Algorithms for the topological watershed

Authors:
Michel Couprie;Laurent Najman;Gilles Bertrand
Affiliations:
Laboratoire A2SI, Groupe ESIEE, IGM, Unité Mixte de Recherche CNRS-UMLV-ESIEE UMR 8049, Noisy-le-Grand, France;Laboratoire A2SI, Groupe ESIEE, IGM, Unité Mixte de Recherche CNRS-UMLV-ESIEE UMR 8049, Noisy-le-Grand, France;Laboratoire A2SI, Groupe ESIEE, IGM, Unité Mixte de Recherche CNRS-UMLV-ESIEE UMR 8049, Noisy-le-Grand, France
Venue:
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Year:
2005

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Abstract

The watershed transformation is an efficient tool for segmenting grayscale images. An original approach to the watershed [1,4] consists in modifying the original image by lowering some points until stability while preserving some topological properties, namely, the connectivity of each lower cross-section. Such a transformation (and its result) is called a topological watershed. In this paper, we propose quasi-linear algorithms for computing topological watersheds. These algorithms are proved to give correct results with respect to the definitions, and their time complexity is analyzed.