Proximity Graphs for Defining Surfaces over Point Clouds

J. Klein und Gabriel Zachmann
In proceedings of Symposium on Point-Based Graphics, Juni 2004
 

Abstract

We present a new definition of an implicit surface over a noisy point cloud. It can be evaluated very fast, but, unlike other definitions based on the moving least squares approach, it does not suffer from artifacts. In order to achieve robustness, we propose to use a different kernel function that approximates geodesic distances on the surface by utilizing a geometric proximity graph. The starting point in the graph is determined by approximate nearest neighbor search. From a variety of possibilities, we have examined the Delaunay graph and the sphere-of-influence graph (SIG). For both, we propose to use modifications, the r-SIG and the pruned Delaunay graph. We have implemented our new surface definition as well as a test environment which allows to visualize and to evaluate the quality of the surfaces. We have evaluated the different surfaces induced by different proximity graphs. The results show that artifacts and the root mean square error are significantly reduced.

Stichwörter: and object representations, approximation of surfaces and contours, curve, solid, surface

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Bibtex

@INPROCEEDINGS{klein-2004-proximity,
     author = {Klein, J. and Zachmann, Gabriel},
      title = {Proximity Graphs for Defining Surfaces over Point Clouds},
  booktitle = {Symposium on Point-Based Graphics},
       year = {2004},
      month = jun,
   keywords = {and object representations, approximation of surfaces and contours, curve, solid, surface},
   abstract = {We present a new definition of an implicit surface over a noisy point cloud. It can be evaluated
               very fast, but, unlike other definitions based on the moving least squares approach, it does not
               suffer from artifacts. In order to achieve robustness, we propose to use a different kernel function
               that approximates geodesic distances on the surface by utilizing a geometric proximity graph. The
               starting point in the graph is determined by approximate nearest neighbor search. From a variety of
               possibilities, we have examined the Delaunay graph and the sphere-of-influence graph (SIG). For
               both, we propose to use modifications, the r-SIG and the pruned Delaunay graph. We have implemented
               our new surface definition as well as a test environment which allows to visualize and to evaluate
               the quality of the surfaces. We have evaluated the different surfaces induced by different proximity
               graphs. The results show that artifacts and the root mean square error are significantly reduced.}
}