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中文摘要：
提出了一种仿射形变条件下形状匹配的矩阵投影方法。首先利用二维点集描述具有仿射形变关系的两个形状，提出了形状点集的标准化形式，并证明了标准化形式之间仅存在旋转变换；其次通过矩阵投影的方法找到标准化形状之间的匹配关系，从而通过重构的方法确定初始形状的匹配关系；最后通过匹配关系确定仿射变换参数，并进行形状配准。试验结果表明本文提出方法对仿射形变具有不变性，并且对形状点集的数目不相等的情况具有较高的精度。
英文摘要：
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.
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