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The paper presents a novel approach for aligning a pair of sparse point sets under the assumption that their disparity is mainly explained by an affine transformation. The basic idea is to decompose the affine transformation matrix into a product of three matrices that can be estimated separately. Two matrices are obtained using Cholesky factorization of the sample covariance matrices, and the remaining matrix using the third order central moments of the point sets. The method is computationally efficient, and the experimental results with real images indicate that the proposed approach can give a good accuracy for alignment. However, only a small amount of clutter can be tolerated. In a general situation, it necessary to apply some preprocessing to segment the objects before applying the algorithm.