Local QFAPHFMs magnitude domain color image watermark detector based on a truncated Weibull–Rayleigh distribution

Designing a high-performance image watermarking algorithm that balances robustness, imperceptibility, and watermark capacity is a key issue that urgently needs attention. This paper proposes a color image watermark detection algorithm based on truncated Weibull-Rayleigh (TW-R) distribution and quaternion fast and accurate polar harmonic Fourier moments (QFAPHFMs) magnitude domain. First, we have demonstrated that the magnitude of QFAPHFMs is an ideal watermark carrier. Second, the digital watermark is embedded into the magnitude coefficients of QFAPHFM using multiplication criteria. In order to address the observed heavy tailed phenomenon in the magnitude of QFAPHFMs, we used the MMLE method based on the TW-R model to achieve accurate estimation of model parameters. Finally, a blind watermark detector was developed using the locally most powerful (LMP) decision rule. The experimental results show that even with a large watermark capacity, the proposed algorithm exhibits excellent imperceptibility and robustness, surpassing the existing advanced methods in terms of performance.