# A Deep-Learning-Based Quality Control Evaluation Method for CT Phantom Images
## 2 Materials and Methods
### Phantom Images for Evaluation Criteria  
For spatial resolution, the CTA YOLOv8 results are shown Figure 11. The mean average precision (mAP) was used as the performance metric to assess object detection accuracy, as the task was to detect each object as either a pass or non-pass.  
Figure 11: (**a**) Sample nonpass images of CTA-YOLOv8 applied for spatial resolution; (**b**) Sample pass images of CTA-YOLOv8 applied for spatial resolution.  
Figure 10: (**a**) YOLOv8 C2f structure; (**b**) the new C2f + Swin Transformer block structure.  
First, to calculate AP, we calculate the number of true positives (TP), false positives (FP), and false negatives (FN). TP is depicting representing the number of positive objects predicted to be positive objects. FP indicates the number of negative objects that are predicted as positive objects. FN represents the number of positive objects that are predicted to be negative objects.  
Second, we calculate precision and recall. Recall is the probability value of how true a judgment or prediction is among those that are true. The denominator is the total number of things that are true, and the numerator is the value that was actually predicted to be true. The formula is calculated as follows:  
\[Recall=\frac{TP}{TP+FN} \tag{1}\]  
Precision is the probability value that the judgment or prediction is actually true. The denominator is the total number of true predictions, and the numerator is the value that was actually predicted to be true. The formula is calculated as follows:  
\[Precision=\frac{TP}{TP+FP} \tag{2}\]  
Finally, we create PR curves that are graphs of the relationship between precision and recall. The graph calculates the precision values of the thresholds for each confidence value when recall is increased by 0.1. Confidence is a score that indicates how reliable the detection is. And if there are multiple objects, mAP, which is the average value for each item of AP, is used. The formula is calculated as follows:  
\[mAP=\frac{\sum_{i=1}^{2}AP_{i}}{2} \tag{3}\]  
Because the presence or absence of detection was more important than the exact location accuracy in the test images, the Intersection over Union (IoU) threshold was set to 50% instead of the typical threshold of 95%. The formula is calculated as follows:  
\[IoU=\frac{area\ of\ overlap}{area\ of\ Union} \tag{4}\]  
Further, a confidence threshold of 50% was used considering the importance of accurately detecting objects over the general object detection confidence.  
For contrast resolution, the CTA YOLO results are shown in Figure 12. The circles are the objects for detection. The object detection process for the images was conducted in a manner similar to that for the spatial resolution. Phantom evaluation criteria were subsequently applied to the detected images. If any of the circles up to the fifth circle was detected, it was considered a pass. Custom Contrast Resolution Accuracy (CCRA) is expressed as the number of images correctly identified as pass or fail among the images obtained through object detection images (TODI) across the number of total test images. The formula is calculated as follows:  
\[CCRA=\frac{TODI}{tthe\ number\ of\ total\ test\ images} \tag{5}\]