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

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 faster 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.