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In this paper, we propose a graph-based shape matching method for deformable objects. In our approach, a graph is generated from an over-segmented input image, and the shape matching problem is treated as finding an optimal cycle in the graph. Given a shape template and a graph generated from the input, a product graph is generated to consider every possible correspondence between graph edges and template sub-parts. Because the proposed approach can estimate reasonable correspondences between a target object and a template, it is possible to extract the target object robustly in the presence of shape deformation and background clutter. The experiments on various examples are also presented to verify the performance of proposed method.