几何矩顺序算法的比较性研究

几何矩是用于推导平移、伸缩和旋转不变量的常用技术。用直接方法计算矩涉及大量的加法和乘法,因而有必要研究几何矩的快速算法。该文首先综述现有的对几何矩进行快速计算的顺序算法,然后用数字实验比较Delta方法、多线段积分方法、以及Li和Shen的格林定理法的性能。多线段积分方法和Delta方法在计算Hu矩不变量方面性能是相同的,但Delta方法仅适于处理二值水平连续图像,而多线段积分方法可以处理任意二值图像。与Li和Shen的格林定理法相比,多线段积分方法在计算精度上性能很完美。

Study of Sequential Moment Computation Methods

Geometric moments are among the most common means of deriving invariants with respect to object translation,scale change and rotation.Direct computation of moments involves a large number of multiplications and additions,hence seeking for fast algorithm for geometric moments become a necessary.We investigate in this paper the previously used sequential moment computation methods,and then compare the performances of Delta method,multiple line segment integral method,and Li and Shen's Green's theorem method by digital experiments.Multiple line segment integral method and Delta method are similar in the aspect of computing Hu's moment invariants.But Delta method suits only binary horizontal continuous images and multiple line segment integral method can process arbitrary binary images.Compared with Li and Shen's Green method,multiple line segment integral method gives near perfect results in computation precision.