Raising and watershed lattices

The watershed segmentation is a popular tool in image pro-cessing. Starting from an initial map, the border thinning transformation produces a map whose minima constitute the catchment basins of the watershed of the initial map. An inter-esting feature of the transformed map (called border kernel) is to convey not only the watershed partition but also numeric in-formation relative to the initial map. In this paper, we provide the space of all border kernels with a semi lattice and pro-pose morphological operations (relative to this lattice) which allow for merging border kernels and building hierarchies of watersheds based in particular on connected filters. Index Terms — Watershed, border kernels, lattice, hierar-chies, data merging, mathematical morpholog