Rows 1-6 of Table 2 display the detection results of PN-based, primarily from one-stage (rows 1-5) and two-stage (row 6) networks. YOLO v5 significantly outperforms other one-stage networks with an Average Precision (AP) of 84.50%, an AP@0.75 of 96.20%, and an AP@0.5 of 98.30%. However, the two-stage Faster RCNN achieved an AP of 87.19%, which is approximately 2.69% higher than YOLO v5. This demonstrates that Faster RCNN exhibits the best performance among the above PN learning frameworks.
PU-based methods with Faster RCNN as the backbone are represented in rows 7-9 of Table 2. They have improved detection performance in comparison with PN-based detectors. Among these methods, our proposed Pi-Index obtained the highest performance with an AP metric of 88.25%, which to some extent indicates the advantage of Pi-Index in estimating the class prior. Moreover, the AP values of Pi-GS [49] and Pi-FT [34] are 0.41% and 0.18% lower than Pi-Index, respectively. The reason may be that their class prior estimates are based on a hyper-parameter or a fixed threshold. This parameter or threshold is determined via grid search, but the search interval of 0.1 may stride over the optimal value and further lead to performance deterioration.
Figure 8 (I) shows the detection results of various methods with APC=1. The different columns correspond to different insulator detection scenarios, while each row is the detection result of a particular method. Rows (a)-(h) display manual labels and prediction results of M-YOLO v3, D-YOLO v3, M-YOLO v4, D-YOLO v4, YOLOv5, Pi-FT, and our Pi -Index. The green solid and red dashed boxes in the figure represent the Ground-Truth bounding Boxes (GT-Boxes) and predicted boxes, respectively. The text in the upper left corner of each GT-Box and predicted box individually indicates the annotated and predicted category, including: “String”, “Good”, “Broken”, and “FlashDamged”. To facilitate the analysis of prediction results, yellow arrows are employed to number those small and densely arranged insulators. The analysis of detection results is divided into two aspects: 1) The count of correctly detected insulators, i.e., whether any insulator strings or insulators were missed or detected repeatedly; 2) The localization accuracy of predicted boxes for the insulator strings or insulators.
In the first column of row (a), there is one insulator string and 13 insulators. In detail, the insulators at positions (1)-(4) and (9)-(12) are labeled as “Good”, while those at positions (5), (7), and (13) are labeled as “Broken”. However, the insulators at positions (6) and (8) are not labeled. All methods successfully identified the insulator string. Furthermore, the comparison of (b)-(e) and (f)-(h) reveals that M/D-YOLO v3 and v4 exhibit larger errors than YOLO v5 and two-stage algorithms in locating the string.
For the small-scale insulators, all methods correctly identify and accurately locate those at positions (1)-(3) and (7). The detection errors of each method are mainly concentrated on positions (5) and (13). Primarily, the “Broken” insulator at position (5) is misidentified as “Good” by M-YOLO v3, D-YOLO v3, and YOLO v5, misclassed as “FlashDamaged” by D-YOLO v4, and repeatedly identified as both “Good” and “Broken” by Pi-FT. Only M-YOLO v4 and the method proposed in this paper manage to correctly identify it. Next, the “Broken” insulator at position (13) was missed by M-YOLO v3, M-YOLO v4, and YOLO v5. It was misidentified as “Good” by D-YOLO v3 and “FlashDamaged” by D-YOLO v4. Only Pi-FT and our proposed method correctly identified it. By comprehensively considering the detection results of position (5) and (13), it reveals that M-YOLO v4, Pi-FT, and Pi-Index demonstrate superior performance.
Compared with Pi-Index, M-YOLO v4 not only misclassed the “Good” at position (9) as “Broken” but also missed the insulators at positions (10)-(12). In the detection results of Pi-FT, false alarms occurred at positions (4) and (5). They individually belong to the categories of “Broken” and “Good”, but are simultaneously identified as both “Good” and “Broken”. This further substantiates the superiority of the Pi-Index over the other two algorithms. There are another two unlabeled targets at positions (6) and (8). Neither M-YOLOv4 nor YOLO v5 recognized them, while M-YOLO v3 and D-YOLOv4 only recognized positions (6) and (8), respectively. By contrast, D-YOLO v3, Pi-FT, and ours recognized the insulators at positions (6) and (8). In summary, our proposed method not only achieves the overall best performance for the labels provided by IDID but also yields competitive results on unlabeled data.
The second column in Figure 8 (I) contains one insulator string that is composed of 12 insulators. However, seven insulators therein were annotated in IDID as either “Good” or “Broken”. The former category includes six insulators at positions (1)-(4), (8), and (9), while the latter category includes only one insulator at position (5). It is worth noting that the insulator at position (9) was repeatedly annotated as “Good”.
Table 3: Detection results of our method and the baseline method with (APC=0.7) in the training process.