depth supervision for prediction performance. As WCE employs an weight in the CE loss, its performance is slightly better than that of CEL. However, when we enforce two pixel-wise supervision (WCEL+L1) on the depth map, the performance cannot improve any more. Thus using two pixel-wise loss terms does not help.

Secondly, we analyze the effectiveness of the supplementary 3D geometric constraint (PL, SNL, VNL). Compared with the baseline (WCEL), three supplementary 3D geometric constraints can promote the network performance with varying degrees. Our proposed VNL combining with WCEL has the best performance, which has improved the baseline performance by up to $8$%.

Thirdly, we analyze the difference of three geometric constraints. As SNL can only exploit geometric relations of homogeneous local regions, its performance is the lowest among the three constraints over all evaluation metrics. Compared with SNL, since PL constrains the global geometric relations, its performance is clearly better. However, the performance of WCEL+PL is not as good as our proposed WCEL+VNL. When we further add our VNL on top of WCEL+PL, the precision can further be slightly improved and is comparable to WCEL+VNL. Therefore, although PL is a global geometric constraint in 3D, the pair-wise constraint cannot encode 