# Object Detection for Brain Cancer Detection and Localization
## 3 Experimental Analysis
### The Results  
Figure 3 presents a collection of plots illustrating the performance of the proposed model for detecting and localizing brain cancer. The 50 epochs were completed in 0.095 h by exploiting an NVIDIA Tesla T4 graphic card with 16 GB of memory, with a CUDA Version equal to 12.0. Moreover, we used the 3.10.12 version of the Python compiler with the Torch library (version 2.0.1). In detail, in Figure 3 there are 12 plots, 6 plots in each line. The first plot in Figure 3 (i.e., the Box plot) shows the box loss metric trend. The plot represents the training step, where the values of the loss are plotted on the \(y\)-axis (ordinates), and the different epochs are represented on the \(x\)-axis (abscissa). In object detection tasks, which involve both localization and classification, the primary method for localizingmultiple objects in an image is through bounding boxes. The loss function used in this context calculates the error between the predicted bounding boxes and the ground truth bounding boxes. The goal of this loss function is to minimize the discrepancy between the predicted and actual bounding boxes. As the loss decreases over epochs, it indicates that the network is learning and improving its ability to accurately predict tight bounding boxes. The second plot in Figure 3 (i.e., Objectness) shows the objectness loss. In the training step, the plot represents the behavior of the objectness and class score in the deep learning model for object detection. The objectness refers to the confidence of the model in the presence of an object within a given bounding box. On the other hand, the class score represents the conditional probability of a specific class, given that an object exists in that box. The total confidence score for each class is obtained by multiplying the objectness and the class score. In this scenario, it is desirable for the objectness to decrease towards zero as the number of epochs increases. This indicates that the model becomes more confident in accurately detecting the presence of objects. Therefore, the plot shows the trend of the objectness scores over the epochs during the training process. The third plot in Figure 3 is related to the Classification. In the training step, the plot illustrates the classification aspect of the object detection task. The objective of classification is twofold: to determine whether an object is present in the image and to identify the specific class of the object. In the plot, the loss for classification is depicted, which assesses the accuracy of the classification for each predicted bounding box. Each bounding box can potentially contain an object class or be classified as \"background\". The loss function commonly employed for classification tasks is the cross-entropy loss. The plot showcases the progression of the cross-entropy loss over the epochs during the training phase. It reflects how well the model is learning to correctly classify objects within the predicted bounding boxes. The val Box, the val Objectness, and the val Classification plots are related to the loss trends for the box loss metric, for the objectness, and for the classification loss relating to the testing dataset: as in the previous plots, in these cases we expect a decreasing trend when the number of epochs increases. The fourth and the fifth plots (i.e., Precision and Recall) show the value for each epoch for the precision and the recall metrics. Precision is a metric that quantifies the proportion of positive predictions that are accurately classified. It takes into consideration the occurrence of false positives, which refers to cases that were incorrectly identified as positive or flagged for inclusion. Precision can be computed as  
\[Precision=\frac{TP}{TP+FP}\]  
Figure 3: The experimental analysis results. Recall, also known as sensitivity or true positive rate, is a metric that assesses the proportion of actual positive instances that were correctly predicted as positive by the model.