title: Quasi-interpolating spline models for hexagonally-sampled data.
abstract: The reconstruction of a continuous-domain representation from sampled data is an essential element of many image processing tasks, in particular, image resampling. Until today, most image data have been available on Cartesian lattices, despite the many theoretical advantages of hexagonal sampling. In this paper, we propose new reconstruction methods for hexagonally sampled data that use the intrinsically 2-D nature of the lattice, and that at the same time remain practical and efficient. To that aim, we deploy box-spline and hex-spline models, which are notably well adapted to hexagonal lattices. We also rely on the quasi-interpolation paradigm to design compelling prefilters; that is, the optimal filter for a prescribed design is found using recent results from approximation theory. The feasibility and efficiency of the proposed methods are illustrated and compared for a hexagonal to Cartesian grid conversion problem.
authors.affiliation: National Research Center for Environment and Health (GSF), Munich, Germany. laurent.condat@gsf.de
authors.forename: Laurent
authors.initials: L
authors.lastname: Condat
authors.forename: Dimitri
authors.initials: D
authors.lastname: Van De Ville
mesh_terms: D000465:Algorithms; D003196:Computer Graphics; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D015203:Reproducibility of Results; D018401:Sample Size; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted