The detection results of (b)-(h) show that all methods have identified the insulator string. However, there was a false alarm in M-YOLO v3, and three more insulator strings were detected in detail. Meanwhile, the predicted boxes from D-YOLO v3, M-YOLO v4, and D-YOLO v4 exhibit a relatively larger error on the right border. On the contrary, YOLO v5, Pi-FT, and Pi-index provide the more accurate localization for the insulator string.
In the detection of insulators, YOLO v5, Pi-FT and our proposed Pi-Index correctly identified seven insulators (annotated in IDID) and the other methods had missed insulators to varying extent. This demonstrates that the Pi-Index achieved competitive results on the annotated insulators in IDID. Furthermore, the IDID dataset lacks annotations at positions (6), (7), (10), (11), and (12). Based on the aforementioned analysis, we further compared the performance of YOLO v5, Faster RCNN, and Pi-Index on unannotated insulators. recognized the unannotated insulators at positions (7) and (10). Therefore, both annotated and unannotated experimental results proved the effectiveness of Pi-Index.

4.4.2 Detection results under 0.7 annotation percentage

A decrease in data annotations inevitably results in a decline in the performance of the model. This circumstance facilitates a more comprehensive exploring the performance of different algorithms under imperfect labeling conditions. In this section, we further increase the proportion of unlabeled targets in the dataset. In detail, we randomly delete 30% of the labels in the IDID dataset. The detection results of different methods are organized in Table 3, and the visualization of annotated and predicted boxes is shown in Figure 8 (II).
From Tables 2 and 3 (1.0 vs. 0.7 APCs), it can be seen that each method’s performance in Table 3 has declined compared with the counterpart in Table 2. Meanwhile, the performance differences between the various methods become more significant while maintaining consistency in trends. As detailed in Table 3, YOLO v5 surpassed other one-stage detectors (rows 1-4) with an AP value of 72.2%. Nevertheless, the AP, AP@0.75, and AP@0.5 of Faster RCNN are 3.84%, 1.08%, and 1.66% higher than those of YOLO v5, respectively.
Compared with Faster RCNN, the AP value of Pi-GS, Pi-FT, and Pi-Index have shown improvements of 2.56%, 2.91%, and 3.53%, respectively. This indicates that the addition of PU loss can effectively alleviate the effect of missing labels. From the last three rows in Table 3, Pi-Index achieved the best performance with an AP value of 79.57%, an AP@0.75 of 89.45%, and an AP@0.5 of 92.64%, which also outperformed other mainstream algorithms in each category’s AP. As depicted in Table 2, when compared to Pi-GS and Pi-FT, Pi-Index exhibits a marginal improvement in the AP metric by less than 0.50%. But in Table 3, the AP of Pi-Index increased by 2.56% and 2.91% compared to those of Pi-GS and Pi-FT, respectively. This proves that the Pi-Index can achieve more significant performance improvements as the amount of unlabeled data increases.
Figure 8 (II) displays the detection results of seven methods, which are identical to those depicted in Figure 8 (I), under an APC of 0.7. The two columns in Figure 8 (II) correspond to two images with insulators. The first image or column contains a total of two insulator strings and 12 insulators. The insulators within the left-hand string are distributed evenly and appear relatively large in the image. Whereas the insulators in the right insulator string are densely arranged, and some insulators therein are occluded due to shooting reasons. Consequently, distinguishing the insulators located on the right side poses a greater challenge compared to those on the left side. According to the IDID dataset, the insulators at positions (2), (3), (5), (6), and (7)-(12) have been annotated as “Good”, while the insulator at position (4) has been labeled as “Broken”.
From (b)-(h) in the first column of Figure 8 (II), all methods have successfully identified the insulator string on the left, whereas they failed to identify the insulator string on the right. This discrepancy is presumably due to a greater degree of occlusion affecting the insulator string on the right. Both M/D-YOLO v3 and M/D-YOLO v4 exhibited larger localization errors for the left insulator string compared to other methods. Specifically, the lower bounds of the predicted boxes for M/D-YOLO v3 and D-YOLO v4 exceeded the ground-truth lower bound by a large amount. The localization error of M-YOLO v4 was reflected in the larger predicted box, which enclosed the GT-Box. Furthermore, the Pi-Index possessed the highest overlap between its predicted box and the GT-Box than YOLO v5 and Pi-FT. These results indicate that the Pi-Index is more accurate for localizing insulator strings.
For small target insulators, M-YOLO v3 and YOLO v5 exhibited subpar performance with an accuracy rate below 50%. D-YOLO v3, M-YOLO v4, and Pi-FT successfully detected seven insulators. The first six insulators detected by all of them are positions (3)-(5), (7), (9), and (10). The seventh insulator detected by D-YOLO v3, M-YOLO v4, and Pi-FT is position (1), (2), and (12), respectively.
Furthermore, D-YOLO v4 and Pi-Index have correctly identified 8 insulators, indicating that these two methods outperformed the previously mentioned methods. For the localization of the left insulator strings, the predicted box of D-YOLO v4 was shifted to the right side of the GT-Box. Additionally, the lower boundary of the predicted box extended beyond the GT-Box. Contrastingly, Pi-Index generated a predicted bounding box that exhibited a large overlap with the GT-Box. Furthermore, we conducted a comparative analysis between D-YOLO v4 and Pi-Index based on their respective performance in detecting insulators within insulator strings. In the case of the left insulator string, both D-YOLO v4 and Pi-Index correctly identified the insulators at positions (1)-(4). However, D-YOLO v4 exhibited a large offset when locating insulators at positions (1) and (2). Within the right insulator string, both D-YOLO v4 and Pi-Index detected four insulators. Despite these detected insulators being located at different positions, there was a significantly greater overlap between GT-Boxes and the predicted bounding boxes produced by Pi-Index than those produced by D-YOLO v4. In conclusion, the proposed Pi-Index exhibits superior performance to the comparison algorithm in terms of both the number of correct detections and localization accuracy.
The second column of both Figure 8 (I) and (II) shared the same image or detection scenario. This scenario consisted of one insulator string and 12 insulators. It is worth noting that the same scenario was applied with different data APCs during the training process, which led to different detection results. The following analysis is based on APC = 0.7.
In Figure 8 (II), with the exception of M-YOLO v3, all other methods failed to successfully identify the insulator string. This may be attributed to the fact that during the process of reducing the APC, labels for insulator strings within similar scenes were randomly eliminated, resulting in their being interpreted by the network as background. However, M-YOLO v3 misclassified the insulators at positions (2)-(7) as an insulator string. Combining the detection results of M-YOLO v3 under APC=1 (in the second column of Figure 8 (I)), it can be seen that M-YOLO v3 identified up to four insulator strings. These identified insulator strings only encompassed a portion of the insulators present within the annotated insulator string. Therefore, we may conclude that M-YOLO v3 has a tendency to identify a series of consecutive insulators as forming an insulator string, rather than detecting the entire insulator string. Contrastingly, the remaining methods failed to detect the insulator string.
Table 4: Detection results of our method and the baseline method with (APC=0.5) in the training process.