Wang Chunpeng, Gao Hongling, Yang Meihong, Li Jian, Ma Bin, Hao Qixian
School of Computer Science and Technology (School of Cyber Security), Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China.
Shandong Provincial Key Laboratory of Computer Networks, Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences), Jinan 250014, China.
Sensors (Basel). 2021 Feb 23;21(4):1544. doi: 10.3390/s21041544.
Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.
连续正交矩以连续函数作为核函数，具有旋转和缩放不变性，近年来得到了极大的发展。在连续正交矩中，极谐傅里叶矩（PHFM）具有优越的性能和强大的图像描述能力。为了提高PHFM在抗噪声和图像重建方面的性能，本文将只能取整数的PHFM扩展为分数阶极谐傅里叶矩（FrPHFM）。首先，对整数阶PHFM的径向多项式进行修改以获得分数阶径向多项式，并基于分数阶径向多项式构造FrPHFM；随后，证明了所提出的FrPHFM具有强大的重建能力、正交性和几何不变性；最后，将所提出的FrPHFM与整数阶PHFM、分数阶径向谐傅里叶矩（FrRHFMs）、分数阶极谐变换（FrPHTs）和分数阶泽尼克矩（FrZMs）的性能进行了比较。实验结果表明，本文构造的FrPHFM在图像重建和目标识别性能方面优于整数阶PHFM和其他分数阶连续正交矩，并且所提出的FrPHFM具有强大的图像描述能力和良好的稳定性。
