An algebraic approach to symmetry detection

We present an algorithm for detecting cyclic and dihedral symmetries of an object. Both symmetry types can be detected by the special patterns they generate in the object\´s Fourier transform. These patterns are effectively detected and analyzed using the "angular difference function" (ADF), which measures the difference in the angular content of images. The ADF is accurately computed by using the pseudo-polar Fourier transform, which rapidly computes the Fourier transform of an object on a near-polar grid. The algorithm detects all the axes of centered and non-centered symmetries. The proposed algorithm is algebraically accurate and uses no interpolations.