Design of orthogonal moment invariants for images with N-Fold rotation symmetry

It requires special considerations when design moment invariants for symmetric images, because some kinds of symmetries can lead to disappearance of some moment invariants. We focused on moment invariant design based on orthogonal moments which are defined over both rectangular area and unit disk. Some properties of orthogonal moments computed from images which possess N-fold rotation symmetry were formulated in this paper. We gave mathematical proofs for these properties, based on which we can design a set of orthogonal moment invariants particularly for symmetric images. The derived invariants are characterized with non-zero values, they are hence able to be more effectively used as features. Several experiments were designed to verify the proposed theories and test different kinds of moment invariants. The experimental results showed the potential applications of the proposed invariants. Besides, they also demonstrated that Gaussian-Hermite moment invariants have superior feature representation and noise robustness compared with general radial moment invariants and complex ones.