# Deep Learning-Based Consistent Object Detection in Distance on Highly Perspective Region
## 3 Generation of a Virtual Video and Appearance Attributes of the Moving Vehicles
### Comparison of AC for Single-Vehicle  
Based on the two distinct datasets, AC with a single vehicle object is investigated with a comparison of the AV of the vehicle on both datasets. The specified vehicle object undertakes uniform motion at a constant velocity of 100 km/h, progressing in the the -Z direction. Then, a script on the UNITY engine was created to save the actual location of the vehicle in world coordinate system, the location of the vehicle on the video, and the object information at a certain time, which was obtained in the run of the UNITY engine. All the information was saved in a file and then used for analyzing the ACs in this section. A comparison of ACs for the actual trajectory of the vehicle object in OI and TI coordinate systems is presented in Figure 7.  
The genuine trajectory of the vehicle aligns with the \(-\)Z direction in WCS. The computation of AV, however, is conducted in the \(-\)y direction within the image plane of Figure 5. The movements of the vehicle on ORG and TRANS are determined in the image plane of CCTV, as shown in Figure 6. Additionally, the bounding box of the vehicle is drawn, and the movement of the base line of the box is harnessed for calculating AV, utilizing pixel values along the vertical axis. The variation in pixel values, termed \"dy\" along with the defined time interval \"dt\", facilitates the expression of AV through the following Equation (2).  
\[\text{AV}=\frac{\text{dy}}{\text{dt}} \tag{2}\]  
The variation in AVs computed on both image planes, ORG and TRANS, is compared in Figure 7a. The observed trend in Figure 7a illustrates a pronounced reduction in AV along the ORG as the vehicle retreats from the installation point of the CCTV. This phenomenon can be attributed to the effects of perspective, wherein the AV tends to approach a nominal value upon traversing a point of 100 m distant from the initial reference line. Conversely, the AV trend for TRANS exhibits an inclination toward constancy, regardless of vehicle location. The mitigating impact of relaxed perspective becomes evident in this context, thereby engendering minimal fluctuations in AV.  
Simultaneously, the relaxation of perspective substantially affects alterations in the area of the vehicle's bounding box in accordance with its actual position. In this case, the area of the object can be calculated as the product of the object's width and height. Figure 7b illustrates these case-specific attributes. To avoid the impact stemming from the gradual diminution of the vehicle's bounding box, attributable to its progressive disappearance beyond the confines of the ROIs, the calculation of the vehicle's box area is limited to distances up to \(-\)150 m. In Figure 7b, the vehicle's area shows a pronounced reduction in the ORG as it progressively moves away from the tunnel CCTV. Conversely, the area variation in the TRANS shows a gradual increase, albeit with a relatively smaller variance.  
Figure 7: Comparison of (**a**) AV, and (**b**) object area between case ORG and case TRANS.  
Collectively considering the two sets of ACs, in the case ORG, it becomes apparent that the perspective in the ORG leads to a divergence from the actual attributes of the vehicle entity. Conversely, the relaxed perspective in the TRANS engenders a noticeable alignment between the calculated AC and the intrinsic attributes of the vehicle entity.  
Furthermore, the change in vehicle object area at location for each case can be seen visually in Figure A3 of Appendix A. In Figure A3, the shape of the object is preserved in the distance for the case ORG, but their sizes are sharply reduced upon moving away, due to the perspective effect. On the other hand, in case TRANS, the shape of the object is gradually elongated vertically by moving from 0 m to \(-150\) m, and the height of the object gradually increases, while the width of the object remains almost unchanged. Based on this viewing phenomenon, the impact of object size changes on the performance of deep learning-based OD models are quantitatively examined in this study.