The aim of this talk is to discuss the construction of minimally supported basis functions for Hermite interpolation on a three directional mesh of the plane. Our model relies on three directional Box-splines and gets advantage from the deep relationship between Hermite and Bézier representation of piecewise bivariate polynomials. Starting by the simpler but analogous univariate case, we will show how the use of Greens' function allows us to unreveil all theoretical properties of the new bivariate Hermite basis functions. The proposed model meets practical requirements such as invariance to affine transformations and good approximation properties.One of its great advantages is its non tensor-product structure which avoids the use of mixed derivatives and makes it suitable to Hermite-like representation of images in terms of samples with local tangents.

This presentation is part of Minisymposium “MS47 - Splines in Imaging (3 parts)”
organized by: Carolina Beccari (Dept. Mathematics, University of Bologna) , Virginie Uhlmann (EPFL, Lausanne) , Michael Unser (EPFL, Lausanne) .

Authors:

Costanza Conti (University of Firenze)

Lucia Romani (University of Milano-Bicocca)

Michael Unser (EPFL, Lausanne)

Keywords:

box-splines, hermite interpolation, image reconstruction, three directions mesh