This paper presents a matrix projection method to match a pair of shapes and to estimate the affine transformation that aligns the two shapes.First,the shapes are considered as 2D point sets,and their canonical forms are proposed.It′s proved that only rotation exists between canonical forms of two shapes under affine distortions.Second,correspondences are found by minimizing the inner product between one matrix and the projection of the other.Then,the affine transformation for shape registration is estimated by the correspondences.The experimental results show that our approach performs better compared with the reference methods under affine distortions.