Shape Representation: Comparison between the Morphological Skeleton and Morphological Shape Decomposition

The morphological skeleton and morphological shape decomposition (MSD) are the two popular approaches for morphological shape representation. Each method represents an object as the union of a number of components, where each component is given by a locus of points dilated by a speciied structuring element homothetic. Anecdotal evidence suggests that for many objects, an MSD-based representation can be more eecient than the morphological skeleton. This paper develops a theoretical comparison between the two methods. Combining the theoretical results with several deened representation cost measures, concrete comparisons are made between the eeciency 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 eeciently than the morphological skeleton for three of four suggested cost measures.