construct the zone of in‡uence of the regional minima for various distance function associated to the topography ([23, 8, 10, 13, 19]) Another class of algorithms are based on thinnings : the topographic surface is progressively lowered in such a way that the regional minima are expanded without merging with each other (S.Beucher et al [3] for geodesic binary thinnings, G.Bertrand [7] for grey tone thinnings based on W destructible points). All these approaches simultaneously create catchment basins by extending the minima, while creating disjoint basins. An early version of this work may be found in [17] and a method for implementing graph algorithms on images in [16]
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