# Object Detection for Brain Cancer Detection and Localization
## 3 Experimental Analysis
### The Results
It takes into account false negatives, which are cases that should have been flagged for inclusion as positive but were incorrectly classified as negative by the model. Recall can be computed as  
\[Recall=\frac{TP}{TP+FN}\]  
As the number of epochs increases, both precision and recall should exhibit an upward trend. This trend, indeed, is demonstrated in the graphs depicting these metrics. Notably, precision and recall values ranging from 0 to 1 are considered desirable. Achieving precision and recall values exceeding 0.9 in the final epochs is particularly noteworthy, as it indicates that the deep learning model has effectively learned and achieved high performance in the task at hand. Specificity (also called true negative rate) represents the probability that an actual negative will test negative. It is computed as follows:  
\[Specificity=\frac{TN}{TN+FP}\]  
AP (i.e., average precision) is a widely used metric for evaluating the accuracy of object detectors: it computes the average precision value by considering the recall values ranging from 0 to 1. Average precision provides a comprehensive measure of the model's performance across different recall levels and is a valuable metric for assessing the accuracy and effectiveness of object detection algorithms. The computation of mean average precision (mAP) involves several components, including intersection over union (IOU), precision, recall, precision-recall curve, and average precision (AP). In object detection, models predict both the bounding box and the category of objects within an image. IOU is utilized to evaluate whether the predicted bounding box accurately matches the ground truth bounding box. It quantifies the overlap between the predicted and actual bounding boxes. The precision-recall curve showcases the trade-off between precision and recall for various classification thresholds. It provides insights into the model's performance across different operating points. AP (average precision) is the average precision calculated at each point on the precision-recall curve. It summarizes the model's overall performance in object detection. To calculate mAP, the AP values obtained from multiple classes or categories are averaged, providing a comprehensive evaluation of the model's performance across all object classes. IOU (intersection over union) is a measure that quantifies the extent of overlap between two bounding boxes. It is calculated as the ratio of the intersection area to the union area of the two bounding boxes. The IOU value ranges from 0.0 to 1.0, where 1.0 indicates a perfect match or complete overlap, and 0.0 indicates no overlap at all. The formula for computing the IOU is defined as follows:  
\[IOU=\frac{Area\ of\ Intersection}{Area\ of\ Union}\]  
This formula compares the regions covered by two bounding boxes and provides a standardized measure of their overlap, which is useful in evaluating the accuracy of bounding box predictions in object detection tasks. During the evaluation of object detection models, it is essential to establish a criterion for determining successful recognition based on the overlap of bounding boxes with ground truth data. IOUs (intersection over union) are employed for this purpose. The metric [EMAIL_ADDRESS] represents the accuracy when an IOU threshold of 0.5 is used. In other words, if the overlap between the predicted bounding box and the ground truth bounding box exceeds 50%, the detection is considered successful. As the IOU threshold increases, the required accuracy for bounding box detection becomes stricter, making it more challenging to achieve. Consequently, a higher IOU threshold, such as [EMAIL_ADDRESS], typically yields a lower mAP value compared to [EMAIL_ADDRESS]. This indicates that achieving accurate bounding box detection with a higher overlap requirement is more difficult. The mean average precision (mAP) is calculated as an average of the average precision (AP) values. Each AP value represents the precision-recall trade-off for a specific class in object detection.