Adjacency lattices and shape-tree semilattices

This paper further investigates a new approach for self-dual morphological processing, where eroded images have all shapes shrunk in a contrast-invariant way. In the binary case, we operate on a given image with morphological operators in the so-called “adjacency lattice,” which is intimately related to the image’s adjacency tree. These operators are generalized to grayscale images by means of the so-called “shape-tree semilattice,” which is based on the tree of shapes of the given image. Apart of reviewing their original definition, different algorithms for computing the shape-tree morphological operators are addressed.