2009/12/07 by Michele Cappellari, Cappellari, Michele · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · #FOS: Physical sciences #Geophysics and Gravity Measurements #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Scientific Research and Discoveries #Stellar, planetary, and galactic studies #astro-ph.IM
paper · pdf · doi:10.48550/arxiv.0912.1303
16 pages, 11 figures, LaTeX. Invited review for the volume "Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings", eds. R. van de Weijgaert, G. Vegter, J. Ritzerveld and V. Icke, Kluwer/Springer (submitted). A reference implementation of the method is available at http://purl.org/cappellari/idl
arxiv created 2009/12/07 · openalex publication_date 2009/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We review the concepts of the Voronoi binning technique (Cappellari & Copin 2003), which optimally solves the problem of preserving the maximum spatial resolution of general two-dimensional data, given a constraint on the minimum signal-to-noise ratio (S/N). This is achieved by partitioning the data in an adaptive fashion using a Voronoi tessellation with nearly hexagonal lattice. We review astrophysical applications of the method to X-ray data, integral-field spectroscopy, Fabry-Perot interferometry, N-body simulations, standard images and other regularly or irregularly sampled data. Voronoi binning, unlike adaptive smoothing, produces maps where the noise in the data can be visually assessed and spurious artifacts can be recognized. The method can be used to bin data according to any general criterion and not just S/N. It can be applied to higher dimensions and it can be used to generate optimal adaptive meshes for numerical simulations.