Radial harmonic‐Fourier moments (RHFMs) are popular for image reconstruction and invariant pattern recognition due to their properties of translation, scaling and rotation invariant. RHFMs possess lower computation complexity as compared to Zernike moments and Bessel‐Fourier moments. However, they always suffer from discontinuity, numerical instability near the center of image, and reconstruction error, especially have a rise for higher order of moments. In this paper, an improvement of radial harmonic‐Fourier moments (IRHFMs) is proposed for effectively avoiding the above‐mentioned problems.In this paper, a 2D fast Fourier transform algorithm also is applied to the image matrix to obtain the IRHFMs. Simulation experimental results demonstrate the proposed IRHFMs perform better than traditional RHFMs and other classic orthogonal moments including the latest image moments, for example, polar harmonic Fourier moments in terms of the image reconstruction capability and rotation invariant recognition accuracy in noise‐free and noisy conditions.

中文翻译：

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快速改进径向谐波-傅立叶矩算法的图像分析

径向谐波傅立叶矩 (RHFM) 由于其平移、缩放和旋转不变的特性，在图像重建和不变模式识别中很受欢迎。与 Zernike 矩和 Bessel-Fourier 矩相比，RHFM 具有较低的计算复杂度。然而，它们总是受到图像中心附近的不连续性、数值不稳定和重建误差的影响，尤其是对于高阶矩的上升。本文提出了一种改进径向谐波傅立叶矩（IRHFMs）的方法，以有效避免上述问题。本文还对图像矩阵应用二维快速傅立叶变换算法来获得IRHFMs。