The classical morphological segmentation paradigm is based on the watershed transform, constructed by flooding the gradient image seen as a topographic surface. For flooding a topographic surface, a topographic distance is defined from which a minimum distance algorithm is derived for the watershed. In a continuous formulation, this is modeled via the eikonal PDE, which can be solved using curve evolution algorithms. Various ultrametric distances between the catchment basins may then be associated to the flooding itself. To each ultrametric distance is associated a multiscale segmentation; each scale being the closed balls of the ultrametric distance.
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