# Fragile Watermarking for Image Authentication Using the Characteristic of SVD
## 3 Proposed Watermarking Scheme  
As mentioned above, the matrix product \(\mathbf{u}_{1}\mathbf{v}_{1}^{\mathrm{T}}\) in each image block is closely related to the image texture information. The more similar the pixel values in each block are, the more obvious this characteristic will be. In this section, we make full use of this property to introduce an effective fragile watermarking for image authentication. The binary texture image obtained in Section 2 is served as the authentication information and inserted into the host image. Figure 4 illustrates the flow chart of the presented watermarking algorithm, which consists of two main stages: watermark insertion on the sending side and the authentication process on the receiving side. The concrete procedures of watermark insertion are introduced as follows.  
Step 1. The LSB plane of the original image is firstly initialized to zeros.  
Step 2. The processed image is partitioned into many sub-blocks with a size of \(N\times N\). The proposed algorithm is based on the fact that the image block has similar pixel values. However, with the increase of the block size, the probability for similar neighboring pixels is decreased. The characteristic mentioned above will be weakened, which will further affect the image segmentation effect. Generally, an incomplete image feature will lead to a higher false positive ratio in tamper detection. To ensure the effectiveness of the proposed method, we choose \(N=4\) in this paper to illustrate the proposed algorithm. The block size \(N\) is also adopted as an encryption key, which will be used on the receiving end.  
Step 3. For each block, the SVD is performed and the matrix \(\mathbf{u}_{1}\mathbf{v}_{1}^{\mathrm{T}}\) is calculated.  
Step 4. By setting appropriate threshold \(T\), a binary image consisting of the texture information is obtained. From Figure 3, we can see that the texture feature of the host image is better described than other thresholds when the threshold \(T=1/4=0.25\). Therefore, the threshold \(T\) is set as 0.25 in this paper.  
Step 5. To ensure the security of the proposed algorithm, an encryption algorithm known as Arnold transform [19] is applied twice in the watermark embedding process. The binary texture image is firstly encrypted with a secret key \(k_{1}\in\{1,2,\cdots,192\}\), and the host image is permuted with a secret key \(k_{2}\in\{1,2,\cdots,192\}\) (\(k_{1}\
eq k_{2}\)).  
Step 6. The embedding process is completed after the permuted LSB plane is replaced by the encrypted watermarking bits.  
Step 7. After inverse Arnold transform with secret key \(k_{2}\), we obtain the watermarked image.  
In image transmission or storage, the content of the digital image might be destroyed by malicious attacks, which makes its texture information inconsistent with the original image. We take advantage of this property to realize tamper detection and localization. The watermarked image is firstly permuted by Arnold transform with secret key \(k_{2}\). Then, the encrypted watermark is extracted from the LSB plane of suspicious image. With the help of secret key \(k_{1}\), we obtain the decrypted watermark. In addition, a new texture image is regenerated via the same first four steps in the watermark embedding process.  
Figure 3: Image segmentation results for different threshold \(T\): (**a**) \(T=0.2\); (**b**) \(T=0.22\); (**c**) \(T=0.24\); (**d**) \(T=0.25\).  
By taking the absolute difference between the regenerated texture image and extracted information, a binary localization map is obtained. From this detection map, the tampered region can be determined.