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In this paper, to represent 2-D shape as a relational structure, i.e. graph, we propose a new shape decomposition scheme composed of two stages: first, a given shape is decomposed into meaningful parts by using the constrained morphological decomposition (CMD) in a recursive manner. More specifically, the CMD adopts the use of the opening operation with the ball-shaped structuring element and the weighted convexity to select the optimal decomposition. Second, the iterative merging stage provides a compact graph-based representation based on the weighted convexity difference. From the experimental results for various and modified 2-D shapes, it is believed that the graph-based representation for 2-D shape coincides with that based on human insight, and also provides robustness to scaling, rotation, noise, shape deformation and occlusion.