## 4 Discussion  
### Medical Image Synthesis with Quantitative Measurements  
In a previous study [62] dealing with the synthesis of brain-structured MRI, a GAN structure that appropriately augments the input image domain is proposed, and some related studies comparing the performance of each generalization when the training steps of various classifiers were enhanced using generated images have been reported [27; 28; 63; 64; 65; 32; 66]. These previous studies on GAN-based DA in the medical imaging field have emphasized the design of the applied GAN and the improved generalization of the target model that was trained using the augmented dataset. However, these studies only included qualitative visual evaluation, and the reasons for quantitatively evaluating the generated images before applying the GAN include:  
1. The practitioner cannot predict what the samples generated from GAN will look like until they are confirmed, unlike conventional DA. 2. It is not easy to visually evaluate how similar the real distribution is to the generated distribution. 3. Models trained without validation of augmented data may learn data that is characteristics of diseases but falls outside of a given class with an arbitrary label. In particular, medical images can be interpreted differently because of diverse disease distributions, then quantitative evaluation of generated medical images is important. In our study, the comparison  
Figure 8: Comparison of the generalization performance of ML-based classifiers before and after GAN-based data augmentation. (**A**) Changes of generalization performance (y-axis) of support vector machine and neural network observed at each axial level (x-axis); (**B**) Difference in generalization performance (y-axis) of ML models before and after GAN-based data augmentation (x-axis). Each ML model for the axial level generally improved with statistical evidence after data augmentation. of various classifiers was excluded, but we focused on the need for visual and quantitative evaluation of the data generated from GAN. Evaluating the synthetic DA data is to examine how identical the generated distributions are to real distributions rather than how identical the generated samples are. The classic approach is to estimate the real distribution using Parzen window estimation to measure the average log-likelihood of the generated samples [29]. This method has the advantage of being intuitive, but a recent study has shown that the estimated log-likelihood at higher dimensional space is not realistic, and above all, this study proves that it does not give a meaningful value that correlates to the reality of the given sample [34]. Another widely known method is the inception score (IS) [31], which uses the average KL divergence between \(\mathbb{P}(y|x)\) and \(\mathbb{P}(y)\) from the class label distribution estimated from the input images by an arbitrary finetuned model (e.g., inception network) to measure the quality and diversity. This method is also intuitive and is known to be correlated with human judgment, but it has the disadvantages of not detecting overfitting for samples the predictive model entirely memorizes, mode collapse for a distribution the model does not learn, or not accounting for a model trapped into bad mode [66]. To overcome these shortcomings, some variants of the inception score with KL divergence have been reported, including modified IS [67], mode score [68], and AM Score [66]. Several approaches for defining new distances in feature space have also been reported [30], including MMD [58], FID [60], and Wasserstein distance [54]. In general, the expected effects from GAN-based DA techniques include (1) generating samples that follow the same distribution as that of the real images to ensure that there are no insufficient datasets, or (2) generating similar but realistic samples to train the model on the creative pattern.