## 4 Experiment and Discussion
### Quantitative Evaluation  
It is difficult to objectively evaluate the algorithms using only visually subjective evaluation of the stylized images; therefore, in terms of quantitative objective evaluation, this section introduces multi-metric evaluation criteria to quantitatively compare the performance of each method in multiple aspects.  
* Feature similarity index (FSIM)  
In terms of objective metrics for image quality assessment, the structural similarity index method (SSIM) [22], which evaluates image quality in terms of three dimensions, image structure, brightness, and contrast, is widely used. SSIM takes values in the range of 0 to 1, and larger values indicate higher image similarity. Moreover, the feature similarity index matrix (FSIM) [23] is an extension of the SSIM based on the algorithm that considers that not all pixels in an image have the same importance; for example, the pixel points at the edges of an object are certainly more important for defining the structure of the object than the pixel points in other background areas, which can be described by the following equation:  
\[\text{FSIM}=\frac{\sum_{x\in\Omega}S_{L}(x)PC_{m}(x)}{\sum\sum_{x\in\Omega}PC_ {m}(x)} \tag{11}\]  
where \(PC_{m}\) denotes phase consistency and \(S_{L}\) is a function of the gradient.  
* Mean SSIM index (MSSIM)  
The mean SSIM index (mean SSIM; MSSIM) [24] characterizes the average of the SSIM values of content images and migrated images, and the SSIM values of style images and migrated images. The formula for calculating the index of mean SSIM can be expressed as  
\[\text{MSSIM}(X,Y)=\frac{1}{M}\sum_{j=1}^{M}\text{SSIM}(x_{j},y_{j}) \tag{12}\]  
where \(X\) and \(Y\) are the reference image and the distorted image, respectively; and \(x_{j}\) and \(y_{j}\) are the image contents of the \(j\)th local window. Moreover, \(M\) is the number of local windows in the image.  
* Image average gradient  
The average gradient of the image reflects the clarity and texture variation of the image; the larger the average gradient is, the clearer the image is, and the more detailed content it contains. It can be calculated with Equation (13).  
\[\text{AvG}=\frac{1}{M\times N}\sum_{i=1}^{M}\sum_{j=1}^{N}\sqrt{\frac{\left( \frac{\partial f}{\partial x}\right)+\left(\frac{\partial f}{\partial x} \right)}{2}} \tag{13}\]  
where \(M\times N\) denotes the size of the image, \(\frac{\partial f}{\partial x}\) denotes the gradient of the horizontal direction of the image, and \(\frac{\partial f}{\partial y}\) indicates the gradient of the image in the vertical direction. Figure 12 gives the quantitative evaluation results of three methods, DE-GAN, StyleGAN, and CycleGAN, using the three metrics. At the same time, to ensure the correctness of the comparison and to reduce chance, three sets of images were used for each method in the comparative analysis.  
As can be seen from Figure 12, the migrated images obtained using the DE-GAN algorithm in this paper have small improvements in FSIM, MSSIM, and average gradient compared with the StyleGAN and CycleGAN algorithms, which indicates that the method in this paper has better performance in terms of structural features, image distortion, image sharpness, and texture details than the other three methods and achieves stylization while preserving the details of the content images to the greatest extent. However, it should be noted that due to the more complex network, the inference speed of DE-GAN is lower than that of StyleGAN and CycleGAN. The comparison of the time taken is shown in Table 1.