Surface Reconstruction from Noisy Point Clouds using Coulomb Potentials

We show that surface reconstruction from point clouds without orientation information can be formulated as a convection problem in a force field based on Coulomb potentials. To efficiently evaluate Coulomb potentials on the volumetric grid on which the evolving surface (current approximation to the final surface) is convected we use the so called ’Particle-Particle Particle-Mesh’ (PPPM) algorithm from molecular dynamics, fully implemented on modern, programmable graphics hardware. Our approach offers a number of advantages. Unlike distance-based methods which are sensitive to noise, the proposed method is highly resilient to shot noise since global Coulomb potentials are used to disregard outliers due to noise. Unlike local fitting, the long-range nature of Coulomb potentials implies that all data points are considered at once, so that global information is used in the fitting process. The method compares favorably with respect to previous approaches in terms of speed and flexibility and is highly resilient to noise.