中文摘要：

正交矩的数值稳定性分析是近年来图像处理中研究的热点。研究对象是正交矩解析式中最为常用的三项递归公式,介绍正交矩的三项递归公式及数值稳定性的概念;然后以欧几里得范数作为恒量其稳定性的标准提出一种基于其计算系数极限存在与否判断其数值稳定性的判据,并给予详尽证明;最后运用两个实例证明此判据的可行性。

英文摘要：

Numerical stability analysis of orthogonal moments is one of the hot topics in the field of image analysis in recent years.This paper studies the most commonly used three recursive formulas among the orthogonal moments analytic ones.First,the concepts of three recursion formulas and numerical stability of orthogonal moments were introduced;Then a new stability criterion was proposed to judge the stability of three recursion relations based on Euclidean norm standard,which was proofed in detail;Finally,two examples were used to demonstrate the feasibility of this criterion.