Fast approximating triangulation of large scattered datasets

Weimer, Henrik; Warren, Joe

doi:10.1016/s0965-9978(98)00095-7

Cited by 13 publications

(1 citation statement)

References 26 publications

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“…However, corresponding data reduction strategies (like thinning [12] or adaptive thinning [11]) usually require the construction of some auxiliary triangulation in order to achieve a multiscale formulation of the problem, see also [13] or [26]. For data approximation using finite elements on unstructured grids, see [41].…”

Section: Adaptive Least Squares Fitting With Waveletsmentioning

confidence: 99%

Multilevel regularization of wavelet based fitting of scattered data ? some experiments

Castaño

Kunoth

2005

Numer Algor

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In [6], an adaptive method to approximate unorganized clouds of points by smooth surfaces based on wavelets has been described. The general fitting algorithm operates on a coarse-tofine basis. It selects on each refinement level in a first step a reduced number of wavelets which are appropriate to represent the features of the data set. In a second step, the fitting surface is constructed as the linear combination of the wavelets which minimizes the distance to the data in a least squares sense. This is followed by a thresholding procedure on the wavelet coefficients to discard those which are too small to contribute much to the surface representation.In this paper, we firstly generalize this strategy to a classically regularized least squares functional by adding a Sobolev norm, taking advantage of the capability of wavelets to characterize Sobolev spaces of even fractional order. After recalling the usual cross-validation technique to determine the involved smoothing parameters, some examples of fitting severely irregularly distributed data, synthetically produced and of geophysical origin, are presented. In order to reduce computational costs, we then introduce a multilevel generalized crossvalidation technique which goes beyond the Sobolev formulation and exploits the hierarchical setting based on wavelets. We illustrate the performance of the new strategy on some geophysical data.

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