提出了一种基于三类边界条件下贝塞尔函数的构造矩—贝塞尔-傅里叶矩, 其定义在极坐标系下, 可视为一种整体正交复数矩;该矩的正交多项式有较多零点, 且多数呈均匀分布.通过对26个大写字母二值图像的重构及1260幅灰度蝴蝶图像的分类实验来验证所提出矩的有效性,同时提取三类边界条件下贝塞尔-傅里叶矩的不同阶矩作为图像分析的特征值(图像描述质)来表征图像.理论分析和实验结果表明: 与正交傅里叶-梅林矩和泽尼克矩相比, 三类边界条件下贝塞尔-傅里叶矩更适用于图像的分析和旋转不变性的目标识别, 且图像重构准确度及不变性识别准确性均更优.

A set of moments was proposed based on Bessel function under three kinds of boundary conditions, named Bessel-Fourier moments, which are defined in polar coordinate and regarded as a generalized orthogonality complex moment. The radical polynomials of the Bessel-Fourier moments have many zero points and most of them are distributed uniformly. The reconstruction experiments of 26 uppercase binary images and the classification experiments of 1260 gray butterfly images were used to validate the proposed method, and different Bessel-Fourier moments under three kinds of boundary conditions wre extracted as the feature values of image analysis (image descriptor). Theoretical and experimental results show that, compared with the orthogonal Fourier-Mellin and Zernike moments, the Bessel-Fourier moments are more suitable in image analysis and rotation-invariant object recognition, and performed better than the orthogonal Fourier-Mellin and Zernike moments in terms of image reconstruction capability and invariant recognition accuracy.