No 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 α and β of Jacobi polynomials. The quality of the description of the proposed method with α and β parameters known is studied. Also, a search is performed of the best parameters, α and β, 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.

We present a detailed analysis of the Jacobi-Fourier moments and their applications in digital image processing. In order to reach numerical stability during the computation of the Jacobi radial polynomials a recursive approach is described. Also, some discussions are done about the best values of the parameters α and β in terms of its performance. Moreover, the digital image applications studied here are divided in low or high orders n of the polynomials. Typically, the pattern recognition applications are based in low order polynomials whilst image reconstruction can be achieved by using high order polynomials. On the other hand, the polar pixel approach is taken into account, in order to increase the numerical accuracy in the calculation of the

Color image reconstruction provides a measure of the feature representation capability of the moment functions. In this work, we present the quaternion Fourier-Legendre moments in polar pixels, which are computationally more fast and have a high-precision compared with other methods. In addition, to improve the performance of the array of polar pixels, we use an inherent property of the Legendre polynomials for the accurate calculation of kernel integration. Moreover, the presented new set of quaternion Fourier-Legendre moments is compared with other families proposed, such as quaternion Zernike moments, quaternion pseudo-Zernike moments, quaternion orthogonal Fourier-Mellin moments, and quaternion Bessel-Fourier moments. Experimental results show the superiority of the new quaternion moments in terms of the reconstruction error.

Abstract. A detailed analysis of the quaternion generic Jacobi-Fourier moments (QGJFMs) for color image description is presented. In order to reach numerical stability, a recursive approach is used during the computation of the generic Jacobi radial polynomials. Moreover, a search criterion is performed to establish the best values for the parameters α and β of the radial Jacobi polynomial families. Additionally, a polar pixel approach is taken into account to increase the numerical accuracy in the calculation of the QGJFMs. To prove the mathematical theory, some color images from optical microscopy and human retina are used. Experiments and results about color image reconstruction are presented.