We show that the transformation with radial polynomial and circular Fourier kernel of two-dimensional image can generate image moments, which are invariant to rotation, translation and scale changes. Among them the orthogonal Fourier-Mellin moments using the generalized Jacobi radial polynomials show better performance that the Zernike moments. We introduce new Chebyshev-Fourier moments using Chebyshev radial polynomials, which improve the behavior of the orthogonal Fourier-Mellin moments in regions close to the center of image. Experimental results are shown for the image description performance of the Chebyshev-Fourier moments in terms of image reconstruction errors and sensitivity to noise. In the cases of binary or contour shapes the Fourier-Mellin moments of single orders are able to describe and reconstruct the shapes.