A new shape decomposition scheme for graph-based representation

Nowadays, the part-based representation of a given shape plays a significant role in shape-related applications, such as those involving content-based retrieval, object recognition, and so on. In this paper, to represent both 2-D and 3-D shapes as a relational structure, i.e. a graph, a new shape decomposition scheme, which recursively performs constrained morphological decomposition (CMD), is proposed. The CMD method adopts the use of the opening operation with the ball-shaped structuring element, and weighted convexity to select the optimal decomposition. For the sake of providing a compact representation, the merging criterion is applied using the weighted convexity difference. Therefore, the proposed scheme uses the split-and-merge approach. Finally, we present experimental results for various, modified 2-D shapes, as well as 3-D shapes represented by triangular meshes. Based on the experimental results, it is believed that the decomposition of a given shape coincides with that based on human insight for both 2-D and 3-D shapes, and also provides robustness to scaling, rotation, noise, shape deformation, and occlusion.