A Modified L-Iterative Algorithm for Fast Computation of Pseudo-Zernike Moments

In the process of image recognition, moment is an important method. Invariant moment is a kind of image recognition method by extracting the translation, rotation and scale invariant features of the images. The paper is mainly dedicated to the rotation invariant feature analysis of the Pseudo-Zernike moment and proposes a modified 1-iterative algorithm for computing the Pseudo-Zernike moments. The method improves the efficiency of calculating Pseudo-Zernike moments by reducing the computational complexities of the Pseudo-Zernike polynomials and the Fourier kernel functions. The 1-iterative method, which avoids the factorial operations and the power series of radius involved in radial polynomials, is employed to compute the Pseudo-Zernike polynomials. The image domain is divided into eight equal parts by four lines, which are x=0, y=0, x=y and x=-y. On computing Pseudo-Zernike moments, the kernel functions are merely calculated in one part. The function values of the other parts can be obtained by the symmetry property about the four lines of the kernel functions. It not only saves the storages for the kernel polynomials but also reduces the computation time. The performance of the algorithm is experimentally examined using a binary image, and it shows that the computational speed of Pseudo-Zernike moments has been substantially improved over the present methods. At the end, the paper verifies the rotation invariance of the Pseudo-Zernike moments calculated by the modified method.