Proximity Graphs for Defining Surfaces over Point Clouds
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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.
Keywords
G.1.2: Numerical Analysis - Approximation of surfaces and contours,
I.3.5: Computer Graphics - Curve, surface, solid, and object representations.
BibTeX entry
@INPROCEEDINGS{Zach04
, author = "Jan Klein and Gabriel Zachmann"
, title = "Proximity Graphs for Defining Surfaces over Point Clouds"
, booktitle = "Symposium on Point-Based Graphics"
, year = 2004
, month = jun # "2--4"
, address = "ETHZ, Z{\"u}rich, Switzerland"
, url = "http://www.gabrielzachmann.org/"
}
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Last modified:
Sat Sep 10 15:56:55 MDT 2005