WindPoly: Polygonal Mesh Reconstruction via Winding Numbers

TL;DR

WindPoly tackles polygonal mesh reconstruction from raw architectural point clouds without normal-vector cues. It combines polygonal plane detection, adaptive spatial partition to create convex polyhedrons, and a polygon-based winding numbers optimization with $w(q)=\sum_{i=1}^N a_i\frac{(p_i-q)\cdot n_i}{4\pi\left\|p_i-q\right\|^3}$ and $E_{dir}=W(q)+V(q)$ to achieve globally consistent orientation. It achieves concise, oriented meshes with preserved geometric details and improved robustness to noise and outliers, outperforming several state-of-the-art methods in experiments. The approach is applicable to architectural CAD-style datasets and supports efficient data compression for urban-scale models.

Abstract

Polygonal mesh reconstruction of a raw point cloud is a valuable topic in the field of computer graphics and 3D vision. Especially to 3D architectural models, polygonal mesh provides concise expressions for fundamental geometric structures while effectively reducing data volume. However, there are some limitations of traditional reconstruction methods: normal vector dependency, noisy points and defective parts sensitivity, and internal geometric structure lost, which reduce the practicality in real scene. In this paper, we propose a robust and efficient polygonal mesh reconstruction method to address the issues in architectural point cloud reconstruction task. It is an iterative adaptation process to detect planar shapes from scattered points. The initial structural polygonal mesh can be established in the constructed convex polyhedral space without assistance of normal vectors. Then, we develop an efficient polygon-based winding number strategy to orient polygonal mesh with global consistency. The significant advantage of our method is to provide a structural reconstruction for architectural point clouds and avoid point-based normal vector analysis. It effectively improves the robustness to noisy points and defective parts. More geometric details can be preserved in the reconstructed polygonal mesh. Experimental results show that our method can reconstruct concise, oriented and faithfully polygonal mesh that are better than results of state-of-the-art methods. More results and details can be found on https://vcc.tech/research/2024/WindPoly

Figures (12)

• Figure 1: Pipeline of WindPoly. (a) raw point cloud, (b) detected polygonal planes, (c) adaptive spatial partition, (d) output by polygon-based winding numbers optimization.
• Figure 2: External plane detection in 2D vision. Gray dotted lines (a) represent the raw point cloud. Red lines represent the external planes (b), blue lines are the other planes located in same side of the external planes (c). Finally, the convex polyhedral space represented by external planes is achieved (d).
• Figure 3: An instance of adaptive spatial partition in 2D vision. In the initial step, intersection numbers of related planes $F_1\sim F_4$ are 1, 2, 2, 2. After partition according to the regulation, the convex polyhedral space is divided into a set of convex polyhedrons.
• Figure 4: An instance of adaptive spatial partition in 3D vision. According to the separating plane searching (a)-(d), the 3D structure can be achieved with internal geometric details (e).
• Figure 5: An instance of polygon-based winding numbers optimization. According to the binary labels of related centroids, the polygonal mesh can be extracted from the convex polyhedron set.