Shape-tree semilattice

摘要

A new, self-dual approach for morphological image processing, based on a semilattice framework, is introduced. The related morphological erosion, in particular, shrinks all 'objects' in an image, regardless to whether they are bright or dark.The theory is first developed for the binary case, where it is closely related to the adjacency tree. Under certain constraints, it is shown to yield a lattice structure, which is complete for discrete images. It is then generalized to grayscale functions thanks to the tree of shapes, a recently introduced generalization of adjacency trees.