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中文摘要：
本文对二阶微分矩阵仿射不变量特征描述问题进行了研究,构造了一种既考虑图像微分特性,又考虑图像积分特性的仿射不变量。算法首先计算二阶微分矩阵及其特征向量和特征值;其次是进行仿射变换的紧化,构造出一组由二阶微分矩阵特征向量和特征值决定的同心椭圆;再次是证明了一组同心椭圆的仿射不变性质,并利用该性质构造一组仿射不变量;最后将该仿射不变量应用于SAR图像配准,取得了良好效果,验证了算法的有效性。仿真结果说明该算法具有较强的抗相干斑噪声干扰和适应较大视角偏差的能力。
英文摘要：
An affine invariant derived from the second derivative matrix is studied and the affine invariant considering not only the differential characteristic of image but also the integral characteristic of image is constructed. First, the second derivative matrix of a given image and its eigenvectors and eigenvalues are computed. Second, the compactification of affine transformation is implemented and a set of ellipses with the same center controlled by the eigenvectors and eigenvalues of the second derivative matrix are constructed. Third, the affine invariant property of the ellipses with the same center is proved, and then a set of affine invariants using the property are constructed. Finally, the affine invariants are applied to the registration of Synthetic Aperture Radar （SAR） image and the effectiveness of the algorithm is verified. The simulation results show that the algorithm can reduce the disturbance from the speckle noise of SAR image and adapt the relatively large deviation of viewpoint.
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