## 2 Materials and Methods
### Evaluation Methods
#### 2.4.2 Evaluation of Detection Accuracy Using Additional Metrics  
While the object detection model evaluated in Section 2.4.1 provided the AP for three classes, AP alone does not fully capture the accuracy of localization, particularly in the context of coronary artery detection. Since the object detection model was trained and evaluated on cross-sectional images from coronary CT scans, bounding boxes of 64 \(\times\) 64 pixels were centered on the vessels of interest. To assess whether the predicted bounding boxes were accurately centered on the target vessels, additional evaluation metrics beyond AP were introduced.  
To quantify the overlap between the predicted bounding boxes and the ground truth annotations, the proportion of bounding boxes achieving IoU > 0.5 was calculated for each class. IoU measures the ratio of the intersection area to the union area between the predicted and ground truth bounding boxes, as follows:  
\[IoU=\frac{\left|B_{p}\cap B_{g}\right|}{\left|B_{p}\cup B_{g}\right|}\]  
where \(B_{p}\) and \(B_{g}\) represent the predicted and ground truth bounding boxes, respectively. The percentage of bounding boxes meeting this threshold was computed and normalized by the total number of annotated vessels per class.  
Similarly, the Dice Similarity Coefficient (DSC) was calculated to evaluate spatial overlap, using the following formula:  
\[DSC=\frac{2\left|B_{p}\cap B_{g}\right|}{\left|B_{p}\right|+\left|B_{g}\right|}\]  
For each coronary artery class--right coronary artery (RCA), left coronary artery--left anterior descending (LCA-LAD), and left coronary artery--circumflex (LCA-CX)--the number of bounding boxes with DSC > 0.5 was determined, and the results were normalized as with IoU.  
To further evaluate localization accuracy, an additional analysis was conducted based on the midpoints of the bounding boxes. Since each bounding box was expected to be centered on a coronary artery, measuring the deviation of the detected bounding box center from the ground truth annotation provided an intuitive assessment of localization performance. The Euclidean distance between the midpoints of the predicted and ground truth bounding boxes was computed using the following equation:  
\[d=\sqrt{\left(x_{p}-x_{g}\right)^{2}-\left(y_{p}-y_{g}\right)^{2}}\]  
where (\(x_{p}\),\(y_{p}\)) represents the coordinates of the predicted bounding box center, and (\(x_{g}\),\(y_{g}\)) represents the coordinates of the ground truth bounding box center. For each image, the centroid of the ground truth bounding box was compared to the centroid of the detected bounding box, and the smallest distance among detected instances was considered as the localization error. The mean of these distances was used as the Mean Absolute Error (MAE) to quantify how far the detected bounding box centers deviated from the actual vessel centers. Additionally, to ensure consistency with the clinical applications, the pixel-wise MAE values were converted into millimeters using the known spatial resolution of the CT images. To account for the variations across the different patient subsets and ensure robust evaluation, a five-fold cross-validation was performed, and all the above metrics (IoU, DSC, and MAE) were evaluated separately for each fold.  
By combining these evaluations, a more comprehensive assessment of detection accuracy was obtained. The IoU- and DSC-based analysis provided insights into the spatial overlap between the detected and ground truth bounding boxes, while the midpoint deviation analysis directly quantified how precisely the bounding boxes were centered on the target vessels (Figure 2). These additional evaluations complemented AP by offering a more detailed understanding of both spatial alignment and localization precision.