from the original paper.

Using authors’ released models.

\[table:surface normals cmp\]

![Recovered surface normal from 3D point cloud. According to the visual effect, the surface normal is in high-quality in planes (1st row) and the complicated curved surface (2nd and last row).[]{data-label="fig:normals"}](./Fig/surface_normal){width="47.00000%"}

Furthermore, we compare the surface normals directly computed from the reconstructed point cloud with that of DORN  [@fu2018deep] and GeoNet  [@qi2018geonet]. Note that we run the released code and model of DORN to obtain depth maps and then calculate surface normals from the depth, while the evaluation of GeoNet is cited from the original paper. In Table \[table:surface normals cmp\], we can see that, with high-order geometric supervision, our method outperforms DORN and GeoNet by a large margin, and even is close to Eigen method which trains to output normals. It suggests that our method can lead the model to learn the shape from images.

Apart from the quantitative comparison, the visual effect is shown in Fig. \[fig:normals\], demonstrating that our directly calculated surface normals are not only accurate in planes (the 1st row), but also are of higher quality in regions with sophisticated curved surface (the 2nd and last row).

Conclusion
==========

In this paper, we have 