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In this paper, we propose an improved autocorrelation function (ACF)-based watermarking that is robust against combined geometric and removal attacks. ACF-based watermarking is known to be effective against geometric attacks. In this watermarking scheme, both the embedded watermark and autocorrelation peaks of the watermark should survive a variety of attacks. However, the autocorrelation peaks are not strong enough. The proposed method improves the robustness of ACF-based watermarking by enhancing the strength of the autocorrelation peaks. Instead of the simple addition of a watermark to an image, the proposed watermark embedder uses the information of an original image more actively during the embedding process, so that the marked image has strong autocorrelation peaks. Experimental results show that the proposed scheme provides better robustness than conventional ACF-based watermarking against a variety of combined geometric-removal attacks.

The development of new quantum watermarking is in full swing, and it is crucial to test the robustness of these proposed watermarking schemes. In this paper, different quantum circuits are introduced to realize geometric transformations on quantum images, which serve as a means of simulating geometric attacks on quantum watermark images. Receivers may get distorted images, and the extracted watermark images may also be disrupted. To recover the geometric order of the quantum watermark images, a strategy is proposed to identify the trajectory of qubit alterations. Quantum circuits can be designed accordingly to restore the original order of the watermark images, which receivers could use before the extraction process to mitigate the impact of geometric attacks. Experimental simulations demonstrate how attacks affect the quantum watermark images and the extracted watermark images. Additionally, it illustrates how quantum recovery circuits step by step act on images that have been geometrically attacked. An analysis of the complexity of geometric restoration circuits reveals that quantum circuits exhibit better performance compared to classical circuits.

Geometric attacks become a serious threat to most existing wavelet-based watermarking by destroying the synchronization between watermark and watermarked images. This paper presents a novel robust watermarking scheme against geometrical distortions. Using invariant centroid (IC) and a feature template in DFT domain, the synchronization can be reconstructed. The double-channel watermarking is embedded into low-frequency band in DWT domain. Experimental results prove that our watermarking scheme has good invisibility and excellent robustness against both normal attacks and geometric attacks; furthermore, this method is blind watermarking.

A new blind image watermarking algorithm robust against both geometric attack and JPEG compression is proposed. The proposed discrete wavelet transform-fast-Fourier transform(DWT-FFT) composite watermarking scheme embeds a gray image in subband in the DWT domain, and embeds a template in magnitude spectrum in FFT domain. Experimental results have demonstrated that the watermark is robust against both affine transformations and JPEG compression well.