as strong geometry information as our proposed VNL. At last, in order to further demonstrate the effectiveness of VNL, we analyze the results of network trained with and without VNL supervision on the KITTI dataset. The visual comparison is shown in Fig. \[fig:kitti dataset\]. One can see that VNL can improve the performance of the network in ambiguous regions. For example, the sign (1st row), the distant pedestrian (2nd row), and traffic light in the last row of the figure can demonstrate the effectiveness of the proposed VNL. In conclusion, the geometric constraints in the 3D space can significantly boost the network performance. Moreover, the global and high-order constraints can enforce stronger supervision than the ‘local’ and pair-wise ones in 3D space.

![Illustration of the impact of the samples size. The more samples will promote the performance.[]{data-label="fig:VNL_PL_Samples"}](./Fig/VNL_DiffSamples){width="37.00000%"}

**Impact of the Amount of Samples.** Previously, we have proved the effectiveness of VNL. Here the impact of the size of samples for VNL is discussed. We sample six different sizes of point groups, 0K, 20K, 40K, 60K, and 80K and 100K, to establish VNL. ‘0K’ means that the model is trained without VNL supervision. The rel error is reported for evaluation. Fig. 