## 4 FDA-SSD Network
### Issues Related to Depth Values  
It is worth noting that our FDA-SSD model still needs to clarify three important issues:  
1. For the FDA-SSD-based detection-and-tracking framework, the detection model has not yet detected the target sample to be tracked when the first frame of the image is given. Therefore, the target depth value cannot be obtained.
2. For the Nth frame image, the input depth value is the depth information calculated from the N \(-\) 1 frame instead of the current frame.
3. The scale of the training sample may not be consistent with the size of the tracking target during visual inspection. The same depth information does not match the same 2D-image scale. Therefore, the algorithm needs to normalize parameters such as the depth and the target scale. The above three issues were discussed and analyzed as follows:  
1. In most detection and spatial-positioning models, the basis of the 3D-spatial-positioning algorithm is to obtain the detection results of the 2D-projection surface. Therefore, during the process of using the FDA-SSD model, the depth-assisted module was not adapted by default when the first frame of the image was initialized for detection. Instead, detectors at all scales were directly employed to detect the target and obtain the initial-value 2D-tracking anchor frame. Then, the spatial-positioning-and-tracking algorithm in Section 5 was adapted to obtain the initial depth value \(D_{0}\) of the target.  
Figure 5: FNN structure of classification for depth value.  
Given the tracking problem based on real-time video streams, adjacent images have strong relevance. In other words, the positions of the \(\mathrm{N}-1\)th frame target and the N frame target are very close in most cases. Therefore, the depth information of the \(\mathrm{N}-1\) frame can be adapted to assist the detection of the Nth frame. There are some extreme situations. For example, the high-speed movement of the target in the radial direction of the camera results in a large gap between the depth values of frame \(\mathrm{N}-1\) and frame N. In this case, we can obtain the movement trend of the target through the target-tracking algorithm and turn on the corresponding scale detector of the corresponding \(\mathrm{N}-1\) frame and its adjacent detectors to expand the scale-detection interval. Concerning general detection, when the depth information of the target moves between two scale detectors, the close FNN output-estimation probabilities \(y_{i}\) and \(y_{i+1}\) indicates that the target can be detected on both the \(i\)-th and \(i+1\)-th scale detectors. At this point, we can open the two road detectors to perform directory detection.
3. Since there may be differences between the sample scale and the real target scale in practical applications, similar triangular properties of the projection should be employed to return the depth value to a unified standard, as illustrated in Figure 6.  
We defined the normalized depth value of the sample in each frame of the image when training the FDA-SSD model:  
\[D_{norm}=\frac{D_{s}}{\lambda_{s}}, \tag{3}\]  
The normalized depth value of the FDA-SSD model when tracking targets in practical applications:  
\[D_{norm}=\frac{D_{0}}{\lambda_{0}}, \tag{4}\]  
It can be observed that when the ratio of the depth value \(D_{s}\) of the training sample to the scale value \(\lambda_{s}\) is equal to the ratio of the depth value \(D_{0}\) of the actual detection target to the scale value \(\lambda_{0}\), the normalized scale \(\lambda_{norm}\) projected on the 2D-image plane is also the same according to the nature of similar triangles. Therefore, the training depth information is actually normalized depth information obtained from the samples. In the test, the input is the normalized deep learning of the target obtained by the tracking algorithm.