On the fast computation of Zernike moments

Zernike moments play a very significant role in pattern recognition, image analysis and in image processing, apart from its traditional field of optics. Among different properties, their invariance and orthogonality are attractive in many applications. Identification of different machine parts on a running conveyor belt or detection between normal and defective machine parts are of significance in industrial applications. It can also be used in identification of other subjects. Unfortunately, their direct computation is very expensive and is a major drawback in applications. In this paper, we have proposed an algorithm for fast computation of Zernike moments. As Zernike moments are orthogonal on the unit disc and applications are in the discrete domain, computations must be carried out considering discrete circles and discrete discs. Their properties play an important role for fast computation of Zernike moments. In this paper we have computed different terms of radial polynomials for different moments using a recursion, instead of computing successively all the terms of a single moment. This introduces fastness in computation. Comparison between different methods supports this fact and establishes the efficiency of the proposed method.