Efficient morphological shape representation

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 computationally 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! representation scheme that typically gives more efficient representations than the morphological skeleton and 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 object representation error, which may yield even more efficient representations.