Abstract
The classical radial harmonic Fourier moments (RHFMs) and the quaternion radial harmonic Fourier moments (QRHFMs) are gray-scale and color image descriptors. The radial harmonic functions with integer orders are not able to extract fine features from the input images. In this paper, the authors derived novel fractional-order radial harmonic functions in polar coordinates. The obtained functions are used to defined novel multi-channel fractional-order radial harmonic moments (FrMRHFMs) for color image description and analysis. The invariants to geometric transformations for these new moments are derived. A theoretical comparison between FrMRHFMs and QRHFMs is performed from the aspects of kernel function and the spectrum analysis. Numerical simulation is carried out to test these new moments in terms of image reconstruction capabilities, invariance to the similarity transformations, color image recognition and the CPU computational times. The obtained theoretical and numerical results clearly show that the proposed FrMRHFMs is superior to the QRHFMs and the existing fractional-order orthogonal moments.
Highlights
The orthogonal moments of gray-scale images were defined in the early 1980s
The results clearly show that proposed FrMRHFMs outperformed the QFrZMs [17] and the conventional quaternion radial harmonic Fourier moments (QRHFMs) [6]
The average elapsed CPU times clearly show that the FrMRHFMs is much faster than QRHFMs [6] and the QFrZMs [17] which is consisting with the results of the complexity analysis as shown in Tables (5) and (6)
Summary
The orthogonal moments of gray-scale images were defined in the early 1980s. These moments have three useful characteristics: First, its ability to represent digital images with a minimum redundancy. Ren et al [5] derived the RHFMs using triangular functions as radial kernels, which possess the property of being invariant to rotation and can be made invariant to translation and scaling by a set of geometric transformations.Wang et al [6] utilized the algebra of quaternions and introduced the QRHFMs for color image representation and retrieval. A new set of fractional-order multi-channel radial harmonic-Fourier moments (FrMRHFMs) for color images analysis is derived.
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