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Abstract
Owing to the computational complexities of orthogonal Mellin polynomials and Jacobi (p=4, q=3) polynomials, Orthogonal Fourier-Mellin moments and Pseudo-Jacobi (p=4, q=3)-Fourier moments have not been extensively used as feature descriptors. The conventional fast algorithms of radial moments focus on reducing the computation complexity of the radial polynomials. Nevertheless, they seldom take the optimisation of computing the kernel Fourier functions into account. In this paper, the authors propose a novel algorithm based on the two properties of kernel functions, which are recurrence relation and symmetry, to accelerate the computation of the two kinds of moments. The recurrence relations derived from the Jacobi polynomials eliminate the factorial iterations and exponent operations in computing the kernel polynomials. The symmetry property helps the authors perform the computation of the kernel functions, which include the kernel polynomials and Fourier functions, only in the region where 0<r<1, 0<θ<π/4. In addition to saving the storage required for the kernel functions, the symmetry property reducing the computation time greatly. The performance of the proposed algorithm on moment computation, as compared to those of the present methods, is experimentally verified by using a set of binary and greyscale images.