# YOLOv8 with Post-Processing for Small Object Detection Enhancement
## 5 Experimental Results  
Precision, Recall, AP (Average Precision), and mean Average Precision (mAP) are key evaluation metrics for assessing the performance of object detection algorithms. These metrics quantitatively measure the detection accuracy and reliability of a model, offering insights into its effectiveness under various conditions [34]. Precision refers to the proportion of correctly detected objects among all detected objects. In other words, it evaluates the model's ability to minimize false positives. Mathematically, precision is defined as follows:  
\[\text{Precision}=\frac{\text{True Positives (TP)}}{\text{True Positives (TP) }+\text{False Positives (FP)}} \tag{4}\]  
Higher precision indicates that the model effectively minimizes false positives, ensuring that only relevant objects are detected. This is a crucial evaluation metric, particularly in applications where false positives present significant challenges. Recall, in contrast, measures the proportion of actual objects correctly detected by the model among all real objects. In other words, it assesses the model's ability to minimize false negatives. Recall is calculated as follows:  
\[\text{Recall}=\frac{\text{True Positives (TP)}}{\text{True Positives (TP) }+\text{False Negatives (FN)}} \tag{5}\]A higher Recall means that the model can detect more objects, especially in critical object detection that should not be missed. AP represents the area under curve (AUC) of the Precision-Recall Curve, which represents the relationship between Precision and Recall, and is used as a single indicator of the performance of the model for a particular class. AP is defined as follows:  
\[\text{AP}=\int_{0}^{1}\text{Precision}(\text{R})\text{dR} \tag{6}\]  
Here, R represents Recall. In practice, AP is computed discretely by sampling Precision and Recall values at various confidence thresholds. AP is used to assess the trade-off between precision and recall for each class. mAP is obtained by averaging AP values across all classes, providing a measure of the model's overall performance. It is defined as follows:  
\[\text{mAP}=\frac{1}{\text{N}}\sum_{i=1}^{\text{N}}\text{AP}_{i} \tag{7}\]  
Here, N denotes the total number of classes. Specifically, [EMAIL_ADDRESS] refers to the average AP computed with a fixed Intersection over Union (IoU) threshold of 0.5. In contrast, [EMAIL_ADDRESS]:0.95 varies the IoU threshold from 0.5 to 0.95 in increments of 0.05 and averages the resulting AP values. [EMAIL_ADDRESS]:0.95 provides a more comprehensive performance evaluation by assessing the model's detection capability under varying IoU thresholds. In this study, these metrics were used for an objective evaluation of detection accuracy, and the results are presented in Table 1. The evaluation was conducted using a subset of the COCO 2017 test dataset. By leveraging the annotation information provided in the dataset, the detection results of the proposed model were compared with those of similar models, and the corresponding evaluation metrics were computed. In safety-critical tasks such as fire or defect detection, Recall and the more stringent [EMAIL_ADDRESS]:0.95 are the primary yardsticks, because missing a true alarm is costlier than raising a few false ones. Conversely, real-time monitoring systems that must minimize nuisance alerts tend to value Precision and the widely adopted [EMAIL_ADDRESS] threshold. Reporting all four metrics, therefore, provides a balanced view tailored to both risk-averse and precision-oriented scenarios. Figure 5 shows the detection results and shows the detection results of YOLOv8n, YOLOv8n-CARAFE, YOLOv8m, and YOLOv8n-CARAFE+CR, the model proposed in this study. It can be seen that the detection rate gradually increases from YOLOv8n to YOLOv8m, where the calculation cost is low. Finally, the model proposed in this study was based on YOLOv8n, but it can be confirmed that the highest detection rate appears through the additional technique proposed.