Investigation of the efficiency of the moving least squares method in the reconstruction of a three-dimensional surface on a supercomputer

TL;DR

The paper tackles the problem of reconstructing 3D surfaces from point clouds on a distributed-memory supercomputer. It develops a parallel moving least squares (MLS) algorithm implemented with MPI and OpenMP, distributing the cloud, exchanging ring-boundary data, and performing local MLS with kd-tree/morton-based neighborhood searches. The results on the Polus cluster show the approach achieves good scalability and robustness to noise, with reconstruction quality strongly influenced by the neighborhood radius $R$ (best when $R$ is chosen near the noise level $\sigma$) and the hybrid MPI+OpenMP version delivering superior performance. The work demonstrates a scalable, point-based surface reconstruction pipeline suitable for large-scale lidar-derived data and related applications, while highlighting practical guidance for parameter selection and potential automation.

Abstract

Currently, the area of geometric modeling and the construction of 3D models based on point clouds from laser sensors is actively developing. One of the basic tasks of geometric modeling is the reconstruction of a surface from a cloud of points. The aim of this work is to develop a parallel least-squares surface reconstruction method on a distributed memory supercomputer that allows achieving optimal results both in scalability and surface reconstruction quality. The focus of the work is on the surface reconstruction algorithm based on the least squares method, in connection with which the algorithm was called the moving least squares method.

Figures (17)

• Figure 1: Point cloud segmentation using a segmented image mask and one-to-one correspondence between lidar and camera data.
• Figure 2: Stitched segmented scans from lidar.
• Figure 3: Stitched scans of street houses.
• Figure 4: Execution of the Delaunay triangulation invariant
• Figure 5: (left) For RBFs, the scalar field to be optimized must be estimated to be zero at the sample points $\Phi(\mathbf{p_i}) = 0$, while for off-surface constraints $\Phi(\mathbf{p_i} + \upalpha\mathbf{n_i}) = \upalpha;$ this choice is appropriate since signed distance functions almost everywhere have a unit gradient norm. The cluster of off-surface samples shows how carefully you need to set constraints in areas of high curvature. (right) Surface reconstructed with RBFs typically has severe geometric and topological artifacts when inconsistent external constraints are provided.