A general theory for the morphological representation of discrete and binary images is presented. The basis of this theory relies on the generation of a set of nonoverlapping segments of an image via repeated erosions and set transformations, which in turn produces a decomposition that guarantees exact reconstruction. The relationship between the proposed representation and some existing shape analysis tools (e.g., discrete size transform, pattern spectrum, skeletons) is investigated, thus introducing the representation as the basis of a unified theory for geometrical image analysis. Particular cases of the general representation scheme are shown to yield a number of useful image decompositions which are directly related to various forms of morphological skeletons. The relationship between the representation and the various forms of morphological skeletons is studied. As a result of this study, a unified theory is developed for the mathematical description of the morphological skeleton decomposition of discrete and binary images.
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