Flexible search-based approach for morphological shape decomposition

Mathematical morphology is well-suited to capturing geometric information. Hence, morphology-based approaches have been popular for object shape representation. The two primary morphology-based approaches, the morphological skeleton and the morphological shape decomposition (MSD), each represent an object as a collection of disjoint sets. A practical shape representation scheme, though, should give a representation that is compuiaiionally efficient to use. Unfortunately, little work has been done for the morphological skeleton and the MSD to address efficiency. We propose a flexible search-based shape decomposition scheme that typically gives more efficient representations than the morphological skeleton or MSD. Our method decomposes an object into a number of simple components based on homothetics of a set of structuring elements. To form the representation, the components are combined using set union and set difference operations. We use three constituent component types and a thorough cost-based search strategy to find efficient representations. We also consider allowing some object representation error, which may yield even more efficient representations.