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A common approach to determining corresponding points on two shapes is to compute the cost of each possible pairing of points and solve the assignment problem (weighted bipartite matching) for the resulting cost matrix. We consider the problem of solving for point correspondences when the shapes of interest are each defined by a single, closed contour. A modification of the standard assignment problem is proposed whereby the correspondences are required to preserve the ordering of the points induced from the shapes' contours. Enforcement of this constraint leads to significantly improved correspondences. Robustness with respect to outliers and shape irregularity is obtained by required only a fraction of feature points to be matched. Furthermore, the minimum matching size may be specified in advance. We present efficient dynamic programming algorithms to solve the proposed optimization problem. Experiments on the Brown and MPEG-7 shape databases demonstrate the effectiveness of the proposed method relative to the standard assignment problem.