Skip to Main content Skip to Navigation
New interface
Book sections

Discrete region merging and watersheds

Abstract : This paper summarizes some results of the authors concerning watershed divides and their use in region merging schemes. The first aspect deals with properties of watershed divides that can be used in particular for hierarchical region merging schemes. We introduce the mosaic to retrieve the altitude of points along the divide set. A desirable property is that, when two minima are separated by a crest in the original image, they are still separated by a crest of the same altitude in the mosaic. Our main result states that this is the case if and only if the mosaic is obtained through a topological thinning. The second aspect is closely related to the thinness of watershed divides. We present fusion graphs, a class of graphs in which any region can be always merged without any problem. This class is equivalent to the one in which watershed divides are thin. Topological thinnings do not always produce thin divides, even on fusion graphs. We also present the class of perfect fusion graphs, in which any pair of neighbouring regions can be merged through their common neighborhood. An important theorem states that the divides of any ultimate topological thinning are thin on any perfect fusion graph.
Document type :
Book sections
Complete list of metadata

Cited literature [22 references]  Display  Hide  Download
Contributor : Laurent Najman Connect in order to contact the contributor
Submitted on : Wednesday, January 11, 2017 - 1:31:17 PM
Last modification on : Thursday, September 29, 2022 - 2:21:15 PM
Long-term archiving on: : Friday, April 14, 2017 - 12:49:44 PM


Files produced by the author(s)


  • HAL Id : hal-00622458, version 1


Laurent Najman, Gilles Bertrand, Michel Couprie, Jean Cousty. Discrete region merging and watersheds. Passare Mikael. Complex Analysis and Digital Geometry. Proceedings from the Kiselmanfest, 2006, 86, Uppsala University, pp.199-222, 2009, Acta Universitatis Upsaliensis, 978-91-554-7672-4. ⟨hal-00622458⟩



Record views


Files downloads