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Top1. Introduction
Zernike Moments (ZMs) are the complex polynomials that are very widely used in many image processing applications like digital image watermarking (Kim et al., 2003; Xin et al., 2004) face recognition (Wiliem et al., 2007) and edge detection (Zhang et al., 2010; Amandeep et al., 2011), etc. In digital image watermarking, watermark bits can be inserted locally or globally either in spatial or frequency domain (Ibrahim et al., 2007). In many local region based watermarking techniques, magnitude of ZMs are selected and modified using dithering (Yongqing et al., 2011) or odd even quantization (Palak et al., 2004) technique. After modification of moments, watermarked image is reconstructed. The visibility of watermark in the watermarked image can be controlled.
Yongqing et al. (2011) have analyzed the invariance property of ZMs and proposed magnitude based watermarking technique. In this watermarking technique, magnitude of selected moments is quantized to insert the watermark bits. The authors have computed ZMs up to high order to support high payload to be embedded as watermark. The watermarking technique proposed by them is robust against rotation, scaling, flipping, additive noise and lossy compression. They have concluded that as the number of embedded watermark bits increases, the Peak Signal to Noise Ratio (PSNR) decreases and hence quality of watermarked image degrades. In the proposed watermarking technique, large number of bits can be inserted as watermark without degrading the quality of watermarked image.
Kim et al. (2003) have also used magnitude of ZMs as invariant feature vector of the host image. This feature vector is modified to insert the watermark bits and using the modified feature vector watermarked image is reconstructed. At the detector end, the feature vector of transformed watermarked image and original feature vector is compared to authenticate the watermarked image. The drawback of this technique is that the computation of ZMs (up to moment order 5) take five minutes for 256 
256 image. To reduce the computation time, we propose the use of q-recursive method for computing Zernike polynomials. Palak et al. (2004) have proposed a watermarking technique based on ZMs and odd even quantization. In this technique, the watermark bits are inserted by quantizing the magnitude of the ZMs using odd-even quantization method. Through experiments, the authors have concluded that this technique has detection ratio of 97% for rotation and of 75% for additive noise.