Polyhedral Surface: Self-supervised Point Cloud Reconstruction Based on
  Polyhedral Surface
Hui Tian Kai Xu
Point cloud reconstruction from raw point cloud has been an important topic
in computer graphics for decades, especially due to its high demand in modeling
and rendering applications. An important way to solve this problem is
establishing a local geometry to fit the local curve. However, previous methods
build either a local plane or polynomial curve. Local plane brings the loss of
sharp feature and the boundary artefacts on open surface. Polynomial curve is
hard to combine with neural network due to the local coordinate consistent
problem. To address this, we propose a novel polyhedral surface to represent
local surface. This method provides more flexible to represent sharp feature
and surface boundary on open surface. It does not require any local coordinate
system, which is important when introducing neural networks. Specifically, we
use normals to construct the polyhedral surface, including both dihedral and
trihedral surfaces using 2 and 3 normals, respectively. Our method achieves
state-of-the-art results on three commonly used datasets (ShapeNetCore, ABC,
and ScanNet). Code will be released upon acceptance.