the pair-wise geometric loss (PL). We reconstruct the point cloud from the depth map and further recover the surface normal from the point cloud. The angular discrepancy between the ground truth and recovered surface normal is defined as the surface normal loss, which is a high-order geometric supervision in 3D space. The pair-wise loss is the direction difference of two vectors in 3D, which are established by randomly sampling paired points in ground-truth and predicted point cloud. The loss function of PL is as follow, $$\ell_{PL} = \frac{1}{N}\sum_{i=0}^{N}(1 - \frac{\overrightarrow{P_{Ai}^{\ast}P_{Bi}^{\ast}} \cdot \overrightarrow{P_{Ai}P_{Bi}}} {\left \| \overrightarrow{P_{Ai}^{\ast}P_{Bi}^{\ast}} \right \| \cdot \left \| \overrightarrow{P_{Ai}P_{Bi}} \right \|})$$ where $(P_{A}^{\ast},P_{B}^{\ast})_{i} $ and $(P_{A}, P_{B})_{i}$ are paired points sampled from the ground truth and the predicted point cloud respectively. $N$ is the total number of pairs.

We also employ the long-range restriction $\mathscr{R}_{2}$ for the paired points. Therefore, similar to VNL, PL can also be seen as a global geometric supervision in 3D space. The experimental results are reported in Table. \[table:Effectiveness of VNL and WCEL\]. WCEL is the baseline for all following experiments.

‘Local’ geometric supervision in 3D.

‘Global’ geometric supervision in 3D.

\[table:Effectiveness of VNL and WCEL\]

Firstly, we analyze the effect of pixel-wise 