TY - JOUR
T1 - Efficient surface reconstruction using generalized Coulomb potentials
AU - Jalba, Andrei C.
AU - Roerdink, Jos B.T.M.
N1 - Relation: http://www.rug.nl/informatica/onderzoek/bernoulli
Rights: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science
PY - 2007
Y1 - 2007
N2 - 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.
AB - 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.
KW - surface reconstruction
KW - implicit surfaces
KW - octrees
KW - generalized Coulomb potentials
KW - polygonization
KW - ALGORITHM
KW - CURVE
KW - CRUST
M3 - Article
SN - 1077-2626
VL - 13
SP - 1512
EP - 1519
JO - IEEE Transactions on Visualization and Computer Graphics
JF - IEEE Transactions on Visualization and Computer Graphics
IS - 6
T2 - IEEE Visualization Conference (Vis 2007)/IEEE Information Visualization Conference (InfoVis 2007)
Y2 - 28 October 2007 through 1 November 2007
ER -