A New Statistical Image Watermark Detector in RHFMs Domain using Beta Exponential Distribution

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.