HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

The steepest watershed: from graphs to images

Abstract : The watershed is a powerful tool for segmenting objects whose contours appear as crest lines on a gradient image. The watershed transform associates to a topographic surface a partition into catchment basins, defined as attraction zones of a drop of water falling on the relief and following a line of steepest descent. Unfortunately, catchment basins may overlap and do not form a partition. Moreover, current watershed algorithms, being shortsighted, do not correctly estimate the steepness of the downwards trajectories and overestimate the overlapping zones of catchment basins. An arbitrary division of these zones between adjacent catchment basin results in a poor localization of the contours. We propose an algorithm without myopia, which considers the total length of a trajectory for estimating its steepness. We first consider topographic surfaces defined on node weighted graphs. The graphs are pruned in order to eliminate all downwards trajectories which are not the steepest. An iterative algorithm with simple neighborhood operations performs the pruning and constructs the catchment basins. The algorithm is then adapted to gray tone images. The graph structure itself is encoded as an image thanks to the fixed neighborhood structure of grids. A pair of adaptative erosions and dilations prune the graph and extend the catchment basins. As a result one obtains a precise detection of the catchment basins and a graph of the steepest trajectories. A last iterative algorithm allows to follow selected downwards trajectories in order to detect particular structures such as rivers or thalweg lines of the topographic surface.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Contributor : Fernand Meyer Connect in order to contact the contributor
Submitted on : Wednesday, April 11, 2012 - 10:55:33 AM
Last modification on : Wednesday, November 17, 2021 - 12:27:12 PM

Links full text


  • HAL Id : hal-00686759, version 1
  • ARXIV : 1204.2134


Fernand Meyer. The steepest watershed: from graphs to images. 2012. ⟨hal-00686759⟩



Record views