Statistical Image Watermark Algorithm for FAPHFMs Domain Based on BKF–Rayleigh Distribution

Abstract

In the field of image watermarking, imperceptibility, robustness, and watermarking capacity are key indicators for evaluating the performance of watermarking techniques. However, these three factors are often mutually constrained, posing a challenge in achieving a balance among them. To address this issue, this paper presents a novel image watermark detection algorithm based on local fast and accurate polar harmonic Fourier moments (FAPHFMs) and the BKF–Rayleigh distribution model. Firstly, the original image is chunked without overlapping, the entropy value is calculated, the high-entropy chunks are selected in descending order, and the local FAPHFM magnitudes are calculated. Secondly, the watermarking signals are embedded into the robust local FAPHFM magnitudes by the multiplication function, and then MMLE based on the RSS method is utilized to estimate the statistical parameters of the BKF–Rayleigh distribution model. Finally, a blind image watermarking detector is designed using BKF–Rayleigh distribution and LO decision criteria. In addition, we derive the closed expression of the watermark detector using the BKF–Rayleigh model. The experiments proved that the algorithm in this paper outperforms the existing methods in terms of performance, maintains robustness well under a large watermarking capacity, and has excellent imperceptibility at the same time. The algorithm maintains a well-balanced relationship between robustness, imperceptibility, and watermarking capacity.