339 citations · 830 across the 27 of their papers we have counts for
6 papers · 1 filter
Discrete Morse Functions and Watersheds
Gilles Bertrand, Nicolas Boutry, Laurent Najman
Any watershed, when defined on a stack on a normal pseudomanifold of dimension d, is a pure (d -- 1)-subcomplex that satisfies a drop-of-water principle. In this paper, we introduc…
A Proof of the Tree of Shapes in n-D
Thierry GÉraud, Nicolas Boutry, Sébastien Crozet +2
In this paper, we prove that the self-dual morphological hierarchical structure computed on a n-D gray-level wellcomposed image u by the algorithm of G{é}raud et al. [1] is exactly…
Gradient Vector Fields of Discrete Morse Functions and Watershed-cuts
Nicolas Boutry, Gilles Bertrand, Laurent Najman
In this paper, we study a class of discrete Morse functions, coming from Discrete Morse Theory, that are equivalent to a class of simplicial stacks, coming from Mathematical Morpho…
Dimensional operators for mathematical morphology on simplicial complexes
Fabio Dias, Jean Cousty, Laurent Najman
In this work we study the framework of mathematical morphology on simplicial complex spaces. Simplicial complexes are widely used to represent multidimensional data, such as meshes…
On morphological hierarchical representations for image processing and spatial data clustering
Pierre Soille, Laurent Najman
Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained re…
On the equivalence between hierarchical segmentations and ultrametric watersheds
Laurent Najman
We study hierarchical segmentation in the framework of edge-weighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exis…