## 3 Experiment Result and Discussion
### Performance Analysis  
We analyze the imperceptibility of the watermark after embedding the ghost imaging encrypted watermark into the carrier light-field image using the cellular automata transformation (CAT) algorithm. We evaluate the imperceptibility of the image from both subjective and objective aspects. First, in our experiments, we compare the 3D images before and after embedding the watermark displayed by the desktop 3D-integrated display from five viewpoints: top, middle, bottom, left and right, as shown in Figures 5 and 6. Figures 5 and 6 show the 3D images before and after embedding the watermark; they are so similar that they cannot be distinguished with human eyes. Therefore, we evaluate the imperceptibility of the embedded watermark by calculating the peak signal to noise ratio (PSNR). PSNR is one of the most common and widely used metrics for the objective evaluation of images, however, it is based on the error between corresponding pixel points, with larger values indicating less distortion. \[\text{MSE}=\frac{1}{\text{H}\times\text{W}}\sum_{i=1}^{\text{H}}\sum_{j=1}^{ \text{W}}(\text{X}(i,j)-\text{Y}(i,j))^{2} \tag{17}\]  
\[\text{PSNR}=10\log_{10}\left(\frac{(2^{n}-1)^{2}}{\text{MSE}}\right) \tag{18}\]  
The MSE is the mean square error (MSE) of the current image X and the reference image Y. H and W are the height and width of the image, respectively; \(n\) is the number of bits per pixel, generally taken as 8, which means the number of grey levels of the pixel is 256. In our experiments, we calculate the PSNR values for several different methods separately at the embedding degree of 0.1. As shown in Table 1, when using the CAT  
Figure 4: The structure of the 3D integrated display: (**a**) the desktop 3D integrated display device; (**b**) diagram of the hexagonal compound lens array. embedding algorithm, the PSNR value reaches 40.12, indicating that the quality of the image after embedding the watermark is extremely good and very close to the original image. We have confirmed the validity of the watermark embedding algorithm through both subjective and objective aspects. Figure 5: Different perspectives of the 3D scene ‘dog’ before the watermark is embedded. Figure 6: Different perspectives of the 3D scene ‘dog’ after the watermark is embedded. Next, we experimentally verify that the watermarking algorithm used in this paper is robust to some attacks. A practical watermarking algorithm should be robust to signal processing, usual geometric distortions and malicious attacks. A highly robust watermarking algorithm should be able to embed and extract properly after attacks such as image compression and noise addition, and the extracted watermark results should be minimally affected. As shown in Figure 7, we verify the robustness of the watermarking algorithm by adding five attacks: Gaussian noise (v = 0.1), white noise, JPEG compression (QF50), Gaussian filtering and rotation by \(10^{\circ}\). As shown in Table 2, the above results show that the watermark can be extracted correctly and with good results for the case of added Gaussian noise and white noise. When the embedded carrier image is rotated, the extracted 2D watermark is distorted and corrupted by the noise. As we can see from the experimental results above, The cellular automata transform (CAT) algorithm has certain disadvantages, although it is more resistant to compression, filtering and noise attacks. The CAT watermarking method we use is a transform domain watermarking method; it is vulnerable to rotation attacks. The transformed domain method refers to some invertible mathematical transformation of the image followed by some modification of the coefficients of the transformed domain. We then perform an inverse transformation to obtain the image. Rotation attacks can disrupt synchronization so that watermark embedding and watermark detection position no longer match. The difficulty in combating this attack lies in the search for the original watermark reference point in the carrier data.