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This paper presents a matrix projection method for matching a pair of shapes, and estimating the affine transformation that aligns the two shapes. First, shapes are considered as 2D disordered point sets, and their normalized forms are given. Then, we prove that only a rotational transform exists between the normalized forms of the two shapes under affine distortions. Second, correspondences are found by minimizing the inner product between one matrix and projection of the other. Finally, the affine transformation for shape registration is estimated by the correspondences. Experimental results show that our approach compares favorably to other methods under affine distortions.

A matrix projection approach for matching shapes under affine distortions