# An Improved Detail-Enhancement CycleGAN Using AdaLIN for Facial Style Transfer
## 4 Experiment
### Results
#### 4.3.2 Objective Evaluation  
In this paper, to comprehensively analyze the generation effect of face images, three objective evaluation metrics are employed. These metrics include the Frechet Inception Distance score (FID), Structural Similarity Index (SSIM), and the multi-scale image quality assessment SSIM method (MS-SSIM). These metrics are utilized to provide a thorough and quantitative assessment of the generated face images' quality, ensuring a comprehensive evaluation of the model's performance.  
(a) FID  
FID, a commonly used evaluation metric for generative adversarial networks (GANs), transforms the data distribution into Gaussian random variables using a feature function. This feature function calculates the distance between two Gaussian distributions based on their mean and covariance matrices, as illustrated in Equation (9):  
\[FID(x,g)=\parallel\mu_{x}-\mu_{g}\parallel_{2}^{2}+T_{r}\left(\Sigma_{x}+ \Sigma_{g}-2\left(\Sigma_{x}\Sigma_{g}\right)^{\frac{1}{2}}\right) \tag{9}\]  
where \(x\) is the real image, \(g\) is the generated image, \(\mu\) denotes the mean, \(\sum\) denotes the covariance matrix, and \(T_{r}\) denotes the trace of the matrix.  
(b) SSIM  
In real visual scenes, images exhibit a strong correlation, and there is a significant relationship between pixels within the same image. The structural similarity metric quantifies this similarity by measuring various information within the image, such as grayscale range, to determine the degree of resemblance between two images.  
(c) MS-SSIM  
In addition, the visibility of image details is influenced by factors such as image signal acquisition density, distance from the image plane to the observer, and the observer's visual system's perceptual ability. As these factors vary, the evaluation of an image also changes. Therefore, to complement the SSIM metrics, this paper introduces another method for image quality assessment called MS-SSIM (Multi-Scale Structural Similarity Index Method). MS-SSIM combines measurements on different scales to obtain an overall evaluation, as shown in Equation (10):  
\[MS-SSIM(x,y)=[l(x,y)]^{\alpha_{M}}\cdot\prod_{M}^{j=1}[c(x,y)]_{j}^{\beta} \cdot[s(x,y)]^{\gamma_{j}} \tag{10}\]  
where function \(l(x,y)\) represents the brightness contrast of the image, function \(c(x,y)\) represents the structural contrast of the image, and function \(s(x,y)\) represents the contrast of the image, parameters \(\alpha_{M}\), \(\beta\) and \(\gamma_{j}\) are used to adjust the relative importance of different components.  
For the experimental results mentioned above, FID was calculated separately, and the results are presented in Table 4. From the computational results, it is evident that the method proposed in this paper achieves better scores in terms of FID. Particularly when compared to the traditional CycleGAN, the algorithm proposed in this paper shows a 26% improvement in FID scores. This is sufficient to illustrate the advantage of the proposed algorithm in preserving the integrity of facial features in portraits.  
For the experimental results mentioned above, SSIM and MS-SSIM were calculated separately, and the results are presented in Table 5, providing a detailed quantitative analysis of our method's performance. As can be clearly observed from the data, the method proposed in this paper consistently achieves superior scores in both SSIM and MS-SSIM metrics compared to other state-of-the-art approaches. This superiority is evident across various test cases and style transfer scenarios. The higher scores indicate that our method more effectively preserves the structural information and perceptual quality of the original images during the style transfer process. Furthermore, these results strongly suggest that the images generated by our method exhibit a distribution that closely aligns with that of real images, demonstrating the effectiveness of our approach in producing realistic and high-quality style-transferred facial images.