The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
Proceedings of the conference on Visualization '01
Estimating surface normals in noisy point cloud data
Proceedings of the nineteenth annual symposium on Computational geometry
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
Provable surface reconstruction from noisy samples
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Provably good moving least squares
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Stability and homotopy of a subset of the medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
An adaptive MLS surface for reconstruction with guarantees
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Surface reconstruction from noisy point clouds
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
Natural neighbor coordinates of points on a surface
Computational Geometry: Theory and Applications
Consolidation of unorganized point clouds for surface reconstruction
ACM SIGGRAPH Asia 2009 papers
ℓ1-Sparse reconstruction of sharp point set surfaces
ACM Transactions on Graphics (TOG)
Sampled medial loci for 3D shape representation
Computer Vision and Image Understanding
Journal of Computational Physics
Optimal graph based segmentation using flow lines with application to airway wall segmentation
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Edge-aware point set resampling
ACM Transactions on Graphics (TOG)
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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.