We consider the problem of approximating normal and feature sizes of a surface from point cloud data that may be noisy. These problems are central to many applications dealing with point cloud data. In the noise-free case, the normals and feature sizes can be approximated by the centers of a set of unique large Delaunay balls called polar balls. In presence of noise, polar balls do not necessarily remain large and hence their centers may not be good for normal and feature size approximations. Earlier works suggest that some large Delaunay balls can play the role of polar balls. However, these results were short in explaining how the big Delaunay balls should be chosen for reliable approximations and how the approximation error depends on various factors. We provide new analyses that fill these gaps. In particular, they lead to new algorithms for practical and reliable normal and feature approximations.


Sample Point Point Cloud Medial Axis Feature Approximation Point Cloud Data 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tamal K. Dey
    • 1
  • Jian Sun
    • 1
  1. 1.The Ohio State UniversityColumbusUSA

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