As mentioned earlier, adding a watermark to an image is a branch of the image processing task, which means we can improve on the zero-watermarking algorithm by some mathematics. The most critical issue of zero-watermarking is improving the algorithm's robustness against geometric attacks (e.g. ...
It is normalized such that l(M ) = 1/2, 1 for SU(M ) and SO(M ) respectively. Of course, Abelian discrete symmetries only have singlet irreducible representations. Here it is clear that tr τ (d(f)) is a charge (called δ(f) in [54]), and from eq. (4.2) one notes that ...
Error metrics that are commonly used include, for example, mean squared error (MSE), mean absolute error (MAE), peak signal to noise ratio (PSNR), sum of squared errors (SSE), sum of absolute difference (SAD), cross-correlation (CC), normalized cross-correlation (NCC), etc. The ...
The minimization of the AIC statistic (Akaike, 1974) was used during this backward elimination. To assess the goodness-of-fit of the model, the independence of the normalized quantile residuals and their normality were assessed, in order to verify whether the model described the systematic part,...
Based on the imputed composition, we used the zeroSum procedure with the default settings, and by using only an l1 penalty, applied on the log-transformed compositional values. These are first total-sum normalized in order to refer to log-contrasts, as requested for this procedure. The tuning...
In practice, since we use large values of N, we take log(p), use Stirling’s approximation [1] for factorials and apply softmax({log(pk)/t}k=1N) to get normalized scores for numerical stability. The parameter t controls the temperature of the resulting distribution. The soft...
This algorithm builds its λn(C) approximation with the normalized principal eigenvector, E1, estimated during the iterative calculation of λ1(C). Next, this algorithm builds its λn(W) estimate with the normalized eigenvector En approximated during the iterative calculation of λn(C). Given ...
In addition, there are extreme impedance values shown in isotropic inversion compared to the anisotropic methods that have more normalized inversion error values. Figure 16. Arbitrary sections extracted from the zero-offset acoustic impedance volumes obtained from (a) isotropic inversion, (b) ...
The index of dispersion, also known as the FF, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), is a normalized measure of the dispersion of a probability distribution that is used in probability theory and statistics to determine whether a set of observed occurrenc...
Initially, it applies the DFT algorithm to the luminance of the watermarked image. Next, it extracts the coefficients positioned along the radius r, corresponding to the circular region where the watermark was originally embedded during the encoding phase. The maximum normalized cross-correlation, ...