广义雅可比-傅立叶矩

Generic Jacobi-Fourier moments

图像正交矩具有数值稳定和方便重构等优点,雅可比-傅立叶矩(JFM)是传统正交矩的推广,然而其定义中的径向函数仅是整数阶多项式。本文改造JFM的径向函数,提出广义JFM,其定义中的径向函数既可以是分数阶的多项式,也可以是更一般的函数,JFM仅是这种构造的特例,并且证明了所提广义JFM的正交性和旋转不变性。数值实验也表明,利用所提方法可构造出重构性能好、抗噪性能强的图像正交矩。

Image orthogonal moments have the advantages of numerical stability and convenient reconstruction, and Jacobi-Fourier moment （JFM） is a promotion of traditional orthogonal moment. However, its definition of the radial function is only integer order polynomial. In this paper,we transform the radial function of JFM and propose a generic Jacobi-Fourier moment. The definition of the radial function can not only be fractional order polynomial, but also can be a more general function, and JFM is just a special case of this kind of structure. Meanwhile, we prove the orthogonality and rotation invariance of proposed generic JFM. Numerical experimental results also show that image orthogonal moments which are more robustness to noise and better reconstruction can be structured using the proposed method.