Algorithms for the topological watershed

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.