圆谐-傅里叶矩及其优化算法的研究

圆谐-傅里叶矩是由平子良和任海萍等人提出的正交矩，具有缩放、平移、旋转不变性，用来描述图像具有很好的性能。但通过仿真实验表明，传统的算法在描述力方面随着阶数的增加图像的描述力越来越差，时间复杂度高等问题。为了能够更好的描述图像，降低时间复杂度，本文提出了对传统算法的改进算法。由于圆谐-傅里叶矩是在极坐标系下定义的，数字图像函数是在直角坐标下定义的，为了使二者统一，引入了伪极坐标系统，不改变数字函数坐标，在伪极坐标下计算圆谐-傅里叶矩，并通过二维快速傅里叶变换，加快矩值的计算。该改进算法解决了在极坐标下计算圆谐-傅里叶矩产生的重采样而影响图像描述力的问题，同时又解决了在直角坐标系下时间复杂度高的问题。

关键字：圆谐-傅里叶矩；二维快速傅里叶变换；伪极坐标

Abstract：
Radial harmonic - Fourier moments by Ziliang Ping and Haiping Ren and others propose orthogonal moments, and have the scaling, translation and rotation invariance, used to describe the image have the very good performance. But through the simulation experiment shows that the traditional algorithm to describe the image as the increase of the order number, has more and more difficult ,and has a high time complexity. In order to better describe the image, reduce the time complexity, this paper proposed a method to improve the  traditional algorithm. Due to the Radial harmonic - Fourier moments are defined in polar coordinates, digital image function is defined in Rectangular coordinates, in order to make the unification, pseudo polar coordinate system is introduced, don't change the digital function coordinates, under the pseudo polar coordinates calculation of Radial harmonic-Fourier moments, and through the 2-D fast Fourier transform, speed up the torque value calculation. The improved method has solved the calculation under polar coordinate Radial harmonic-Fourier moments produced by the re-sampling and effect the image description problem, and solved under rectangular coordinate system at the same time the problem of high time complexity.

Keywords: Radial-Harmonic-Fourier Moments;2-D fast Fourier transform;Pseudo polar coordinates
 

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