# CPDet: Circle-Permutation-Aware Object Detection for Heat Exchanger Cleaning
## 4 Results
### Discussion
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Methods** & \(mAP_{50}\) & \(mAP_{50}\) & \(mAP_{50.95}\) & **F1 Score** & **FPS** & **FLOPs** & **Memory Usage** \\ \hline YOLOv8s & 80.55\% & 71.75\% & 73.63\% & 74.96 & 114 & 43.9M & 13.51G \\ YOLOv8m & 82.21\% & 72.56\% & 74.91\% & 76.19 & 77 & 114.3M & 14.92G \\ YOLOv81 & 83.13\% & 72.84\% & 75.87\% & 78.88 & 53 & 229.1M & 16.72G \\ CPDet(v68) & 82.46\%(+1.91\%) & 73.35\%(+1.60\%) & 76.22\%(+2.59\%) & 77.99\%(+3.03) & 83 & 46.1M & 13.94G \\ CPDet(v8m) & 83.78\%(+1.57\%) & 74.16\%(+1.60\%) & 77.97\%(+3.06) & 78.15\%(+1.9\%) & 69 & 116.5M & 15.83G \\ CPDet(v8l) & 84.26\%(+1.13\%) & 75.85\%(+3.01\%) & 78.50\%(+2.63\%) & 79.58\%(+0.75) & 62 & 231.3M & 17.26G \\ YOLOv5s & 77.95\% & 72.96\% & 74.28 & 74.28 & 125 & 32.1M & 13.27G \\ YOLOv5m & 78.42\% & 73.75\% & 74.56\% & 74.65 & 94 & 98.2M & 15.85G \\ YOLOv5l & 79.93\% & 74.62\% & 74.34\% & 75.51 & 82 & 218.1M & 17.37G \\ \hline CPDet(v5s) & 80.83\%(+2.88\%) & 73.43\%(+0.47\%) & 74.60\%(+2.26\%) & 75.78\%(+1.50) & 91 & 34.2M & 13.98G \\ CPDet(v5m) & 81.71\%(+3.29\%) & 74.50\%(+0.75\%) & 75.24\%(+1.73\%) & 77.13\%(+2.48) & 85 & 100.3M & 16.45G \\ CPDet(v5l) & 82.95\%(+3.02\%) & 75.24\%(+0.62\%) & 76.13\%(+1.79\%) & 78.64\%(+3.13) & 80 & 220.2M & 18.87G \\ YOLOv10s & 80.94\% & 72.80\% & 72.98\% & 77.96 & 146 & 27.0M & 12.20G \\ YOLOv10m & 78.12\% & 73.98\% & 73.64\% & 77.62 & 125 & 79.3M & 14.00G \\ YOLOv10l & 79.65\% & 74.47\% & 74.71\% & 78.32 & 114 & 192.8M & 15.21G \\ CPDet(v10s) & 83.49\%(+2.55\%) & 73.89\%(+1.09\%) & 74.75\%(+1.77\%) & 78.37\%(+0.41) & 114 & 28.9M & 13.11G \\ CPDet(v10m) & 85.00\%(+3.67\%) & 75.23\%(+1.27\%) & 75.67\%(+1.79\%) & 78.91\%(+1.29) & 94 & 81.2M & 14.93G \\ CPDet(v10l) & 85.87\%(+2.88\%) & 75.09\%(+0.21\%) & 76.71\%(+2.41\%) & 79.02\%(+0.7) & 82 & 194.7M & 16.28G \\ \hline \hline \end{tabular} Note: “s”, “m”, “1” in (v8, v8m, v8l) means small, middle, and large models of YOLO benchmark. The blue background is to highlight the effect of adding our proposed module to the baseline using the method in parentheses, the red font represents the increment of each metric in that line compared to its corresponding baseline.  
\end{table} 
Table 8: The performance of the YOLO series and our method on the test set. the F1 Score increased by 6.5 for CPDet(v5), and the False Negative Rate (FNR), False Positive Rate(FPR) decreased by 0.11 and 0.07, respectively, for CPDet(v10), which means that on each image to be detected, there was about a 10% reduction in missed detections and false positives. Furthermore, by examining the model results running on the test set comparison in Table 7, it can be observed that for CPDet(v3), CPDet(v5), and CPDet(v10), different-size models saw an improvement of two to four percentage points in the \(mAP_{50}\). This intuitively reflects the effectiveness and plug-and-play practicality of our proposed module. However, compared to the general methods, our method showed a significant growth in fps and flops, the inference speed of CPDet(v8s) and CPDet(v10s) decreased by approximately 30 frames per second, and the flops increased near to 2.2 \(M\)  the same situation also occurred in other CPDet methods. Therefore, our method has limitations in terms of speed and computational complexity. Inevitably, compared to general methods, our method is only applicable to the current heat exchanger dataset; thus, there also exist limitations in terms of application generality. In Figure 10, we have selected examples from overly dark and overly exposed scenes for detection, and it can be more intuitively seen that the instances of False Negatives and False Positives significantly decreased after the incorporation of our method. According to the visual examples in Figures 10 and 11, it was observed that the False Negatives were primarily concentrated in the circle domain area, while the False Positives were mainly concentrated in the background domain area.