Orthogonal moments have become a powerful tool for object representation and image analysis. Radial harmonic Fourier moments (RHFMs) are one of such image descriptors based on a set of orthogonal projection bases, which outperform other moments because of their computational efficiency. However, the conventional computational framework of RHFMs produces geometric error and numerical integration error, which will affect the accuracy of RHFMs, thus degrading the image reconstruction performance. To overcome this shortcoming, we propose a new computational framework of RHFMs, namely accurate quaternion radial harmonic Fourier moments (AQRHFMs), for color image processing, and also analyze the properties of AQRHFMs. Firstly, we propose a precise computation method of RHFMs to reduce the geometric and numerical errors. Secondly, by using the algebra of quaternions, we extend the accurate RHFMs to AQRHFMs in order to deal with the color images in a holistic manner. Experimental results show the proposed AQRHFMs achieve promising performance in image reconstruction and object recognition in both noise-free and noisy conditions.

中文翻译：

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精确的四元数径向谐波傅里叶矩用于彩色图像重建和目标识别

正交矩已成为对象表示和图像分析的强大工具。径向谐波傅立叶矩（RHFM）是基于一组正交投影基的此类图像描述符，由于其计算效率高，因此优于其他矩。但是，传统的RHFMs计算框架会产生几何误差和数值积分误差，这会影响RHFMs的精度，从而降低图像重建性能。为了克服这一缺点，我们提出了一种新的RHFM计算框架，即用于彩色图像处理的精确四元数径向谐波傅里叶矩（AQRHFM），并分析了AQRHFM的特性。首先，我们提出了一种RHFM的精确计算方法，以减少几何和数值误差。其次，通过使用四元数代数，我们将准确的RHFM扩展到AQRHFM，以便以整体方式处理彩色图像。实验结果表明，所提出的AQRHFM在无噪声和嘈杂的条件下，在图像重建和目标识别方面均具有良好的性能。