## 2 What Is a Generative Adversarial Network?
### Main Metrics Used
It is a simple and widely used metric but does not consider perceptual differences between the images [24]. * _Kernel Inception Distance (KID)_: This measures the similarity between the feature distributions of the real and generated images using a kernel-based method. It calculates the squared distance between the kernel means embeddings of the two distributions, where the feature space of a pre-trained Inception-v3 network defines the kernel. A lower value indicates that the generated images are more similar to the real images regarding their high-level features [61]. In [62], the problem of evaluating the quality of samplings generated by a machine learning model is addressed. Two well-known metrics are used: precision and recall, and accuracy. These measure the proportion of generated samplings that are correct, i.e., that resemble the real samplings. Recall measures the proportion of actual samplings that are correctly generated. However, the precision and recall metrics have certain limitations when assessing the fidelity and diversity of generated samplings. Fidelity refers to the similarity between generated and real samplings, while diversity measures the extent to which the generated samplings represent the full range of variability in the real samplings. Two novel metrics, namely, density, and coverage, are introduced to address these limitations. Density evaluates the proportion of total variability in the real samplings captured by the generated samplings, while coverage assesses how well the generated samplings match the actual distribution of samplings. Furthermore, the study suggests that random embeddings outperform ImageNet pre-trained embeddings, mainly when the target distribution significantly differs from the ImageNet statistics. This highlights the importance of carefully selecting appropriate embeddings when evaluating the quality of generated samplings. In the study conducted in [63], the focus is on evaluating the quality of generated Earth observation images using state-of-the-art GAN models. The authors compare the results obtained from these models with high-quality unconditional image synthesis achieved in other domains. To assess the quality of the generated images, they employ two widely used metrics, namely FID and KID. These metrics measure the similarity between the distributions of fake and real images by analyzing the feature maps of an Inception-v3 classifier. However, the paper concludes that while FID and KID are commonly used metrics, they may not accurately represent the visual quality of images. The authors find that models performing well in terms of FID and KID on smaller datasets may be more suitable for tasks where training data need to be balanced. This implies that the metrics alone may not provide a comprehensive assessment of visual quality and should be considered alongside other factors when evaluating the performance of GAN models for Earth observation image generation. The evaluation measures employed include FID, W-DISTANCE, and MMD, which calculate the distance between two distributions [64]. On the other hand, IS and its variants, such as m-IS, mode score, and AM score, utilize conditional and frontier distributions of generated or real data to assess the diversity and fidelity of samplings. Average log-likelihood and range metrics are utilized to evaluate probability distributions. Reconstruction error and specific quality measures assess the dissimilarity between generated images and their related or nearest counterparts in the training set. An ideal evaluation metric should possess well-defined bounds and demonstrate sensitivity to image distortions and transformations [57]. GANs undergo evaluation using various metrics to gauge the quality of the generated images. Each metric has advantages and limitations, and the selection should align with the specific evaluation objectives. Typically, the IS and FID metrics are widely employed to assess the quality and diversity of the generated images.