Polyhedral Surface: Self-supervised Point Cloud Reconstruction Based on Polyhedral Surface

TL;DR

This work tackles open-surface point cloud reconstruction by introducing anglehedral surfaces—dihedral and trihedral patches defined by normals—that remove the need for a fixed local coordinate system. A self-supervised pipeline predicts a displacement field $s(q)$ whose length $\|s(q)\|_2$ acts as an unsigned distance to the surface, with a two-stage decoding that merges neighboring geometric priors and a refinement step via a Point Transformer. The approach combines adaptive geometry selection, local-geometry merging, and refinement losses to achieve state-of-the-art results on ShapeNetCore, ABC, and ScanNet, notably reducing Chamfer distance on ABC by a substantial margin. This coordinate-free, feature-preserving framework advances point cloud reconstruction by better capturing sharp features and boundaries while maintaining differentiability for neural-network training; future work will address noise robustness and varying point density.

Abstract

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.

Figures (14)

• Figure 1: Anglehedral surface often appears in scenes or shapes. The examples separately show the priority of the anglehedral surface in representing the surface boundary when 3 normals lie on the same plane and sharp surface. SuperUDF only makes use of the local geometry plane while ours makes use of the local geometry Anglehedral surface.
• Figure 2: The advantage of anglehedral surface illustrated in 2D cases. (a) is situation where there is only plane. (b) is the situation where there are plane and anglehedral surface. From the mesh of red circle, the mesh represented by anglehedral surface is close to the GT.
• Figure 3: The pipeline of the whole processing.
• Figure 4: The distance from query point to trihedral surface and dihedral surface.
• Figure 5: Visualized results of our method and state-of-the-art alternatives on ShapeNet. (S) mean supervised method and (U) means unsupervised method. Methods are NPull, CAP, GIFS, SuperUDF and Ours. The number of input point cloud is 3000.