Adaptive Thinning for Terrain Modelling and Image Compression

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 minimize 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 postprocessing least squares optimization and a customized coding scheme, often gives better or comparable results to the wavelet-based scheme SPIHT.