# GAN Training Acceleration Using Frechet Descriptor-Based Coreset
## 4 Experiments and Results
### Experiment II: Validation Experiments Using 3D Human Kidney MR Images  
In this experiment, we investigated the proposed FDD-Coreset approach on 3D MR images to measure the number (\(N_{glom}\)) and apparent volume (\(aV_{glom}\)) of glomeruli in healthy and diseased human donor kidneys that were not accepted for transplant. Since we have three 3D MR human kidney images, and each of them has voxel dimensions of 896 \(\times\) 512 \(\times\) 512 and the input of the BlobGAN is a 3D patch with voxel dimensions of 64 \(\times\) 64 \(\times\) 32, we divided each human kidney into 1792 3D patches (64 \(\times\) 64 \(\times\) 32) to validate the performance of the BlobGAN. The final identification mask of the whole kidney was reconstructed by stacking all 3D patches. To train the BlobGAN, \(\lambda_{cycle}\) and \(\lambda_{convex}\) were set to 10, \(\lambda_{identity}\) was set to 0.5, the learning rate was 0.0002, and the Adam optimizer was used with a batch size set to 1. We compared the total computation time from Coreset selection to training Coreset on the BlobGAN on 3D MR human kidney images. Similarly with Section 4.2, we have the original random sampled 1000 3D blob images to train the BlobGAN as the baseline, so we generated Coreset (size \(k=10\)) through the IED-Coreset and the FDD-Coreset (size \(k=10\)), respectively, and trained these groups of Coreset on the BlobGAN by 20 epochs. Once these Coreset are generated, we compare the total computational time from the Coreset generation to the BlobGAN training and summarize them in Table 4, from where we can see the results show that the BlobGAN trained on the IED-Coreset with \(k=10\) on three human kidneys takes the longest time. The BlobGAN trained on the FDD-Coreset with \(k=10\) on three kidneys all perform significantly faster (76 times) than training on the entire dataset. The BlobGAN trained on the FDD-Coreset with \(k=10\) on three kidneys performs, in all cases, significantly faster (460 times) than training on the IED-Coreset with \(k=10\). We can conclude that training the BlobGAN on the FDD-Coreset with \(k=10\) on 3D MR human kidney images is significantly computationally more efficient than the entire dataset and the IED-Coreset with \(k=10\), and this is consistent with the comparison of computation time in Section 4.2. \(N_{glom}\) and mean \(aV_{glom}\) are reported in Tables 5 and 6, where the BlobGAN trained on the entire dataset (1000 random samples), the BlobGAN trained on the IED-Coreset with \(k=10\) and the BlobGAN trained on the FDD-Coreset with \(k=10\) are compared to the data from unbiased dissector-fractionator stereology [18]. We used these stereology data from [19] as ground truth and calculated \(aV_{glom}\) based on the method from [37]. The \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Human Kidney** & **Entire Dataset** & **IED-Coreset (\(k\) = 10)** & **FDD-Coreset (\(k\) = 10)** \\ \hline CF 1 & 91,325.20 & 547,800.21 & 1195.58 \\ CF 2 & 91,382.40 & 547,801.81 & 1180.38 \\ CF 3 & 91,515.60 & 547,772.61 & 1199.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Computation time comparison of BlobGAN trained on entire dataset (1000 random samples), IED-Coreset (\(k\) = 10) and proposed FDD-Coreset (\(k\) = 10) on 3D human kidney images (unit: seconds).