In this paper, we briefly review the fractional-order circular moments, such as fractional-order Zernike moments, fractional-order Fourier–Mellin moments, fractional-order Legendre–Fourier moments, and fractional-order Chebyshev–Fourier moments, which can characterize, analyze, and manipulate the information contained in an image with minimal redundancy. Also, they depend on an $\alpha$ parameter for better feature extraction. Therefore, we propose a procedure to find the optimal $\alpha$ in terms of image reconstruction error and classification. We validate the search for the best rotation-invariant features using the MNIST and MNIST-R datasets. Finally, we present the study results and conclusions.

在本文中，我们简要回顾了分数阶圆矩，例如分数阶 Zernike 矩、分数阶 Fourier-Mellin 矩、分数阶 Legendre-Fourier 矩和分数阶 Chebyshev-Fourier 矩，它们可以表征以最小的冗余度分析和处理图像中包含的信息。此外，它们依赖于$\alpha$参数以更好地提取特征。因此，我们提出了一个程序来寻找最优$\alpha$在图像重建误差和分类方面。我们使用 MNIST 和 MNIST-R 数据集验证对最佳旋转不变特征的搜索。最后，我们展示了研究结果和结论。