Efficient Surface Reconstruction using Generalized Coulomb Potentials

Abstract

Abstract-We propose a novel, geometrically adaptive method for surface reconstruction from noisy and sparse point clouds, without orientation information. The method employs a fast convection algorithm to attract the evolving surface towards the data points. The force field in which the surface is convected is based on generalized Coulomb potentials evaluated on an adaptive grid (i.e., an octree) using a fast, hierarchical algorithm. Formulating reconstruction as a convection problem in a velocity field generated by Coulomb potentials offers a number of advantages. Unlike methods which compute the distance from the data set to the implicit surface, which are sensitive to noise due to the very reliance on the distance transform, our method is highly resilient to shot noise since global, generalized Coulomb potentials can be used to disregard the presence of outliers due to noise. Coulomb potentials represent longrange interactions that consider all data points at once, and thus they convey global information which is crucial in the fitting process. Both the spatial and temporal complexities of our spatially-adaptive method are proportional to the size of the reconstructed object, which makes our method compare favorably with respect to previous approaches in terms of speed and flexibility. Experiments with sparse as well as noisy data sets show that the method is capable of delivering crisp and detailed yet smooth surfaces.

Fast Sparse Level Sets on Graphics Hardware

“…Using velocity fields based on the distance transform as in [39] is not an option, since at very large grid resolutions, e.g., 2048 3 voxels, the storage requirements would be more than 30 GB of RAM. Instead, we use inversedistance velocity fields similar to [12], which can be evaluated on-the-fly using memory-efficient octree grids. Specifically, the velocity field is based on Shepard interpolation [35] of normalized direction vectors between locations in the narrow band and input point samples.…”

“…Surface reconstruction from unorganized point clouds has been intensively studied; see [3], [12], [13], [16], [27], [40] and references therein. Despite the increased availability of commodity parallel platforms, there has been very little work on parallel algorithms for surface reconstruction.…”

“…Therefore, evaluating V for an active tile can be done as follows. First, the potential P is efficiently approximated using the BarnesHut algorithm [2] similar to [12]. Then, the resulting scalar values are used to compute the normalized gradient of P (using central differences), to finally yield V.…”

“…The field is evaluated on the fly using the "tree algorithm" of Barnes and Hut [2], see Section IV and [12].…”

“…The proposed method for surface reconstruction withstands large numbers of outliers, due to its reliance on inversedistance potentials [12]. Moreover, increasing the stiffness of the interface, by adjusting the curvature term in Eq.…”