Quaternion Bessel–Fourier moments and their invariant descriptors for object reconstruction and recognition

• Quaternion Bessel–Fourier moments for color image reconstruction and recognition.
• An accurate estimation method for rotation angle throughout quaternion moments.
• The invariant descriptor using the moment magnitudes and phase coefficients.

In this paper, the quaternion Bessel–Fourier moments are introduced. The significance of phase information in quaternion Bessel–Fourier moments is investigated and an accurate estimation method for rotation angle is described. Furthermore, a new set of invariant descriptors based on the magnitude and the phase information of quaternion Bessel–Fourier moments is derived. Experimental results show that quaternion Bessel–Fourier moments lead to better performance for color image reconstruction than the other quaternion orthogonal moments such as quaternion Zernike moments, quaternion pseudo-Zernike moments and quaternion orthogonal Fourier–Mellin moments. In addition, the angles estimated by the proposed moments are more accurate than those obtained by using other quaternion orthogonal moments. The proposed invariant descriptors show also better robustness to geometric and photometric transformations.