Color Image Reconstruction Using Quaternion Legendre-Fourier Moments in Polar Pixels

Abstract

Color image reconstruction provides a measure of the feature representation capability of the moment functions. In this work, we present the quaternion Fourier-Legendre moments in polar pixels, which are computationally more fast and have a high-precision compared with other methods. In addition, to improve the performance of the array of polar pixels, we use an inherent property of the Legendre polynomials for the accurate calculation of kernel integration. Moreover, the presented new set of quaternion Fourier-Legendre moments is compared with other families proposed, such as quaternion Zernike moments, quaternion pseudo-Zernike moments, quaternion orthogonal Fourier-Mellin moments, and quaternion Bessel-Fourier moments. Experimental results show the superiority of the new quaternion moments in terms of the reconstruction error.

Exact Legendre–Fourier moments in improved polar pixels configuration for image analysis

“…The proposed configuration demonstrates that it is not necessary for polar pixels to have the same size as stated by Xin et al [4]. Also, this configuration can be implemented on other families of circular moments, such as radial moments [34], quaternion colour moments in polar pixels [35], moment invariants in the Radon space [25], and fractional‐order orthogonal moments [24].…”

Geometrically Invariant Color Medical Image Null-Watermarking Based on Precise Quaternion Polar Harmonic Fourier Moments

“…Image moments are effective tools for image analysis, which are widely used in the field of image watermarking in recent years [21], [22]. With the quaternion-based image analysis receiving more and more attention in the field of color image processing, the researchers combined the quaternion theory with the image moments to construct quaternion moments suitable for color images, including quaternion Fourier-Mellin moments (QOFMM) [23], quaternion Zernike moments (QZM) [24], quaternion polar harmonic transforms (QPHTs) [25], quaternion radial Tchebichef moments (QRTM) [26], quaternion radial Krawtchouk moments (QRKM) [27], quaternion radial dual Hahn moments (QRdHM) [27], quaternion Bessel-Fourier moments (QBFM) [28], QEM [29], quaternion Legendre-Fourier moments (QLFM) [30], quaternion rotational moments (QROTM) [31], quaternion pseudo-Zernike moments (QPZM) [31], quaternion radial harmonic Fourier moments (QRHFM) [32], quaternion radial substituted Chebyshev moments (QRSCM) [33], quaternion Chebyshev-Fourier moments (QCHFM) [4], and quaternion polar harmonic Fourier moments (QPHFM) [4], etc. Due to their good stability and geometric invariance, quaternion moments have been widely used in the field of color image watermarking in recent years.…”

Over 50 Years of Image Moments and Moment Invariants

“…In this context, the group of Geometric [60], Zernike [150], Pseudo-Zernike [150], Fourier-Mellin [133], Legendre [150] traditional moments, initially was enriched with the Tchebichef [96], Krawtchouk [185], dual-Hahn [201,187], Racah [199], discrete moments exhibiting high computation accuracy. More moments such as Polar Harmonic Transforms [184,49,48] Wavelet [11,117,141], Gaussian-Hermite [182], Bessel-Fourier [175], Jacobi-Fourier [121,12], Gegenbauer [82,55], Charlier [46], Comoments [189], Exponent [59], Variant [43] and Spline [19] moments were introduced in a way to nd more informative and robust descriptors.…”