Fast computation of Zernike moments in polar coordinates

Zernike moments (ZMs) are widely used in many image analysis and pattern recognition problems because of their superiority compared with other moments. However, they suffer from high computation cost and inherent error. Previous researches have shown that the algorithm, computing ZMs in polar system, improves the ZMs accuracy of the reconstruction and invariance properties dramatically. In this study, the authors firstly modify a direct method for computing ZMs in polar coordinates and present a recursive relation. Then, this study presents an algorithm for fast computation of ZMs, based on the improved polar pixel tiling scheme. Owing to the symmetrical property, ZMs can be obtained by computing only one-sixteenth circle of the radial polynomials, which means that the number of pixels involved in the computation of ZMs is only 6.25% of the previous method. This leads to a significant reduction in the computational complexity requirements. A comparison with the other conventional method is performed in detail. The obtained results show the superiority of the proposed method.