In this work, the analytical Fourier-Mellin transform (AFMT) is used to derive two algorithms for, first, the estimation of the orientation parameter between two objects with the same shape, and second, the detection of all rotational symmetric axes in gray-level images. These algorithms are based on the computation of the Hausdorff distance between shapes when expressed in the Fourier-Mellin domain. Experiments are conducted on gray-level images, confirming the robustness of the algorithms and the accuracy of the estimated parameters.