Invariant Image Watermarking Using Accurate Zernike Moments

Abstract

problem statement: Digital image watermarking is the most popular method for image authentication, copyright protection and content description. Zernike moments are the most widely used moments in image processing and pattern recognition. The magnitudes of Zernike moments are rotation invariant so they can be used just as a watermark signal or be further modified to carry embedded data. The computed Zernike moments in Cartesian coordinate are not accurate due to geometrical and numerical error. Approach: In this study, we employed a robust image-watermarking algorithm using accurate Zernike moments. These moments are computed in polar coordinate, where both approximation and geometric errors are removed. Accurate Zernike moments are used in image watermarking and proved to be robust against different kind of geometric attacks. The performance of the proposed algorithm is evaluated using standard images. Results: Experimental results show that, accurate Zernike moments achieve higher degree of robustness than those approximated ones against rotation, scaling, flipping, JPEG compression and affine transformation. Conclusion: By computing accurate Zernike moments, the embedded bits watermark can be extracted at low error rate.

Classification of foodborne pathogens using near infrared (NIR) laser scatter imaging system with multivariate calibration

“…For rotational invariance, Zernike moment invariances based on orthogonal polynomials, was first introduced by Teague29, with the property that it is straightforward to invert and thus easy to generate moment equivalent images based on a set of moments.…”

Image adaptive and high‐capacity watermarking system using accurate Zernike moments

“…The inaccuracies in the moment computation not only limit capacity, but also affect robustness and imperceptibility. An attempt is made by Ismail et al [20] to enhance the robustness and imperceptibility of watermark embedding by adopting an accurate computational framework for ZMs in polar domain [21]. However, the inaccuracy in moment computation persists for moment order > 44 because of numerical instability.…”

“…By far, the approach proposed by Xin et al [13] is the most effective method for geometrically invariant watermarking and the work of Ismail et al [20] is based on their approach. More recently, Li et al [22] proposed polar harmonic transforms (PHTs) for invariant watermarking and adopted the general computational framework developed by Xin et al [13], with slightly different watermark embedding and extraction processes.…”

Accurate Orthogonal Circular Moment Invariants of Gray-Level Images

“…Based on this attractive property, these orthogonal moments are widely used in different image processing and pattern recognition applications. See for examples (Abandah and Anssari, 2009, Radhika et al, 2010, Ismail et al, 2010. Despite of this fact, the conventional approach for computing these circular moments and their invariants encounter two major problems.…”