## 3 Experiment and Analysis
### Experiment on MS-ST  
In order to accurately judge the optimal sorting position and pose, we propose the MS-ST, which estimates the occlusion degree of the target while obtaining the optimal sorting region. In the network, Fourier transform and depth estimation were used as supervision signals to complete the training of the model. As shown in Figure 9, the MS-ST algorithm accurately segmented the sound sorting region of parcels and estimated the occlusion degree of the parcel, which presented as a score range from 0 to 1. After calculating the 3D point cloud of the sorting area, the RANSAC algorithm was used to fit the sorting plane of the parcels. It can be seen that even if there are noise points coming from the sensors, the fitting algorithm can still accurately calculate the sorting plane. That is, it can prove the method, which is use for gaining the sorting pose, has strong robustness. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Recall (\%)** & **FPS** \\ \hline YOLOv5s + Self-Attention & 96.62 & 13.51 \\ + normalization & 96.85 (+0.23) & 13.33 \\ + normalization and MAG & 97.24 (+0.62) & 13.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The influences of the normalization and MAG. Figure 9: The result of MS-ST shows the accurate segmentation of the sorting region of parcels and the estimation of the occlusion degree. We conducted experiments on the improvements generated by the added multi-modal supervision signal on the network detection accuracy. The experimental results are shown in Table 4 below. Adding different supervision signals improved both pixel accuracy (PA) and mean intersection over union (MIOU). As shown in Table 4, the PA of the pickable region improved 3.12% by adding a FFT signal. The edge information of the target could be effectively obtained by using the frequency domain features as the supervision signal. On the other hand, using the depth image as a supervision signal could effectively capture the rich gradient information of the objects to be sorted. Additionally, the MIOU was raised to 95.41% significantly, by adding a depth signal alone. After adding FFT and depth at the same time, the segmentation accuracy of the sorting region was improved by 7.79%. It was proven that the signals of the two modalities complete the supplementary information in different dimensions, which improved the segmentation accuracy of the network. After the sorting plane was obtained, the geometric center of the segmented point cloud on the plane was calculated as the sorting position. The normal vector of the sorting plane was used as the sorting pose. In order to further prove the detection accuracy of this algorithm for sorting position and pose, a comparative experiment was conducted with two other methods [19; 20] for parcel sorting. The experimental results are shown in Table 5 below. As can be seen in Table 5, MS-ST improved the detection accuracy to a certain extent for sorting position compared with the other two methods. In the detection of sorting poses, MS-ST greatly improved the accuracy compared with the others. In addition, according to the standard deviations obtained from multiple groups of experiments, our method has better stability, especially in pose detection. This is because the RSDNN proposed by the authors of [19] and the VSMT proposed in the paper [20] adopt a method based on key point detection, and the normal vector of sorting plane is determined by those key points. When encountering a parcel with a large degree of inclination, there will be a certain degree of error in the estimation of the key points' positions. At the same time, due to the small number of key points and the short distances between them, the normal vector is easily affected by sensor noise, which could cause large detection error of pose. Differently from those methods, MS-ST is based on the Swin Transformer architecture, and it achieves accurate segmentation of the sorting region by fusing multi-modal information.