We study the watersheds in edge-weighted graphs. We define the watershed cuts following
the intuitive idea of drops of water flowing on a topographic surface. We first establish the …

The level sets of a map are the sets of points with level above a given threshold. The connected
components of the level sets, thanks to the inclusion relation, can be organized in a tree …

We recently introduced watershed cuts, a notion of watershed in edge-weighted graphs. In
this paper, our main contribution is a thinning paradigm from which we derive three …

We propose an original approach to the watershed problem, based on topology. We
introduce a 1D topology for grayscale images, and more generally for weighted graphs. This …

Based on discrete mathematical morphology, we introduce in this paper a new watershed
framework which allows for segmenting spatio-temporal images, that we apply to medical …

We propose a new definition and an algorithm for the discrete bisector function, which is an
important tool for analyzing and filtering Euclidean skeletons. We also introduce a new …

The watershed transformation is an efficient tool for segmenting grayscale images. An original
approach to the watershed (Bertrand, Journal of Mathematical Imaging and Vision, Vol. 22…

A point of a discrete object is called simple if it can be deleted from this object without altering
topology. In this article, we present new characterizations of simple points which hold in …

The video segmentation problem consists in the identification of the boundary between
consecutive shots. The common approach to solve this problem is based on dissimilarity …

In recent work, we introduced some topological notions for grayscale images based on a
cross-section topology. In particular, the notion of destructible point, which corresponds to the …