## 5 Experiments
### Performance  
The matching is evaluated as follows. For fair comparisons, we refer to the results of the group of methods including USIP detector [42], MDGAT descriptor and SuperGlue matcher. Specifically, we re-check SuperGlue matcher with several threshold assignments algorithm and threshold-free. After that, we run MDGAT-matcher instead of the combination between MDGAT descriptor and SuperGlue matcher. As show in Table 1 and Figure 3, the DFGAT achieves the best performance in matching ability with about 80% for Precision, 89% for Accuracy, 76% for Recall and 0.783 for the F1-score. Although the USIP can detect keypoints by using an unsupervised learning network, it struggles to predict keypoints with a limited number of data and density-invariant requirements. The further reason is that the USIP method is not integrated with the descriptions framework which limits the full exploitation of the geometric characteristics of the point cloud.  
We further evaluate the registration ability of the DFGAT as shown in Table 2. We compare the metric scores achieved against several strong baselines: the hand-crafted  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Matcher** & **Precision** & **Accuracy** & **Recall** & **F1-Score** \\ \hline MDGAT Desc. + SuperGlue(0.1) & 54.3 & 76.7 & 57.7 & 0.559 \\ MDGAT Desc. + SuperGlue(0.2) & 57.6 & 75.8 & 49.2 & 0.531 \\ MDGAT Desc. + SuperGlue(0.3) & 62.2 & 72.7 & 39.4 & 0.482 \\ MDGAT Desc. + SuperGlue(0) & 57.7 & 72.2 & 35.4 & 0.439 \\ MDGAT (Desc. + matcher) & 70.3 & 86.7 & 69.4 & 0.698 \\
**DFGAT** & **80.4** & **90.2** & **76.1** & **0.782** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Matching performance.  
Figure 3: Visualization of matching results on KITTI. The first column are keypoints detected and matched using our method and MDGAT. The second column are ground-truth results without raw point clouds while the third column represents ground-truth results including raw point clouds. Our method performs better in terms of keypoints matching with more correct pairs (green) and fewer wrong pairs (red).  
methods RANSAC [23], FPFH [24], SHOT [30], and USIP. For the learning-based method, theMDGAT + SuperGlue [4] is selected. As shown in Table 2, our network achieves the lowest registration failure rate of 0.117% among all the baselines and has a comparable inlier ratio to that of the MDGAT-matcher. The reason is that our descriptor can create better learnable features, and after the Sinkhorn algorithm assignment, the scores matrices have many more positive pairs. For fair comparison with MDGAT, our approach uses the number of desired keypoints 256 and has large improvements in RTE, RRE, and the success ratio. In addition, as shown in Table 3, our model can achieve the lowest score (0.24\({}^{\circ}\)) on the RRE scale and the highest percentage success (99.88%), while the DJFeat still remains the best in RTE with 6.90 cm. It is noteworthy that our approach uses only 256 keypoints for each point cloud, whereas in other methods, they originally used no less than 1024 keypoints. In terms of training time, our model takes only 40 epochs in comparison with 1000 epochs for the MDGAT-matcher because we use better strategy in the keypoints selection and description.