## 4 Experiment Results
### Deep-Affine Transformation Results  
Based on the above analysis, we assume that the corresponding relationship between the two vehicle images roughly accord with an affine transformation. To remove the non-coplanar problem, our method adopts deep information. The deep-affine matrix is used to  
Figure 8: KITTI images and their monocular depth map images.  
Figure 7: Matching feature pairs between front and back vehicles: (**a**) matching pairs based on similarity, and (**b**) matching pairs after RANSAC.  
estimate the occluded objects' points in the host vehicle's images, which is mapping from the same objects' points in the front vehicle's image. To fully test the geometric projection effect of deep-affine projection, more than 200 images in KITTI were selected as testing data. The results are shown in Figure 9.  
In Figure 9, the image (a) represents the front vehicle image and the image (b) is the processed host vehicle image by adding the white panel. The picture (c) shows the ground truth. Images (d) and (e) give the results of transformed front images based on affine transformation and deep-affine transformation. Compared with image (d), image (e) is more approximate to ground truth both in size and location. The outstanding results indicate that adding depth information is effective to improve the results of transformed images.  
Moreover, quantitative evaluation is used to measure the performance of deep-affine transformation. Figure 10 gives the IoU (intersection over union) results. The average IoU and IoU statistical data are shown in Table 1 and Figure 11. The IoU can be computed as:  
\[IoU=\frac{ObjectBox\cap GroundTruth}{ObjectBox\cup GroundTruth}\]Figure 9: Comparison results of affine and deep-affine transformation: (**a**) front vehicle image, (**b**) back vehicle image with occlusion, (**c**) ground truth image, (**d**) results of affine transformation, (**e**) results of deep-affine transformation, (**f**) front vehicle image, (**g**) back vehicle image with occlusion, (**h**) ground truth image, (**i**) results of affine transformation, and (**j**) results of deep-affine transformation.  
In Figure 10, red boxes are the ground truth bounding box, yellow boxes show the result of affine transformation, and the green box represents the result of our deep-affine transformation. The higher the value of IoU is, the closer the result is to the ground truth. The proposed method can achieve good performance and it shows good robustness  
Figure 11: Statistical results of IoU for affine and deep-affine transformation.  
Figure 10: IoU results of affine and deep-affine transformation.  
with regard to the changes in different views and variable distance, as well as excellent environment adaptability with regard to illumination variations and differing backgrounds.  
Table 1 illuminates the average IoU on different groups. A total of 10 groups (10 images in a group) are randomly selected from KITTI data and the IoU average value results are listed in Table 1. By adding the depth information to adjust affine transformation, the IoU value can be improved remarkably.  
Statistical data of IoU value are shown in Figure 11. The value of IoU ranges from 0 to 1 and is divided into five intervals. The pie chart gives the statistical information of each interval. The deep-affine transformation performs better than the normal affine transformation, largely due to the effective fusion of deep features. As shown in Figure 10, the IoU values of affine projection are mainly concentrated between 0 and 0.2. By comparison, the results of deep-affine transformation mainly fall in (0.4, 0.6) and (0.6, 0.8).