Abstract
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.
Highlights
The rapid development of information and network technologies has brought about great changes to human life and production
In this paper, the idea of fractional order is incorporated into PHFMs, fractional-order radial polynomials are constructed by modifying the integer-order radial polynomials of PHFMs to extend the traditional PHFMs to fractional polar harmonic Fourier moments (FrPHFMs), the properties of fractional-order polar harmonic Fourier moments (FrPHFMs) are analyzed in detail, and it is experimentally verified that the proposed FrPHFMs have better performance than integer-order PHFMs and other fractional-order continuous orthogonal moments in image reconstruction and object recognition
Other sections of this paper are organized as follows: Section 2 introduces the FrPHFMs construction process in detail and analyzes the geometric invariance of FrPHFMs; Section 3 mainly analyzes the properties of FrPHFMs from two perspectives, namely the changes in, and the rate of change of, their radial polynomials; Section 4 describes in detail the experiments and discussions with respect to image reconstruction, geometric invariance, and object recognition; and Section 5 draws a conclusion of this study
Summary
The rapid development of information and network technologies has brought about great changes to human life and production. In this paper, the idea of fractional order is incorporated into PHFMs, fractional-order radial polynomials are constructed by modifying the integer-order radial polynomials of PHFMs to extend the traditional PHFMs to fractional polar harmonic Fourier moments (FrPHFMs), the properties of FrPHFMs are analyzed in detail, and it is experimentally verified that the proposed FrPHFMs have better performance than integer-order PHFMs and other fractional-order continuous orthogonal moments in image reconstruction and object recognition. Other sections of this paper are organized as follows: Section 2 introduces the FrPHFMs construction process in detail and analyzes the geometric invariance of FrPHFMs; Section 3 mainly analyzes the properties of FrPHFMs from two perspectives, namely the changes in, and the rate of change of, their radial polynomials; Section 4 describes in detail the experiments and discussions with respect to image reconstruction, geometric invariance, and object recognition; and Section 5 draws a conclusion of this study
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