# Automatic Boundary Extraction for Photovoltaic Plants Using the Deep Learning U-Net Model
## 3 Results and Discussion
### Results with DL-Based Techniques  
The training data consisted of 2864 aerial images selected at random: 90% of the training dataset in the Amir database. The validation data were the remaining 10% of the same training dataset. Figure 5a shows the loss function and _IoU_ metric of the FCN model during the training and validation process. The general trend of the two curves is consistent, showing that the network converges rapidly and is stable at iteration 30, and the loss value tends to 0.04%. Figure 5b shows the _DC_ metric of the model during the training and validation stage. The general trend of the two curves is consistent at iteration 30. On the other hand, using the same metrics, the U-net model proposed in this work shows a better performance. Figure 6a shows the loss function and _IoU_ metric of the model during the training and validation stage. The common trend of the two curves shows the network converges quickly and is stable at iteration 16, and the loss value tends to 0.03%. Figure 6b shows the _DC_ metric of the model all along the training and validation phase. The prevalent trend of the two curves is consistent and in iteration 16. In the evaluation stage, 716 images were used along with the trained FCN model for PV plant detection. Some relevant results are shown in Figure 7. In this figure, the columns correspond to different PV plants. The first row contains the original images; the second row, the original masks; and, the third one, the predicted masks. The images used were taken in deserted regions and vegetation zones. The FCN model detects the PV plants in vegetation zones with some false positives. As an example, the second and third predictions of Figure 7 identify a lake and vegetation as part of the PV plants. In deserted regions, PV plants are detected more precisely. Although these images have very high precision, their predicted shape does not fully correspond to the original mask. Hence, it was necessary to review the performance metrics of the algorithm [63]. The segmentation results in the evaluation stage, using the same 716 images and the trained U-Net model, are shown in Figure 8. The arrangement is the same as in the previous Figure 7. It is noteworthy that this model correctly segments the photovoltaic plant while the other model does not achieve this result, as can be seen in the second and third predictions in Figure 8.  
Figure 5: Performance and metrics of the FCN model using the training and validation sets. Figure 6: Performance and metrics of the U-net model obtained using the training and validation sets. Afterwards, the trained model tested 716 samples. Table 3 shows the results and comparison among the TIP technique, the U-net proposed model and the FCN model used by [11], which was replicated in this study. The FCN and the proposed U-net models were  
Figure 8: Evaluation with test data U-net Model. Figure 7: Evaluation with test data FCN Model. compared. The accuracies obtained for the FCN model in the stages of training and testing were 97.99% and 94.16% respectively [11]. For U-Net proposed, the accuracy obtained in the stages of training and testing were 97.07% and 95.44%, respectively. Both results can be seen in Table 3.  
To compare the FCN model proposed by [PERSON] [11], and the U-net model proposed in this work, the two most used metrics in semantic segmentation problems were used. The FCN model was implemented with the standard _IoU_ metric, whose result for the training stage was 94.13%,and the validation stage was 90.91% and for test stage was 87.47%. The _DC_ metric of the validation 92.96% and test 89.61% which deviates a little from the training 95.10%. However, using the same metrics the U-net model proposed in this work shows a better performance. The _IoU_ metric obtained was 93.57% in the training stage, 93.51% in the validation stage, and 91.42% in the test stage. The _DC_ metric of the validation 94.44% was almost the same as that of the training 94.03% which deviates a little from the test 91.42%. Table 3 shows these results.