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We review the concepts of the Voronoi binning technique (Cappellari & Copin2003), which optimally solves the problem of preserving the maximum spatialresolution of general two-dimensional data, given a constraint on the minimumsignal-to-noise ratio (S/N). This is achieved by partitioning the data in anadaptive fashion using a Voronoi tessellation with nearly hexagonal lattice. Wereview astrophysical applications of the method to X-ray data, integral-fieldspectroscopy, Fabry-Perot interferometry, N-body simulations, standard imagesand other regularly or irregularly sampled data. Voronoi binning, unlikeadaptive smoothing, produces maps where the noise in the data can be visuallyassessed and spurious artifacts can be recognized. The method can be used tobin data according to any general criterion and not just S/N. It can be appliedto higher dimensions and it can be used to generate optimal adaptive meshes fornumerical simulations.

Voronoi binning: Optimal adaptive tessellations of multi-dimensional data