提出了雅可比-傅里叶矩,它是用雅可比多项式作为径向函数,用傅里叶因子作为角向函数构造而成的,是广义正交傅里叶-梅林矩.经过归一化处理后的雅克比-傅立叶矩具有平移、尺度、旋转、灰度多畸不变性.从归一化图像重建误差、噪声灵敏度等方面对雅可比-傅里叶矩的图像描述能力进行了研究,结果显示雅可比-傅里叶矩在各种参量选择的情况下,具有良好的图像描述和抗噪声能力,是一个优良的图像特征.以前的研究多为单纯构建某一个函数,而现在将其扩展为构建一个函数族,开阔了矩描述量的研究视野.

Jacobi-Fourier moments (JFM),which choose Jacobi polynomial as radial function and Fourier factor as angle function are proposed. The new moments are generalized Orthogonal Fourier-Mellin moments. Jacobi-Fourier moments can be normalized to be invariant for shifting,scaling,rotation and intensity distortion of an image. The normalized image reconstruction error (NIRE) and noise sensitivity of Jacobi-Fourier moments are also investigated. Results show that Jacobi-Fourier moments are good image feathers with strong image description ability andn noise resistange power. Compared with other researches, the research view is extended from reconstructing a certain function to reconstructing a function family.