Raising in watershed lattices

The watershed segmentation is a popular tool in image processing. 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 interesting feature of the transformed map (called border kernel) is to convey not only the watershed partition but also numeric information relative to the initial map. In this paper, we provide the space of all border kernels with a semi lattice and propose morphological operations (relative to this lattice) which allow for merging border kernels and building hierarchies of watersheds based in particular on connected filters.