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In computer vision, shape matching is a challenging problem, especially when articulation and deformation of parts occur. These variations may be insignificant in terms of human recognition, but often cause a matching algorithm to give results that are inconsistent with our perception. In this paper, we propose a novel shape descriptor of planar contours, called contour flexibility, which represents the deformable potential at each point along a contour. With this descriptor, The local and global features can be obtained from the contour. We then present a shape matching scheme based on the features obtained. Experiments with comparisons to recently published algorithms show that our algorithm performs best.