Lignes de partage des eaux discrètes : théorie et application à la segmentation d'images cardiaques

Abstract : The notion of a cleft models a frontier in a graph. Merging two regions, as requested by some image segmentation methods, is not straightforward. We introduce four classes of (fusion) graphs in which these difficulties are progressively avoided. We show that one of these classes is the one in which any cleft is thin. We introduce an adjacency relation, called perfect fusion grid, in which any two neighboring regions can be merged while preserving all other regions.

The notion of a topological watershed (TW), used for image segmentation, extend the one of a cleft to vertex-weighted graphs. We extend the properties of clefts in fusion graphs to the case of maps and give a monotone linear-time watershed algorithm on perfect fusion grids.
Thanks to line graphs, the properties of TWs in perfect fusion grids are extended to edge-weighted graphs.

We investigate in depth the watersheds in edge-weighted graphs. The watersheds can be defned following the intuitive idea of drops of water
flowing on a topographic surface. We establish both watershed consistency and optimality. We propose two linear-time algorithms
which are, to the best of our knowledge, the most efficient watershed algorithms.

Based on these results, we develop a software to automatically segment the left ventricular myocardium in 3D+t MR images. Quantitative and qualitative evaluations, based on the comparison with hand-made expert segmentations, assess the quality of the obtained segmentations.
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Jean Cousty. Lignes de partage des eaux discrètes : théorie et application à la segmentation d'images cardiaques. Informatique [cs]. Université de Marne la Vallée, 2007. Français. ⟨tel-00321885⟩

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