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Abstract
The detection of watermarks can be achieved by statistical approaches. How to select robust modeling object, appropriate statistical model, and decision rules is one of the major issues in statistical image watermark detection. In this paper, we propose a new image watermark detector in robust fast radial harmonic Fourier moments (FRHFMs) magnitudes domain, wherein the Beta-exponential distribution model and locally most powerful (LMP) decision rule are used. We first investigate the statistical modeling of the robust FRHFMs magnitudes by the Beta-exponential distribution. It is shown that the Beta-exponential distribution model fits the empirical data more accurately than the formerly employed statistical distributions, such as the Cauchy, Weibull, BKF, and Exponential, do. Motivated by the statistical modeling results, we design a blind image watermark detector in FRHFMs magnitudes domain by using Beta-exponential distribution and LMP test. Also, we utilize the Beta-exponential model to derive the closed-form expressions for the watermark detector. We provide comparative experimental results to alternative approaches to demonstrate the advantages of the proposed image watermark detector.
Highlights
With the rapid development of multimedia and Internet technologies, digital data can be acquired, represented, manipulated and distributed without any quality degradation
We propose a locally optimal (LO) image watermark detector by modeling fast radial harmonic Fourier moments (FRHFMs) magnitudes with Beta exponential distribution
We compare our approach with the state-of-the-art methods such as Etemad’s t LS[11], Rabizadeh’s Bessel K Form (BKF)[12], Sadreazami’s Cauchy[15], Amirmazlaghani’s CT-GARCH[38], Sadreazami’s normal inverse Gaussian (NIG)[5], Amini’s CHMM[24], Amirmazlaghani’s WT-GARCH [37], and Amini’s WHMM[7] based approaches
Summary
With the rapid development of multimedia and Internet technologies, digital data can be acquired, represented, manipulated and distributed without any quality degradation. Intellectual property right protection has become a major issue worldwide. Two basic approaches regarding digital image watermarking include watermark decoding [1][2][3] and watermark detection [4][5][6][7]. We need to determine if particular watermark information exists in the given data using a binary decision criterion. This paper mainly studies the copyright protection of images, so watermark detection based on a binary decision criterion is sufficient to declare legal ownership. When watermark carrier signals obey Gaussian distribution, the correlation-based detection method is optimal. Research results have shown that digital signals in both the frequency and spatial domains do not obey Gaussian distribution [5]. The detection method considering statistical properties of the carrier image coefficients can improve the correctness of watermark detection
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