CIRCNET: MESHING 3D POINT CLOUDS WITH CIRCUMCENTER DETECTION

Abstract

Reconstructing 3D point clouds into triangle meshes is a key problem in computational geometry and surface reconstruction. Point cloud triangulation solves this problem by providing edge information to the input points. Since no vertex interpolation is involved, it is beneficial to preserve sharp details on the surface. Taking advantage of learning-based techniques in triangulation, existing methods enumerate the complete combinations of candidate triangles, which is both complex and inefficient. In this paper, we leverage the duality between a triangle and its circumcenter, and introduce a deep neural network that detects the circumcenters to achieve point cloud triangulation. Specifically, we introduce multiple anchor priors to divide the neighborhood space of each point. The neural network then learns to predict the presences and locations of circumcenters under the guidance of those anchors. We extract the triangles dual to the detected circumcenters to form a primitive mesh, from which an edge-manifold mesh is produced via simple post-processing. Unlike existing learning-based triangulation methods, the proposed method bypasses an exhaustive enumeration of triangle combinations and local surface parameterization. We validate the efficiency, generalization, and robustness of our method on prominent datasets of both watertight and open surfaces. The code and trained models are provided at https://github.com/Ruitao-L/CircNet.

1. INTRODUCTION

Point cloud triangulation (Cazals & Giesen 2004) aims at reconstructing triangle meshes of object surfaces by adding edge information to their point cloud representations. The input point clouds are usually produced by either scanning sensors (e.g., LiDAR) or surface sampling methods. Compared to implicit surface reconstruction (e.g., Kazhdan et al. 2006) , explicit triangulation has the advantages of preserving the original input points and fine-grained details of the surface. Moreover, it does not require oriented normals which are difficult to obtain in practice. Recent advances in geometric deep learning have seen widespread applications of neural functions for surface representations (e.g., Park et al. 2019; Sitzmann et al. 2020b; a; Erler et al. 2020; Gropp et al. 2020; Atzmon & Lipman 2020a; b; Ben-Shabat et al. 2022; Ma et al. 2021; 2022) . In comparison, only a few methods have been proposed to directly learn triangulation of point clouds by using neural networks. This is probably attributed to the combinatorial nature of the triangulation task, hindering the uptake of learning-based methods. The existing works have to enumerate combinations of candidate triangles around each input point, and use neural networks to predict their existence in the triangle mesh (Sharp & Ovsjanikov 2020; Liu et al. 2020) . Figure 1 (a) illustrates the local complexity of those combinatorial methods using a point with four neighboring points. Typically, for a point with K neighbors, the combinatorial methods propose K 2 or O(K 2 ) candidate triangles. Different from these methods, we propose to exploit the duality relationship between a triangle and its circumcenter to implement point cloud triangulation. That is, each vertex of a triangle is equally distant to its circumcenter. We use this characteristic to find triangle triplets from their circumcenters. Figure. 1(b) shows the duality based on the same example of Fig. 1(a) . Our method recovers the vertex triplets of triangle (p, q 1 , q 3 ) based on its circumcenter c and the equidistant characteristic, i.e. ∥p -c∥ = ∥q 1 -c∥ = ∥q 3 -c∥. To obtain circumcenters for point cloud triangulation, we introduce a neural network that is able to detect the circumcenters of all triangles in a mesh. To the best of our knowledge, this is the first single-shot detection architecture for point cloud triangulation. We are inspired by the one-stage methods in object detection (e.g., Liu et al. 2016 ).

