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OnePass Delaunay Filtering for Homeomorphic 3D Surface Reconstruction

Summary: One­Pass Delaunay Filtering for
Homeomorphic 3D Surface Reconstruction
Nina Amenta \Lambda Sunghee Choi y
April 12, 1999
We give a simple algorithm for surface reconstruction from a set
of point samples in R 3 , using only one three­dimensional Voronoi dia­
gram computation. We also give a fairly simple proof that the recon­
struction is topologically correct when the input is a sufficiently dense
sample from a smooth surface.
1 Introduction
We give an algorithm for fitting a surface triangulation to a set S of point
samples in three dimensional space. We assume no additional information
besides the three­dimensional coordinates of the points. Practical variants of
this problem, in which more information might be given, arise in computer
graphics, reverse engineering, medical imaging and computer vision.
Like many previous algorithms, our approach is to select some subset of the
Delaunay triangles of S as the surface triangulation. This is a natural idea,
\Lambda Computer Sciences, University of Texas, Austin, TX 78712. Supported by NSF grant


Source: Amenta, Nina - Department of Computer Science, University of California, Davis


Collections: Biology and Medicine; Computer Technologies and Information Sciences