Efficient Surface Reconstruction using Generalized Coulomb Potentials

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...

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Bibliographic Details
Published in:IEEE transactions on visualization and computer graphics 2007-11, Vol.13 (6), p.1512-1519
Main Authors: Jalba, A.C., Roerdink, J.B.T.
Format: Article
Language:English
Subjects:
Algorithms
Clouds
Convection
Coulomb potential
Data points
Fittings
Generalized Coulomb potentials
Implicit surfaces
Mathematics
Noise
Noise level
Noise robustness
Octrees
Polygonization
Reconstruction
Studies
Surface contamination
Surface fitting
Surface reconstruction
Tagging
Topology
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Summary: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 long-range 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.
ISSN:1077-2626
1941-0506
DOI:10.1109/TVCG.2007.70553