Point Cloud Resampling by Simulating Electric Charges on Metallic Surfaces

Abstract

3D point cloud resampling based on computational geometry is still a challenging problem. In this paper, we propose a point cloud resampling algorithm inspired by the physical characteristics of the repulsion forces between point electrons. The points in the point cloud are considered as electrons that reside on a virtual metallic surface. We iteratively update the positions of the points by simulating the electromagnetic forces between them. Intuitively, the input point cloud becomes evenly distributed by the repulsive forces. We further adopt an acceleration and damping terms in our simulation. This system can be viewed as a momentum method in mathematical optimization and thus increases the convergence stability and uniformity performance. The net force of the repulsion forces may contain a normal directional force with respect to the local surface, which can make the point diverge from the surface. To prevent this, we introduce a simple restriction method that limits the repulsion forces between the points to an approximated local plane. This approach mimics the natural phenomenon in which positive electrons cannot escape from the metallic surface. However, this is still an approximation because the surfaces are often curved rather than being strict planes. Therefore, we project the points to the nearest local surface after the movement. In addition, we approximate the net repulsion force using the K-nearest neighbor to accelerate our algorithm. Furthermore, we propose a new measurement criterion that evaluates the uniformity of the resampled point cloud to compare the proposed algorithm with baselines. In experiments, our algorithm demonstrates superior performance in terms of uniformization, convergence, and run-time.