Foundations of Computational Mathematics

, Volume 8, Issue 4, pp 409–425 | Cite as

Meshfree Thinning of 3D Point Clouds

  • Nira Dyn
  • Armin IskeEmail author
  • Holger Wendland


An efficient data reduction scheme for the simplification of a surface given by a large set X of 3D point-samples is proposed. The data reduction relies on a recursive point removal algorithm, termed thinning, which outputs a data hierarchy of point-samples for multiresolution surface approximation. The thinning algorithm works with a point removal criterion, which measures the significances of the points in their local neighbourhoods, and which removes a least significant point at each step. For any point x in the current point set YX, its significance reflects the approximation quality of a local surface reconstructed from neighbouring points in Y. The local surface reconstruction is done over an estimated tangent plane at x by using radial basis functions. The approximation quality of the surface reconstruction around x is measured by using its maximal deviation from the given point-samples X in a local neighbourhood of x. The resulting thinning algorithm is meshfree, i.e., its performance is solely based upon the geometry of the input 3D surface point-samples, and so it does not require any further topological information, such as point connectivities. Computational details of the thinning algorithm and the required data structures for efficient implementation are explained and its complexity is discussed. Two examples are presented for illustration.


Surface simplification Thinning algorithms Meshfree methods Approximation by radial basis functions 3D point cloud 

AMS Subject Classifications

65D07 65D15 65D17 65D18 


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Copyright information

© SFoCM 2007

Authors and Affiliations

  1. 1.Department of MathematicsTel-Aviv UniversityTel-AvivIsrael
  2. 2.Department of MathematicsUniversity of HamburgHamburgGermany
  3. 3.Department of MathematicsUniversity of SussexBrightonUK

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