Point Cloud Surfaces using Geometric Proximity Graphs

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We present a new definition of an implicit surface over a noisy point cloud, based on the weighted least squares approach. It can be evaluated very fast, but artifacts are significantly reduced.

We propose to use a different kernel function that approximates geodesic distances on the surface by utilizing a geometric proximity graph. From a variety of possibilities, we have examined the Delaunay graph and the sphere-of-influence graph (SIG), for which we propose several extensions.

The proximity graph also allows us to estimate the local sampling density, which we utilize to automatically adapt the bandwidth of the kernel and to detect boundaries. Consequently, our method is able to handle point clouds of varying sampling density without manual tuning.

Our method can be integrated into other surface definitions, such as moving least squares, so that these benefits carry over.

Weighted least squares, moving least squares, proximity graphs, surface approximation, implicit surfaces, local polynomial regression.
BibTeX entry
,  author = "Jan Klein and Gabriel Zachmann"
,  title = "Point Cloud Surfaces using Geometric Proximity Graphs"
,  journal = "Computers \& Graphics"
,  year = 2004
,  volume = 28
,  number = 6
,  pages = "839--850"
,  url = "http://dx.doi.org/10.1016/j.cag.2004.08.012"
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Gabriel Zachmann
Last modified: Sat Sep 10 15:57:06 MDT 2005