# CPDet: Circle-Permutation-Aware Object Detection for Heat Exchanger Cleaning
## 4 Results
### Ablation Experiments  
We used the \(mAP\) as the evaluation metric for the ablation experiments, where \(mAP_{50}\), \(mAP_{90}\), and \(mAP_{50.95}\) represent the average precision calculated at IoU thresholds of 0.5, 0.9, and within the range from 0.5 to 0.95, respectively. In analyzing interval prior information, this work applied the trimmed mean, arithmetic mean, mode, and median to generate representative interval priors, where the trimmed mean is an average that excludes a small fraction of the highest and lowest values to reduce the impact of outliers. The arithmetic mean is the sum of all values divided by the number of values, representing the average. The mode is the value that occurs most frequently in a dataset. The median is the middle \begin{table}
\begin{tabular}{l c} \hline \hline
**Detection Head** & **Anchor Size** \\ \hline Small & [10,13], [16,30], [33,23] \\ Medium & [30,61], [62,45], [59,119] \\ Large & [116,90], [156,198], [373,326] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Anchor box size. Figure 8: The circle representation provides a more intuitive localization for the circle holes compared to the square representation. Additionally, the circular representation fits the circle holes more closely, leading to more accurate area calculations. Therefore, using the circular area to control the water output of the cleaning machine is more precise. value when a dataset is ordered from least to greatest. When utilizing the trimmed mean as the interval statistical approach, we set a trimming ratio of 10%, which was based on practical considerations, and a trimming rate of 10% was used to effectively removed a portion of the outliers while ensuring that a substantial portion of the data remained incorporated into the final mean calculation, thereby securing the representativeness of the outcome. Depending on the statistical method of prior information will have a certain impact on the training results. According to Table 3, the trimmed mean (10%) method various indicators of the training results were the best. Compared to the arithmetic mean, the trimmed mean enhanced the robustness of the analysis and marked the results more reliable by preprocessing the data, which involved eliminating potential outliers. The statistical anomaly for interval prior information is particularly important. The more the prior interval can represent the intervals between circular targets in the entire dataset, the more accurate the subsequent prior fusion results of the circle domain and background domain features will be. Table 3 shows the statistical interval prior values obtained at different trimming rates (for the convenience of subsequent calculations, the interval prior directly assumes integral values), as well as the average accuracy obtained when applying these prior values for subsequent model training. It can be clearly found that when the trimming rate was 10%, the \(mAP_{50.95}\) was maximized, indicating that the interval prior value obtained when the trimming rate was 10% is the most representative of the intervals between circular targets in the entire dataset. Table 4 shows the circle domain and background- domain extracted under different interval information, and it can be intuitively seen that the pixel interval value obtained with a trimming rate of 10% can well separate the circle domain and background domain. Figure 9 shows that the interval prior significantly affected the segmentation outcome. At a trimming rate of 10%, the intervals obtained are the most precise. Inaccuracies in the interval prior can result in the conflation of the circle domain with the background domain, which can adversely impact the feature extraction in subsequent networks. Simultaneously, a comparative experiment was conducted targeting the weakening background domain, involving attenuating the coefficient matrix across a range from 0 to 1 in increments of 0.2, as shown in Table 5. The experimental outcomes reveal that the optimal performance was achieved when the weakening factor was set at 0.6.