## 2 What Is a Generative Adversarial Network?
### Main Metrics Used
The IS metric quantifies the quality and diversity by calculating the KL-divergence between the class probabilities of the generated and real images. On the other hand, the FID metric measures the distance between the feature distributions of the generated and real images within a high-dimensional feature space. In contrast, the LPIPS, SSIM, and KID metrics focus more on measuring perceptual and high-level feature similarities between the real and developed images. LPIPS estimates the perceptual similitude between pairs of images by comparing their feature representations in a deep neural network. SSIM computes the structural similarity between the authentic and developed images based on luminance, contrast, and structural differences. KID uses kernel methods to measure the discrepancy between the empirical dispersals of the characteristics extracted from the real and developed images. Finally, MSE is a simple and fast metric that measures the pixel-wise difference between the generated and real images. However, it may be better used to evaluate the visual quality of GAN-generated images, as it needs to consider perceptual similarities or high-level features. Therefore, the metric preference should be based on the specific conditions of the evaluation task and the strengths and weaknesses of each metric. These are just the standard metrics that can be used to estimate the implementation of GANs. The choice of metric will depend on the specific problem we are trying to solve and the desired properties of the generated images. Simply comparing the original dataset with the new dataset of synthetic images is not enough, as it is possible to generate a significant number of flawed images that do not reflect the real data. This is where careful analysis and the comparison of real and synthetic images become crucial. It should be known that GANs have their advantages and disadvantages, which is why if we are guided and understand the data we have, we can obtain better results, as may be the case in the generation of synthetic faces, where not all faces that are generated are perfect. Many of these have many defects, which do not overcome the filter at a glance [56]. By using a combination of metrics well suited to the task at hand, researchers can gain a deeper understanding of the strengths and weaknesses of their GAN models. This, in turn,can lead to improvements in the development and evaluation of GAN models, which is crucial for advancing the field of generative modeling [65]. Moreover, selecting appropriate metrics can also impact the applicability of GAN models in real-world scenarios, such as in computer vision applications, where high-quality and diverse image generation is a key requirement [66]. Figure 5 is primarily intended to illustrate that, although generative adversarial networks (GANs) are often associated with high-definition image generation, our comprehensive literature review reveals a wide variety of metrics used to evaluate GAN-generated images. These metrics have been variously applied in different contexts, demonstrating their versatility beyond GANs. It is important to note that all the metrics mentioned in our article are derived from a thorough analysis of the state of the art in this field. Among the most commonly used metrics are FID, PSNR, IS, and SSIM, with FID being particularly relevant due to its specific definition for generative models such as GANs. In Table 2, we have summarized the total information we found in the literature reviewed in this research related to the architectures, datasets, and metrics used. It is information that allows us to see that, as in several articles in the literature, there is no absolute metric, so we will always find trends of use in the most used metrics, such as FID or IS, which in turn are in some cases accompanied by another metric, which varies according to the research. We can also see that there is a clear tendency to use the CIFAR-10  
Figure 5: The frequency of main metrics in the literature review.