Weighted spherical Bessel–Fourier image moments
In order to improve the performance of image reconstruction and image recognition accuracy in classic image orthogonal moments, a new set of moments based on the weighted spherical Bessel polynomial of the first kind is proposed, named weighted spherical Bessel–Fourier moments (WSBFMs), which are orthogonal in polar coordinate domain and can be thought as generalized and orthogonal complex moments. Then, the set of proposed WSBFMs is derived from the weighted spherical Bessel polynomial and image rotation-invariant is easily to achieve. Compared with Zernike, orthogonal Fourier–Mellion and Bessel polynomials of the same degree, the weighted spherical Bessel orthogonal radial polynomials have more zeros value, and these zeros value are more uniformly distributed. It makes WSBFMs more suitable for geometric invariant recognition as a generalization of orthogonal complex moments. Finally, Theoretical and experimental results show the superiority of the new orthogonal moments in terms of image reconstruction capability and invariant object recognition accuracy under noise-free, noisy and smooth distortion condition.
KeywordsOrthogonal moments Spherical Bessel polynomial Object recognition Image reconstruction Polar coordinate
This work was supported by National Natural Science Foundation of China (Grant No. 61472298), Basic research project of Weinan science and Technology Bureau (Grant No. 2017JCYJ-2-6) and by project of Shaan xi Provincial supports discipline(mathematics). The authors would like to thank the anonymous referees for their valuable comments and suggestions.