Quaternion weighted spherical Bessel-Fourier moment and its invariant for color image reconstruction and object recognition

Abstract

Moments with capable of representing global features have been widely used in image analysis, pattern recognition and computer vision applications. However, existing image moment theories are still mainly paid close attention to gray-scale images. In this paper, a new quaternion moment termed as Quaternion weighted Spherical Bessel–Fourier Moment (QSBFM) is proposed to address the issue of color image analysis. Moreover, the relationship between QSBFM and the conventional weighted spherical Bessel–Fourier moment has been established so that the computational cost of QSBFM can be efficiently reduced. Furthermore, the natively geometric invariance of QSBFM is presented and discussed in detail. Experimental results show that the proposed QSBFM outperforms frequently-used quaternion moments including quaternion Bessel–Fourier moment, quaternion Radial-Harmonic-Fourier moment, quaternion Chebyshev-Fourier moment and quaternion orthogonal Fourier–Mellin moment in terms of the color image reconstruction capability and invariant recognition accuracy in noise-free, Salt & Pepper noise and the Gaussian noise conditions.