Fast computation of Jacobi-Fourier moments for invariant image recognition

Fast Computation of Chebyshev-Harmonic Fourier Moments

“…These relations can also be derived from our work in [9] for the fast computation of the JFMs of which CHFMs is a special case. However, the formulation in [9] requires much more arithmetic operations to compute , 1 ..., ,…”

“…This characteristic is practically not achievable because of the finite precision arithmetic used in the digital computers. It is shown that the major cause of numerical instability is due to factorial terms involved in the polynomial function [9]. The proposed recursive computation of CHFMs polynomials not only reduces time complexity, but it also improves numerical stability.…”

“…The computations of CHFMs involve factorial terms, which are computation intensive. Upneja and Singh [9] have proposed fast computation of JFMs of which CHFMs are a special case. However, when the method [9] is applied on the CHFMs, the number of arithmetic operations involved in the coefficients of the recursive relation is very high.…”

“…Upneja and Singh [9] have proposed fast computation of JFMs of which CHFMs are a special case. However, when the method [9] is applied on the CHFMs, the number of arithmetic operations involved in the coefficients of the recursive relation is very high. Another method uses 8-way symmetry for the computation of the radial function () p Rr involved in CHFMs [10].…”

Exact Legendre–Fourier moments in improved polar pixels configuration for image analysis

“…Camacho‐Bello et al [8] used recurrence relations and numerical integration to reduce numerical integration errors and this approach was shown to be less accurate but more numerically stable for higher order polynomials. Sáez‐Landete [9] recently showed that the configuration of Xin et al [4] and the use of recurrence relations improved the reconstruction performance compared with the algorithm proposed by Upneja and Singh [10] for fast, accurate computations of circular moments.…”