# A Deep Learning-Based Fragment Detection Approach for the Arena Fragmentation Test
## 2 Deep Learning-Based Fragment Detection
### Faster R-CNN Based Fragment Detection Algorithm  
A Faster R-CNN network can learn to detect specific objects through supervised learning. For such supervised learning, a labeled image showing the position (bounding box) of the object in the learning data is required. In addition, due to the nature of deep learning, a large amount of learning data is required for learning. However, warhead fragment images have no public image and are difficult to acquire compared to general images. In this study, a warhead fragment image dataset was created using a high-speed camera, and a suitable fine-tuning technique was used to perform effective learning with the dataset.  
The warhead fragment image dataset will be described in detail in Section 3.1, and this section describes the Faster R-CNN network suitable for warhead fragment detection. In this paper, the Faster R-CNN object detector was trained to detect the FPF. There are two classes: (1) FPF and (2) non-FPF. The false positives indicate non-FPFs (i.e., background or flames), which are incorrectly determined as FPFs by the Faster R-CNN. On the other hand, the false negatives indicate FPFs that are incorrectly determined as non-FPFs by the Faster R-CNN.  
The proposed warhead fragment detector uses a pre-trained Faster R-CNN object detector, which includes an Inception-v2 [29] model trained with the MS-COCO [30] dataset. The warhead fragment image dataset was then used to fine-tune the pre-trained Faster R-CNN's feature extractor and classifier. As described above, the RPN used in the Faster R-CNN searches for each pixel location for a bounding box representing the location of the object from the extracted feature point map. In this case, the bounding box candidates may be previously defined in a form suitable for warhead fragments based on a predefined anchor box size and aspect ratio.  
The original paper combines three scales (0.5, 1, and 2) and three aspect ratios (2:1, 1:1, and 1:2) based on an anchor box with a \(256^{2}\) pixel area, as shown in Table 1. A total of nine anchor boxes were previously defined. However, since warhead fragments are small objects with a minimum area of 3 pixels compared to the \(640\times 480\) warhead fragment image size, it is not suitable to use 256 anchor boxes for warhead fragment detection. Therefore, in order to accurately detect warhead fragments, this study shows that the RPN anchor box is divided into five scales (0.125\(\times\), 0.25\(\times\), 0.5\(\times\), 1\(\times\), and 2\(\times\)) based on a \(64^{2}\) pixel area anchor box.  
By combining three aspect ratios (4:3, 1:1, and 3:4), a total of 15 anchor boxes were newly defined to be suitable for detecting warhead fragments and used for learning as shown in Figure 8. In the original Faster R-CNN, for each anchor box, if the intersection-over-union (IoU) was more than 0.7 then there was an object and if the IoU was less than 0.3 then there was no object. Different from that, in this paper, if the IoU was more than 0.1 then there was a FPF. This is because the size of FPFs is very small.  
Our contributions in the task of Faster R-CNN based fragment detection are summarized as follows:  
* To the best of our knowledge, our work is the first to demonstrate the applicability of deep learning based object detection approaches for analyzing AFT images acquired by a high-speed camera;  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Types of Objects** & **Scale** & **Aspect Ratio** \\ \hline General object & \(\{128^{2},\,256^{2},\,512^{2}\}\) & \{2:1, 1:1, 1:2\} \\ Warhead fragment & \(\{8^{2},\,16^{2},\,32^{2},\,64^{2},\,128^{2}\}\) & \{4:3, 1:1, 3:4\} \\ \hline \hline \end{tabular}
\end{table}
Table 1: The hyper-parameters of the anchor boxes.  
* We have verified that a two-step approach (such as Faster R-CNN) is more suitable for detecting warhead fragments (very small objects) compared with a single-stage approach (such as SSD);
* We have empirically found the hyper-parameters of anchor boxes that are optimal for detecting warhead fragments.