Adaptive thinning, as recently suggested by Dyn, Floater and Iske, is a recursive point removal scheme for the construction of hierarchical subsets from bivariate scattered data such that the piecewise linear functions over the Delaunay triangulation of the subsets are close to the given data. In this research, adaptive thinning algorithms are used in combination with customized coding schemes for scattered data in order to obtain new flexible methods for digital image compression and their efficient transmission across the internet. First numerical results show the good performance of the resulting compression scheme in comparison with traditional wavelet-based techniques, such as SPIHT and others.