Pseudo-Jacobi (p = 4, q = 3)-Fourier moments (PJFMs) based on Jacobi polynomials are described. The new orthogonal radial polynomials have almost uniformly distributed (n + 2) zeros in the region of small radial distance 0 < or = r < or = 1. Both theoretical and experimental results indicate that PJFMs are better than orthogonal Fourier-Mellin moments in terms of reconstruction errors and signal-to-noise ratio. The PJFMs are normalized to shift, rotation, scale, and intensity invariance, and some pattern-recognition experiments are described.