Morphology on label images: Flat-type operators and connections

We consider morphological operations on images whose pixel values are considered as labels without ordering between them, except for a least element perpendicular to (meaning no label) and a greatest element inverted perpendicular (meaning conflicting labels). Flat dilations and erosions can be defined as in usual grey-level morphology. Since the lattice of label images is not distributive, non-flat operators can be obtained by combination of flat ones. Given any connectivity on sets, there is a connection on label images for which the connected components of an image correspond precisely to its flat zones with their labels attached. Some specific applications of label morphology are given. In the sequel of this paper [20], we will examine geodesic dilations and reconstructions on label images, and show how this variant of mathematical morphology can be applied to the segmentation of moving objects in video sequences [2, 3].