Counteracting geometrical attacks on robust image watermarking by constructing a deformable pyramid transform

Counteracting geometrical attacks remains one of the most challenging problems in robust watermarking. In this paper, we resist rotation, scaling, and translation (RST) by constructing a kind of deformable pyramid transform (DPT) that is shift-invariant, steerable, and scalable. The DPT is extended from a closed-form polar-separable steerable pyramid transform (SPT). The radial component of the SPT's basis filters is taken as the kernel of the scalable basis filters, and the angular component is used for the steerable basis filters. The shift-invariance is inherited from the SPT by retaining undecimated high-pass and band-pass subbands. Based on the designed DPT, we theoretically derive interpolation functions for steerability and scalability and synchronization mechanisms for translation, rotation, and scaling. By exploiting the preferable characteristics of DPT, we develop a new template-based robust image watermarking scheme that is resilient to RST. Translation invariance is achieved by taking the Fourier magnitude of the cover image as the DPT's input. The resilience to rotation and scaling is obtained using the synchronization mechanisms for rotation and scaling, for which an efficient template-matching algorithm has been devised. Extensive simulations show that the proposed scheme is highly robust to geometrical attacks, such as RST, cropping, and row/column line removal, as well as common signal processing attacks such as JPEG compression, additive white Gaussian noise, and median filtering.