Efficient computations for generalized Zernike moments and image recovery

Zernike moments are a set of orthogonal moments which have been successfully applied in the fields of image processing and pattern recognition. An innovative calculation method for Zernike moments, named generalized Zernike moments, is presented in this study. The generalized Zernike moment is a variant of Zernike moment. In this paper, we are proposing methods to calculate high-order generalized Zernike moments. Two kinds of recurrence for calculating generalized Zernike moments were introduced with rigorous proofs. Through the usage of the symmetries operated by the Dihedral group of order eight, the proposed method is fast and stable. The experimental results show that of the proposed method took 4.206s to compute the top 500-order generalized Zernike moments of an image with 512 by 512 pixels. Furthermore, by choosing the extra parameter α in the recurrence, the method enhanced the accuracy remarkably compared to the regular Zernike moments. Its normalized mean square error is 0.00144067 when α was set to 66 and the top 500-order moments were used to reconstruct the image. This error is 40.47% smaller than the one obtained by using the regular Zernike moments.