We provide a new comparison between hexagonal and orthogonal lattices, based on approximation theory. For each of the lattices, we select the "natural" spline basis function as generator for a shift-invariant function space; i.e., the tensor-product B-splines for the orthogonal lattice and the non-separable hex-splines for the hexagonal lattice. For a given order of approximation, we compare the asymptotic constants of the error kernels, which give a very good indication of the approximation quality. We find that the approximation quality on the hexagonal lattice is consistently better, when choosing lattices with the same sampling density. The area sampling gain related to these asymptotic constants quickly converges when the order of approximation of the basis functions increases. Surprisingly, nearest-neighbor interpolation does not allow to profit from the hexagonal grid. For practical purposes, the second-order hex-spline (i.e., constituted by linear patches) appears as a particularly useful candidate to exploit the advantages of hexagonal lattices when representing images on them.


    Zugriff

    Zugriff prüfen

    Verfügbarkeit in meiner Bibliothek prüfen

    Bestellung bei Subito €


    Exportieren, teilen und zitieren



    Titel :

    Hexagonal versus orthogonal lattices: a new comparison using approximation theory


    Beteiligte:
    Condat, L. (Autor:in) / Van De Ville, D. (Autor:in) / Blu, T. (Autor:in)


    Erscheinungsdatum :

    2005-01-01


    Format / Umfang :

    941890 byte




    Medientyp :

    Aufsatz (Konferenz)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch



    Hexagonal Versus Orthogonal Lattices: A new Comparison using Approximation Theory

    Condat, L. / Van De Ville, D. / Blu, T. | British Library Conference Proceedings | 2005



    A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models

    Guinta, A. / Watson, L. / AIAA et al. | British Library Conference Proceedings | 1998


    Fast Gravitational Field Model Using Adaptive Orthogonal Finite Element Approximation

    Younes, A. | British Library Conference Proceedings | 2014