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.

In a digital watermarking technology system, robustness, imperceptibility and payload capacity are the three core performance indicators that restrict one another. How to achieve the optimal balance between the three is still the key scientific challenge to be solved in this field. This paper proposes a digital watermarking algorithm based on the magnitude coefficient of Non-Subsampled Shearlet Transform Fast and Accurate Polar Harmonic Fourier Moments (NSST-FAPHFMs) and the Weibull–Power Cauchy (W-PC) statistical model. The algorithm consists of two stages: watermark embedding and detection. In the embedding phase, the original image is first decomposed by NSST multi-scale decomposition, and the high-frequency subbands are divided into non-overlapping blocks and partitioned. High-energy coefficient blocks are extracted to obtain NSST-FAPHFM magnitude coefficient features, which serve as robust carriers for watermark embedding. In the detection phase, the W-PC distribution is used to accurately statistically model the above magnitude coefficients to characterize their heavy-tailed characteristics and strong correlation structure. Maximum likelihood estimation (MLE) is employed to estimate the model parameters, and a blind watermark detection mechanism is further constructed by integrating the W-PC model with the Local Optimal Detector (LOD) under the Neyman–Pearson (N-P) criterion. Experimental results show that the proposed algorithm has good imperceptibility, and the area under the receiver operating characteristic curve (AUROC) can reach 0.9991 without attack. The algorithm maintains strong robustness against various attacks and can effectively realize the joint optimization of the three core performance indicators of the watermarking system.