Adaptive Thinning for Terrain Modelling and Image Compression

  • Laurent Demaret
  • Nira Dyn
  • Michael S. Floater
  • Armin Iske
Part of the Mathematics and Visualization book series (MATHVISUAL)


Adaptive thinning algorithms are greedy point removal schemes for bivariate scattered data sets with corresponding function values, where the points are recursively removed according to some data-dependent criterion. Each subset of points, together with its function values, defines a linear spline over its Delaunay triangulation. The basic criterion for the removal of the next point is to minimise the error between the resulting linear spline at the bivariate data points and the original function values. This leads to a hierarchy of linear splines of coarser and coarser resolutions.

This paper surveys the various removal strategies developed in our earlier papers, and the application of adaptive thinning to terrain modelling and to image compression. In our image test examples, we found that our thinning scheme, adapted to diminish the least squares error, combined with a post-processing least squares optimisation and a customised coding scheme, often gives better or comparable results to the wavelet-based scheme SPIHT.


Image Compression Delaunay Triangulation Scattered Data Compression Scheme Pixel Position 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Laurent Demaret
    • 1
  • Nira Dyn
    • 2
  • Michael S. Floater
    • 3
  • Armin Iske
    • 1
  1. 1.Zentrum MathematikTechnische Universität MünchenMunichGermany
  2. 2.School of Mathematical SciencesTel-Aviv UniversityIsrael
  3. 3.Computer Science DepartmentOslo UniversityNorway

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