## Abstract

A high-precision and fast algorithm for computation of Jacobi–Fourier moments (JFMs) is presented. A fast recursive method is developed for the radial polynomials that occur in the kernel function of the JFMs. The proposed method is numerically stable and very fast in comparison with the conventional direct method. Moreover, the algorithm is suitable for computation of the JFMs of the highest orders. The JFMs are generic expressions to generate orthogonal moments changing the parameters $\alpha $ and $\beta $ of Jacobi polynomials. The quality of the description of the proposed method with $\alpha $ and $\beta $ parameters known is studied. Also, a search is performed of the best parameters, $\alpha $ and $\beta $, which significantly improves the quality of the reconstructed image and recognition. Experiments are performed on standard test images with various sets of JFMs to prove the superiority of the proposed method in comparison with the direct method. Furthermore, the proposed method is compared with other existing methods in terms of speed and accuracy.

© 2013 Optical Society of America

Full Article | PDF Article**OSA Recommended Articles**

ZiLiang Ping, RiGeng Wu, and YunLong Sheng

J. Opt. Soc. Am. A **19**(9) 1748-1754 (2002)

Mhamed Sayyouri, Abdeslam Hmimid, and Hassan Qjidaa

J. Opt. Soc. Am. A **30**(11) 2381-2394 (2013)

Guleng Amu, Surong Hasi, Xingyu Yang, and Ziliang Ping

Appl. Opt. **43**(10) 2093-2101 (2004)