Mathematical modeling and stochastic analysis for RST invariant watermarking algorithm

In this paper, a mathematical model is established for RST (Rotation, Scaling, Translation) invariant image watermarking. The cover image is approximated using the mixture Generalized Gaussian distribution. To embed the watermark, the cover image is segmented into several homogeneous regions using MAP (Maximum A Posterior probability) segmentation. Each segmented region is represented using a Generalized Gaussian distribution with a specific shape parameter. The local variance and mean are estimated using EM (Expectation Maximization) algorithm for each segmented region. The higher the local variance, the smaller the shape parameter. Stochastic analysis for the probability error including false positive probability of the RST invariant image watermarking algorithm is addressed in terms of the relative entropy and the PSNR of the watermarked image.