Image coding via morphological transformations: a general theory

A general theory for the morphological representation of discrete and binary images is presented. The theory relies on the generation of a set of nonoverlapping segments of an image by repeated erosions and set transformations, which in turn produces a decomposition that guarantees exact reconstruction. The morphological image-representation transform and its properties are examined, with focus on the relationship between the transform and some existing shape-analysis tools, thus introducing the transform as the basis of a unified geometrical image analysis. Particular cases of the general representation scheme are shown to yield a number of useful image representations which are directly related to various forms of digital morphological skeletons. Also considered is the relationship between the transform and the various forms of morphological skeletons