# Review on Semi-Fragile Watermarking Algorithms for Content Authentication of Digital Images
## 5 Overview on Semi-fragile Watermarking Algorithms
### Recoverable Semi-Fragile Watermarking Algorithms
#### 5.2.1 DCT Domain  
According to the important properties of JPEG compression, a semi-fragile watermarking algorithm based on the JPEG compression's invariant feature of DCT coefficients was proposed by [PERSON] and [PERSON] [26]. The algorithm puts every two image sub-blocks as a block pair, so it can tolerate JPEG compression and distinguish it from malicious tampering effectively. As for the tamper detection accuracy, the algorithm can guarantee a zero false positive rate and get remarkable performance in terms of false negative rate. In addition, the algorithm can tolerate some normal image processing operations, like brightness adjustment. It can identify and locate the tampered areas, and can even recover them by using the original approximation. However, since the authentication performed by this algorithm is independent for any sub-blocks, it must rely on another one or even more sub-blocks in the sub-block pair, which reduces the location accuracy of the watermark. Additionally, there are some defects about the security of the algorithm, and the convergence of watermark-embedding algorithm has not been proved. In [27], [PERSON] and [PERSON] proposed an iterative embedding algorithm based on the invariant feature of JPEG compression in the DCT domain. The authentication watermark is obtained by processing the DCT coefficients of the image sub-blocks through the Hash function. At the same time, the image index, block index, and user keys are combined together to resist the VQ attack. This paper offers the effect of the rounding error in the DCT process to the algorithm, and proves the convergence using theory and experimental results. The \(R_{\text{FP}}\) of the algorithm will be zero after undergoing acceptable JPEG compression. The algorithm can accept JPEG compression when its QF is larger than 50% and channel additive white Gaussian noise (AWGN) with small variance. Local tampering can be effectively detected, located, and recovered. However, the recovery process is only aiming at the direct current (DC) coefficients, and due to the impact of the predetermined quantization table, the block effect may appear in the recovered areas. To achieve better invisibility under JPEG compression and improve the ability of tampering recovery, [PERSON] et al. [28] used the method of modulo operation based on weight function to realize the hidden purpose. By modulating the seven intermediate frequency DCT coefficients in the range of \(\pm 1\), the process of watermark embedding is achieved. To enhance security, the algorithm reorganizes the recovery watermark of all the blocks in the host image based on the key, and then embeds them. The quantization step is set by combining the standard JPEG quantization table with the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Non-Malicious Tampering** & \begin{tabular}{c} **QF of Resisting** \\ **to JPEG (\%)** \\ \end{tabular} & \
\begin{tabular}{c} **PSNR of** \\ **Watermarked** \\ **Image (dB)** \\ \end{tabular} &
\begin{tabular}{c} **The Ability of Tamper** \\ **Detection and Location** \\ \end{tabular} \\ \hline
[20] & JPEG & QF \(\geq\) 60 & 30.0–44.2 & – \\ \hline
[22] & \
\begin{tabular}{c} Gaussian noise, salt and \\ pepper noise, cyclic filtering, \\ median filtering, and JPEG \\ \end{tabular} & QF \(\geq\) 50 & 48.0–56.0 &
\begin{tabular}{c} Location accuracy: in units \\ of 8 \(\times\) 8 pixels \\ \end{tabular} \\ \hline
[23] & JPEG & QF \(\geq\) 80 & 34.26–66.20 &
\begin{tabular}{c} Location accuracy: in units \\ of 2 \(\times\) 2 pixels \\ \end{tabular} \\ \hline
[24] & JPEG2000 & QF \(\geq\) 40 & 51.0–62.0 & – \\ \hline
[25] & \
\begin{tabular}{c} JPEG, JPEG2000, blurring, \\ Gaussian low pass filtering, \\ salt and pepper noise and \\ median filtering \\ \end{tabular} & QF \(\geq\) 30 & 41.39 &
\begin{tabular}{c} Location accuracy: in units \\ of 12 \(\times\) 12 pixels \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._variable scaling factor to achieve the balance between imperceptibility and robustness.