Comparison Between the Morphological Skeleton and Morphological Shape Decomposition.

Joseph M. Reinhardt, William E. Higgins

Abstract: 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.