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Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

by 1,2,3, 1,2, 1,2, 1,2, 1,2,* and 1,2
1
School of Computer Science and Technology (School of Cyber Security), Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
2
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
3
Shandong Provincial Key Laboratory for Distributed Computer Software Novel Technology, Jinan 250358, China
*
Author to whom correspondence should be addressed.
Academic Editor: Yitzhak Yitzhaky
Sensors 2021, 21(4), 1544; https://doi.org/10.3390/s21041544
Received: 8 December 2020 / Revised: 8 February 2021 / Accepted: 8 February 2021 / Published: 23 February 2021
(This article belongs to the Section Sensing and Imaging)
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. View Full-Text
Keywords: fractional-order polar harmonic Fourier moments; continuous orthogonal moments; geometric invariance; image reconstruction; object recognition fractional-order polar harmonic Fourier moments; continuous orthogonal moments; geometric invariance; image reconstruction; object recognition
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MDPI and ACS Style

Wang, C.; Gao, H.; Yang, M.; Li, J.; Ma, B.; Hao, Q. Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments. Sensors 2021, 21, 1544. https://doi.org/10.3390/s21041544

AMA Style

Wang C, Gao H, Yang M, Li J, Ma B, Hao Q. Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments. Sensors. 2021; 21(4):1544. https://doi.org/10.3390/s21041544

Chicago/Turabian Style

Wang, Chunpeng; Gao, Hongling; Yang, Meihong; Li, Jian; Ma, Bin; Hao, Qixian. 2021. "Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments" Sensors 21, no. 4: 1544. https://doi.org/10.3390/s21041544

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