Comparison between the morphological skeleton and morphological shape decomposition

The morphological skeleton and morphological shape decomposition (MSD) are two popular approaches for morphological shape representation. Each method represents an object as an algebraic combination of a number of components, where each component is given by a locus of points dilated by a specified structuring-element homothetic. This correspondence develops a theoretical comparison between the two methods. Combining the theoretical results with several representation cost measures, we make a concrete comparison of the efficiency of the two methods. The results indicate that for complex objects-i.e., objects requiring a full range of homothetic sizes in the morphological skeleton representation-the MSD represents objects more efficiently than the morphological skeleton for three of four suggested cost measures.