Van De Ville, D.Blu, T.Unser, M.Philips, W.Lemahieu, I.Van de Walle, R.2005-11-302005-11-302005-11-30200410.1109/TIP.2004.827231https://infoscience.epfl.ch/handle/20.500.14299/220718WOS:0002214664000035221This paper proposes a new family of bivariate, non-separable splines, called hex-splines, especially designed for hexagonal lattices. The starting point of the construction is the indicator function of the Voronoi cell, which is used to define in a natural way the first-order hex-spline. Higher order hex-splines are obtained by successive convolutions. A mathematical analysis of this new bivariate spline family is presented. In particular, we derive a closed form for a hex-spline of arbitrary order. We also discuss important properties, such as their Fourier transform and the fact they form a Riesz basis. We also highlight the approximation order. For conventional rectangular lattices, hex-splines revert to classical separable tensor-product B-splines. Finally, some prototypical applications and experimental results demonstrate the usefulness of hex-splines for handling hexagonally sampled data.Hex-Splinestext::journal::journal article::research article