Image analysis by Bessel–Fourier moments

In this paper, we proposed a new set of moments based on the Bessel function of the first kind, named Bessel–Fourier moments (BFMs), which are more suitable than orthogonal Fourier–Mellin and Zernike moments for image analysis and rotation invariant pattern recognition. Compared with orthogonal Fourier–Mellin and Zernike polynomials of the same degree, the new orthogonal radial polynomials have more zeros, and these zeros are more evenly distributed. The Bessel–Fourier moments can be thought of as generalized orthogonalized complex moments. Theoretical and experimental results show that the Bessel–Fourier moments perform better than the orthogonal Fourier–Mellin and Zernike moments (OFMMs and ZMs) in terms of image reconstruction capability and invariant recognition accuracy in noise-free, noisy and smooth distortion conditions.