Generalized Rotational Moment Invariants For Robust Object Recognition

High-order Hu moment invariant functions have always been required to solve a variety of problems. Up to this point, there was no generalized approach to extend the first six Hu moment invariants to higher orders. Therefore, this paper presents a generalized algorithm to determine rotationally invariant Hu moment invariants of any desired order, which are invariant to scaling, translation and rotation. Rotation has been stated to be a vital transformation that causes the non-linear transformation of an image, unlike scaling and translation, which are linear transformations of an image. Invariance to linear transforms can be achieved with the raw moments. However, non-linear transformations such as rotation require a unique combination of the raw moments to nullify the effects of the rotation transform. The algorithm proposed in this paper enables us to identify this specific combination of moments of specific order to achieve rotational invariance. The correctness of the proposed algorithm has been verified with appropriate proofs. The performance of a sample of new moment invariant functions generated from the proposed algorithm has been appraised specifically for rotational invariance with sample image data.