# A Hybrid Domain Color Image Watermarking Scheme Based on Hyperchaotic Mapping
## 3 The Proposed Watermarking Scheme
### Robustness Analysis  
In this section, we focus on evaluating the robustness of the proposed scheme against various attacks. Based on this, we use three main metrics: PSNR, NCC and BER. These three indicators play a crucial role in evaluating the performance of the scheme. PSNR is used to show the perceptual transparency of the watermark image relative to the original cover image. The NCC value directly reflects the anti-attack ability of the scheme. The higher the  
Figure 8: Histogram comparison between cover image and embedded watermark image. Figure 7: Watermarked image and corresponding extracted watermark image. value is, the stronger the resistance of the scheme to the attack is. The decrease in bit error rate means that the degree of watermark distortion is smaller, which is very important in maintaining the integrity of watermark information. In this paper, various attacks are comprehensively tested. These attacks are mainly divided into four categories: noise attack, enhanced technology attack, geometric transformation attack and compression attack. In the experiment, we compare the attacked cover image and the successfully restored watermark. The comparison results are shown in Figures 9 and 10, where [a-l] represent different types of attacks, respectively: no attack, salt and pepper noise (v = 0.05), Gaussian noise (m = 0, v = 0.05), speckle noise (v = 0.05), sharpening, Gaussian filtering, mean filtering, rotation 10\({}^{\circ}\), vertical flipping, cropping 20%, JPEG compression (QF = 90), and JPEG 2000 compression (QF = 90). These attacks represent a variety of situations that may be encountered in the real world, and our scheme has been thoroughly tested to ensure robustness in all situations. Through our experimental results, we can clearly see that our scheme can effectively resist other attacks, except rotation and cropping attacks, and the extracted watermark image has only slight distortion. This shows that our scheme has high robustness and can effectively deal with attacks in various situations in the real world, thus protecting the integrity and stability of watermark  
Table 3 describes the PSNR of the attacked watermark cover image, Table 4 describes the PSNR of the watermark image extracted from different attacks, Table 5 describes the NCC of the watermark image extracted from different attacks, and Table 6 describes the BER of the watermark image extracted from different attacks. Under the condition of no attack, the average PSNR of this method is 45.6849 dB, the average NCC of this method is 1, and the average bit error rate is 0. And under various attacks, the average NCC and average BER can maintain a good level. Table 7 describes the robustness comparison results with other watermarking schemes. Taking the Baboon cover image as an example, it can be seen from Table 7 that the watermarking scheme in this paper can effectively extract the watermark image in the face of various attacks. It can be seen from Table 3 that when the cover image is attacked by different attacks, there is a big difference between the PSNR of the attacked image and the original image, and the quality of the image is significantly reduced, but the watermark image extracted from it can still maintain high quality. The average PSNR of the extracted watermark can maintain 20 dB, indicating that the watermark scheme in this paper has good robustness. From the comparison with other schemes in Table 7, it can also be seen that most of the NCC values of the schemes in this paper are higher than other schemes, indicating that the scheme in this paper has higher robustness. Figure 10: Watermark images extracted from different attacks.