Estimation of rotation angle and anisotropic scaling rate using pilot signals for watermarking

We propose a method for simultaneously estimating the rotation angle and anisotropic scaling rates. Conventional watermarking methods are robust against non-geometric attacks. However, these methods need to synchronize to resist geometric attacks. Invariant features, such as SIFT, have been used for the synchronization. In this paper, we focus on pilot signals for estimating geometric attacks. By embedding a grid-shaped pilot signal and detecting its change, individual attacks on the scaling rate and rotation angle can be estimated. However, it has been difficult to estimate combined attacks. Our proposed method for estimating rotation angle and anisotropic scaling rates uses Radon coefficients. A Radon transform is applied to the signal obtained by QIM from a stego image. Periodic strong peaks appear in the coefficients at rotation angles. The period of the peaks is also calculated. From the rotation angle and the period at which the peaks appear, the rotation angle and the anisotropic scaling rates can be estimated. Computational results show that the rotation angle can be successfully estimated with an absolute error below 0.2 degrees. In more than half of the results, the absolute error of the anisotropic scaling rates was almost zero.