## 3 Results
### Efficiency of Object Detection  
#### 3.3.1 Performance of vePOD Faster R-CNN  
We also evaluated the execution time of vePOD CNNs for detecting objects. Figure 5 shows the performance of vePOD Faster R-CNN and Faster R-CNN in processing 800 \(\times\) 800 images.  
For Faster R-CNN, the feature map generation using a backbone CNN takes 6.8 s, which accounts for 53.3% of the execution time. This is because the number of neural networks in the CNN backbone is more than five times the number in other parts of the detection network. VePOD Faster R-CNN takes a similar amount of time to generate feature maps and region proposals, as it uses the same CNN backbone and RPN network as Faster R-CNN.  
Secret sharing uses storage and network bandwidth resources. We evaluated the transmission efficiency of vePOD. To transfer secret shares, vePOD Faster R-CNN takes 2.6 s under 300 Mbps bandwidth, which accounts for 5.9% of the overall execution time. In terms of the storage cost, we compare the size of secret shares with that of the original sensor data in Figure 10. Please see Section 3.3.4 for more details.  
Figure 4: vePOD Faster R-CNN achieves the same detection accuracy as Faster R-CNN.  
The major performance difference between vePOD Faster R-CNN and Faster R-CNN lies in the ROI pooling. Secure ROI pooling in vePOD Faster R-CNN takes 34 s, while Faster R-CNN uses 3.9 s.  
This prolongation of the execution time is caused by the secure function, which calculates and merges a relative difference table for every region proposal specific patch.  
To gain a deeper understanding of the preceding result, we study the impact of the number of region proposals on the performance of secure ROI pooling. Figure 6 presents the results. Faster R-CNN uses fixed-size input feature maps (\(50\times 50\times 512\), i.e., width, height, and channel). The number of region proposals directly influences the execution time of the secure function. The time is comparable when there are 100 or 500 region proposals. Specifically, for 100 region proposals, the original ROI pooling takes 1.7 s and the secure ROI pooling uses 1.9 s. However, when there are over 1000 region proposals, the execution time differs more; i.e., the original ROI pooling takes 3.9 s to process 2000 region proposals. In contrast, the secure ROI pooling uses 34.0 s. In addition to the number of region proposals, the shape of the ROI affects the performance of the secure ROI pooling as well. More specifically, larger ROIs lead to an increased execution time caused by secure operations to construct the relative difference tables; for example, an ROI with size 12 \(\times\) 12 (width, height) takes an additional 0.007 s computation time compared to an ROI with size \(3\times 3\).  
Intuitively, when more secret shares are created from a vehicle's sensor data, vePOD Faster R-CNN achieves better privacy protection. However, this also increase the computation cost. Figure 6 plots the relationship between the execution time of the secure ROI pooling and the number of secret shares. Each secret share is processed by an edge node. The extra time caused by adding one more secret share is not significant, e.g., from 34.1 s for two secret shares to 37.1 s for three secret shares, an 8.1% increase. This is because most of the operations in the secure ROI pooling remain the same, except for adding an extra relative difference table from the additional secret share in every ROI patch.  
Figure 5: Comparison of the execution time of the key components in vePOD Faster R-CNN and Faster R-CNN.