Improved algorithm for Zernike moments

The Zernike moments can achieve high accuracy and strong robustness for the classification and retrieval of images, but involve huge amount of computation caused by its complex definition. It has limited its exploitation in online real-time applications or big data processing. So researches on how to improve the computation speed of Zernike moments are carried out. One of the existing high-accuracy algorithms for Zernike moments, which is called ZMGM algorithm, treats Zernike moments as the linear combination of geometric moments. Based on the ZMGM algorithm, we make two accelerating improvements and propose a fast algorithm. Firstly, a simplified linear combination is achieved by merging all the terms corresponding to the same geometric moment. So that the multiplication times is reduced. In this case, combined coefficients can be separated, pre-computed and stored for further computation of Zernike moments. Secondly, to speed up the computation of combined coefficients, a fast algorithm for the coefficient matrix of Zernike radial polynomials is proposed. The elements of this matrix are the main components of combined coefficients. Complexity analysis and numerical experiments show that, compared with the ZMGM algorithm, our proposed algorithm can significantly reduce the complexity and improve the computation speed. The optimization effect becomes more obvious as the order increases.