中文摘要：

提出一种多畸变不变的正交图像矩：雅可比-傅立叶矩。其核函数由径向雅可比多项式和角向傅立叶复指数因子组成。雅可比多项式中的两个参数p和q的变化能够形成各种正交多项式，因而形成各种正交图像矩：勒让德-傅立叶矩（p=1，q=1）、切比雪夫-傅立叶矩（P=2，q=3／2）、正交傅立叶-梅林矩（p=2，q=2）和Zernike矩以及变形Zemike矩，等等。因此雅可比-傅立叶矩是核函数由径向多项式和角向傅立叶复指数因子组成的正交图像矩的一般形式，为这种正交图像矩的数学分析和优化提供了理论基础。

英文摘要：

A multi-distorted invariant orthogonal moments, Jacobi-Fourier moments（JFM）, were proposed. I he integral Kernel of the moments was composed of radial Jacobi polynomial and angular Fourier complex componential factor. The variation of two parameters in Jacobi polynomial,p and q,can form various types of orthogonal moments：Legendre-Fourier moments （p=1, q= 1）;Chebyshev-Fourier moments （p=2, q=3/2）; Orthogonal Fourier-Mellin moments （p=2,q=2） Zernike moments and Pseudo-zernike moments,and so on. Therefore,JacobbFourier moments are generic expression of orthogonal moments formed by a radial orthogonal polynomial and angular Fourier complex component factor, providing a common mathematical tool for performance analysis of the orthogonal moments,