Abstract
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.
Highlights
Counteracting geometrical attacks such as rotation, scaling, and translation (RST) remains one of the most challenging problems for robust watermarking
We develop a new geometrical correctionbased robust image watermarking scheme by constructing a deformable pyramid transform (DPT) that is shiftinvariant, steerable, and scalable
The radial component of the steerable pyramid transform (SPT)'s basis filters was taken as the kernel for designing the scalable basis filters
Summary
Counteracting geometrical attacks such as rotation, scaling, and translation (RST) remains one of the most challenging problems for robust watermarking. We develop a new geometrical correctionbased robust image watermarking scheme by constructing a deformable pyramid transform (DPT) that is shiftinvariant, steerable, and scalable. This is motivated by the scheme of [24], in which a steerable pyramid transform (SPT) with shift-invariance and steerability [29] is exploited to estimate, with an auxiliary inserted template, the rotation angle. In the interest of counteracting RST in robust image watermarking, we are motivated to extend the SPT with shift-invariance and steerability to include scalability This is termed the DPT for convenience. We determine a suitable number of scalable basis filters, J, derive the closed-form Cj(r), and obtain the interpolation functions for steerability and scalability
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