Smoothing of Meshes and Point Clouds Using Weighted Geometry-Aware Bases

  • Tim Volodine
  • Denis Vanderstraeten
  • Dirk Roose
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4077)


In Sorkine et al. proposed a least squares based representation of meshes, which is suitable for compression and modeling. In this paper we look at this representation from the viewpoint of Tikhonov regularization. We show that this viewpoint yields a smoothing algorithm, which can be seen as shape approximation using weighted geometry aware bases, where the weighting factor is determined by the algorithm. The algorithm combines the Laplacian smoothing approach with the smoothing spline approach, where a global deviation constraint is imposed on the approximation. We use the generalized Laplacian matrix to measure smoothness and show how it can be modified in order to obtain smoothing behavior similar to that of curvature flow and feature preserving smoothing algorithms. The method is applicable to meshes, polygonal curves and point clouds in arbitrary dimensional spaces.


Point Cloud Tikhonov Regularization Laplacian Matrix Sheet Metal Part Smoothing Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tim Volodine
    • 1
  • Denis Vanderstraeten
    • 2
  • Dirk Roose
    • 1
  1. 1.Department of Computer ScienceKULeuvenLeuvenBelgium
  2. 2.Metris N.V.LeuvenBelgium

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