LFS-Aware Surface Reconstruction from Unoriented 3D Point Clouds

TL;DR

This work tackles the challenge of producing isotropic triangle meshes from unoriented 3D point clouds by jointly estimating an implicit surface and an LFS-aware mesh sizing function, enabling direct mesh extraction without remeshing. The method combines a reach-aware multi-domain implicit function with a robust signing process and an LFS-based sizing strategy to generate adaptive, high-quality meshes, while preserving sharp features and resisting noise, outliers, and holes. Key contributions include a Voronoi-free LFS estimation that fuses curvature and shape diameter, a multi-domain implicit solver with signed robust distance, and a Delaunay-refinement-based meshing pipeline that enforces LFS-aware isotropy. Experimental results demonstrate robust performance across synthetic and real data, outperforming several baselines in reconstruction accuracy and preserving topology and features, with practical impact for CAD, simulations, and visualization.

Abstract

We present a novel approach for generating isotropic surface triangle meshes directly from unoriented 3D point clouds, with the mesh density adapting to the estimated local feature size (LFS). Popular reconstruction pipelines first reconstruct a dense mesh from the input point cloud and then apply remeshing to obtain an isotropic mesh. The sequential pipeline makes it hard to find a lower-density mesh while preserving more details. Instead, our approach reconstructs both an implicit function and an LFS-aware mesh sizing function directly from the input point cloud, which is then used to produce the final LFS-aware mesh without remeshing. We combine local curvature radius and shape diameter to estimate the LFS directly from the input point clouds. Additionally, we propose a new mesh solver to solve an implicit function whose zero level set delineates the surface without requiring normal orientation. The added value of our approach is generating isotropic meshes directly from 3D point clouds with an LFS-aware density, thus achieving a trade-off between geometric detail and mesh complexity. Our experiments also demonstrate the robustness of our method to noise, outliers, and missing data and can preserve sharp features for CAD point clouds.

Figures (27)

• Figure 1: A step-by-step reconstruction example. (a) Our algorithm takes the unoriented point sets as input. (b) First, we estimate the local feature size (LFS) directly on the inputs. (c) Second, we construct a reach-aware multi-domain. We show the boundary of the multi-domain: an envelope domain embedded in a sphere domain. (d) Third, we use a new mesh solver to solve an implicit function defined on the multi-domain whose zero level set is the target surface. We present a clip view of the implicit function. (e) We extract the LFS-aware mesh from the solved implicit function.
• Figure 2: Overview. The input is a defective point cloud, with or without normals. The algorithm first estimates LFS as the minimum of the local curvature radius and half of the shape diameter. An implicit function is solved on a multi-domain discretization obtained by Delaunay refinement, so as to fill large holes. Yellow dashed lines delineate the filled holes, "+" denotes the positive vertices, and "-" denotes the negative vertices. Finally, the output LFS-aware mesh is generated by Delaunay refinement.
• Figure 3: LFS captures the local curvature, thickness, and separation. The reach is the minimum of the LFS for the whole shape. The red dashed line depicts the medial axis.
• Figure 4: Dual cone search. The red dashed line depicts the medial axis. The shape diameter is the minimum of the thickness and separation.
• Figure 5: Solving for a signed implicit function from the sign guesses for edges. (a) The sign guess for an edge is determined by detecting the crossings with sublevel sets of the unsigned distance function to the points. An edge is labeled $-1$ if it crosses the point clouds, and $+1$ otherwise. (b) A signed implicit function is then solved from the sign guesses of the edges. Red crosses denote the positive vertices, and blue minus signs denote the negative vertices. The signed implicit function is piecewise linear.