Image moments have been extensively used as feature descriptors. However, the quantization error introduced in discrete signals presents problems, especially when dealing with small-size images. This results in the fact that the invariant properties of moments are compromised. In this paper, we present a technique suitable for the calculation of moments from a continuous signal, derived by piecewise polynomial interpolation of the corresponding discrete one. The computed moments exhibit significantly increased accuracy while requiring trivial computational effort. Zernike moments are then computed using the proposed scheme and are shown to display increased stability to geometrical transformations.