Based on local quaternion polar complex exponential transform (QPCET) and Cauchy–Rayleigh distribution, we propose a statistical color image watermarking scheme in this paper, which can achieve the trade-off among imperceptibility, robustness and data payload. Our color image watermarking scheme consists of two parts, namely embedding and detecting. In the embedding process, we divide the color host image into non-overlapping blocks and compute the local QPCET of color image blocks and then insert the watermark signal into the robust local QPCET magnitudes through multiplicative approach. In the detecting phase, robust local QPCET magnitudes are firstly modeled by employing the Cauchy–Rayleigh distribution, where the statistical properties of local QPCET magnitudes are captured accurately. Then, genetic algorithm-based maximum likelihood approach is introduced to estimate the statistical parameters of Cauchy–Rayleigh distribution model. And finally a color image watermark detector for multiplicative watermarking is developed using Cauchy–Rayleigh distribution and locally most powerful test. Also, we utilize the Cauchy–Rayleigh statistical model to derive the closed-form expressions for the watermark detector. Experimental results on some standard test images and comparison with well-known existing methods demonstrate the efficacy and superiority of the proposed scheme.

基于局部四元数极性复数指数变换（QPCET）和柯西-瑞利分布，我们提出了一种统计彩色图像水印方案，该方案可以实现隐身性，鲁棒性和数据有效载荷之间的权衡。我们的彩色图像水印方案由两部分组成，即嵌入和检测。在嵌入过程中，我们将彩色主机图像划分为非重叠块，并计算彩色图像块的局部QPCET，然后通过乘法将水印信号插入到鲁棒的局部QPCET量值中。在检测阶段，首先通过使用柯西-瑞利分布对鲁棒的局部QPCET量值进行建模，从而准确捕获局部QPCET量值的统计特性。然后，引入了基于遗传算法的最大似然法来估计柯西-瑞利分布模型的统计参数。最后，使用柯西-瑞利分布和局部最强大的测试，开发了用于乘法水印的彩色图像水印检测器。另外，我们利用柯西-瑞利统计模型推导水印检测器的闭式表达式。在一些标准测试图像上的实验结果以及与已知的现有方法的比较证明了该方案的有效性和优越性。我们利用Cauchy-Rayleigh统计模型推导水印检测器的闭式表达式。在一些标准测试图像上的实验结果以及与已知的现有方法的比较证明了该方案的有效性和优越性。我们利用Cauchy-Rayleigh统计模型得出水印检测器的闭式表达式。在一些标准测试图像上的实验结果以及与已知的现有方法的比较证明了该方案的有效性和优越性。