Comparison Between the Morphological Skeleton and Morphological Shape Decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hierarchical representation of 2-D shapes using convex polygons: A morphological approach
Pattern Recognition Letters
A Linear Systolic Array for Real-Time Morphological Image Processing
Journal of VLSI Signal Processing Systems
Morphological Reversible Contour Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape representation based on mathematical morphology
Pattern Recognition Letters
Three-Dimensional Surface Mesh Segmentation Using Curvedness-Based Region Growing Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Decomposition of two-dimensional shapes for efficient retrieval
Image and Vision Computing
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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