Algorithms for the Topological Watershed

The watershed transformation is an efficient tool for segmenting grayscale images. An original approach to the watershed [1,9] consists in modifying the original image by lowering some points while preserving some topological properties, namely, the connectivity of each lower cross-section. Such a transformation (and its result) is called a W-thinning, a topological watershed being an “ultimate” W-thinning. In this paper, we study algorithms to compute topological watersheds. We propose and prove a characterization of the points that can be lowered during a W-thinning, which may be checked locally and efficiently implemented thanks to a data structure called component tree. We introduce the notion of M-watershed of an image F, which is a W-thinning of F in which the minima cannot be extended anymore without changing the connectivity of the lower cross-sections. The set of points in an M-watershed of F which do not belong to any regional minimum corresponds to a binary watershed of...

• Type: Conference
• Year: 2005
• Where: DGCI
• Authors: Michel Couprie, Laurent Najman, Gilles Bertrand
• Keywords: DGCI 2005, Lower Cross-sections, Topological Watersheds, Watershed Transformation