Multilevel Methods for Sparse Representation of Topographical Data

Multigrid/Multiresolution Interpolation: Reducing Oversmoothing and Other Sampling Effects

“…When dealing with large areas involving continental scale features data size grows rapidly making it almost impossible to efficiently estimate elevation at points where data are not available, hence techniques are required that are able to efficiently handle large data sets. This interest in multiple scales across large geographical areas has led naturally to multiscale algorithms, either to improve computation of traditional geostatistical interpolations [43], to get advantage of wavelet interpolation algorithms [44], to complete information (especially in bathymetries) by "superresolution" (techniques inherited from digital image inpainting) [45,46], to store and get access to scale-dependent information [47], to analyze scale-dependent geomorphological features [5,9], or even to extrapolate the topography to finer resolutions than available from the data in what is called geostatistical simulation [48,49].…”