Efficient Surface Reconstruction from Noisy Data using Regularized Membrane Potentials

We present a novel, physically-motivated method for surface reconstruction that can recover smooth surfaces from noisy and sparse data sets, without using orientation information. A new volumetric technique based on regularized-membrane potentials for aggregating the input sample points is introduced, which manages improved noise tolerability and outlier removal, without sacrificing much with respect to detail (feature) recovery. In this method, sample points are first aggregated on a volumetric grid. A labeling algorithm that relies on intrinsic properties of the smooth scalar field emerging after aggregation is used to classify grid points as exterior or interior to the surface. We also introduce a mesh-smoothing paradigm based on a mass-spring system, enhanced with a bending-energy minimizing term to ensure that the final triangulated surface is smoother than piecewise linear. The method compares favorably with respect to previous approaches in terms of speed and flexibility.