Robust color image watermarking using invariant quaternion Legendre-Fourier moments

Geometrically Invariant Color Medical Image Null-Watermarking Based on Precise Quaternion Polar Harmonic Fourier Moments

“…The results show that the proposed scheme delivers significantly better performance than schemes [48], [49] under various attacks. The comparison results between this scheme and the other five geometrically invariant watermarking schemes are shown in Table 3, which indicate the robustness of the proposed scheme is superior to schemes [29], [32]- [34], [37] under various attacks. The results of the three aforementioned comparisons indicate that the scheme proposed in this paper is highly robust and superior to other schemes mentioned above.…”

“…Niu et al [32] put forward a geometrically invariant color image watermarking algorithm based on QRHFM, which not only has good imperceptibility, but also is robust to various attacks. Hosny and Darwish [37] constructed a precise, fast and numerically stable method to calculate the QLFM in polar coordinates, and based on which, they designed a geometrically invariant color image watermarking scheme. Then they [38] presented a fast and precise watermarking scheme based on PCET and quaternion PCET (QPCET) for both gray-level and color medical images, respectively.…”

“…To show the superiority of the scheme, we compare it with other four kinds of watermarking schemes. (1) three representative similar image null-watermarking schemes [8], [9], [14], (2) quaternion theory-based color medical image watermarking scheme [48], (3) lossless medical image watermarking scheme [49], and (4) five representative geometrically invariant quaternion momentsbased watermarking schemes [29], [32]- [34], [37]. Based on these four considerations, the following nine references are selected for comparison: reference [8], which proposed a wavelet domain based image public copyright certification scheme, which could effectively resist interpretation attacks and was highly robust in resisting various malicious attacks; reference [9], which proposed a novel adaptive image copyright protection scheme, in which the verification information was constructed by using Sobel edge detection scheme to detect the edge features of the image, achieving good effects; reference [14], which proposed a QEM based color image null-watermarking scheme, which could effectively resist various geometric attacks and common image processing attacks; reference [48], which constructed quaternion Hadamard transform (QHT) based on quaternion theory and proposed a color image watermarking scheme on the basis thereof; reference [49], which proposed a robust lossless medical image watermarking scheme applicable to e-health systems, with embedding factors K = 10 and K = 20; references [29], [32]- [34], [37], which are representative geometrically invariant watermarking schemes based on five quaternion moments, i.e., QEM, QPHTs, QRHFM, QLFM, and QRSCM, respectively.…”

“…Comparison of the robustness (BCR) between the proposed scheme and geometrically invariant quaternion moments-based watermarking schemes [29], [32]- [34], [37].…”

Synchronisation correction‐based colour image watermarking using proximal classifier with consistency and multivariate generalised Gaussian model

“…Introduction: As an important copyright protection technology for digital images, the robustness against geometrical distortions has always been a key research issue for researchers. There exist mainly three kinds of digital image watermarking methods of resisting geometrical distortions, including invariant domain-based method [1], feature-based method [2], and synchronisation correction-based (SCB) method [3][4][5]. Recently, with the development of a statistical model and support vector machine (SVM), synchronisation correction has become popular.…”