目的 全局的仿射变换配准需估计出仿射变换的参数，现有算法要么效果不佳，要么对二值图像无能为力。本文改造传统质心的定义，提出广义质心的概念。方法 传统的质心以二重积分定义，所提广义质心利用变形累次积分定义，传统质心只是这种广义质心的特例。本文给出了广义质心保持仿射变换前后对应关系的条件，并提出了一种利用这种广义质心进行仿射变换参数恢复的算法。结果 该算法对灰度和二值图像的仿射变换参数恢复都适用，实验结果也表明现有的交叉权重矩方法耗时是本文算法耗时的25倍，但它们的恢复效果相差不大，并且本文算法要比现有的图像矩构造非线性方程组方法恢复效果好。结论 本文提出了广义质心，利用这种广义质心进行仿射变换参数恢复算法，对二值图像和灰度图像均适用，恢复效果较好，并且计算量较小。

Objective Global image registration aimed at finding a transformation aligning two images can be approximated by estimating parameters of affine deformations. Some of the existing methods are inapplicable to binary images. The burden of computation process in other methods is more expensive. In this paper, we modified the definition of centroid for images and proposed the concept of generalized centroid. By combining the generalized centroid, we proposed an algorithm to achieve the estimation for parameters of affine deformations. Method Unlike the traditional centroid, the generalized centroid is defined by a modified repeated integral. The traditional centroid is only a special case of the proposed generalized centroid. To maintain the affine deformation relation, we present the condition in which the generalized centroid needs to be satisfied. We propose an algorithm to achieve the estimation for parameters of affine deformations. The basic idea of the algorithm is that we should find three sets of corresponding points in the original image and corresponding deformation image using these three pairs of points and establish equations to determine the parameters of affine deformations. Result The proposed centroids are applicable not only to gray images but also to binary images. Compared with the cross-weighted moment method to estimate the parameters of affine deformations, the proposed method requires less calculation and the recovery effect of the two methods is not significantly different. Compared with the method of constructing a nonlinear equation group using the image moment, the proposed method has a good ability to estimate the parameters of affine deformations. Conclusion By combining the generalized centroid, we proposed an algorithm to achieve the estimation for parameters of affine deformations. The proposed method is applicable to gray images and binary images. Moreover, the recovery effect is better and the calculation is less.