Hex-splines: a novel spline family for hexagonal lattices
Hex-splines: a novel spline family for hexagonal lattices
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六角样条：六角格子的新型样条系列
DOI：
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发表时间：
2004
影响因子：
10.6
通讯作者：
R. Walle
中科院分区：
文献类型：
--
作者：
D. Ville;T. Blu;M. Unser;W. Philips;I. Lemahieu;R. Walle
This paper proposes a new family of bivariate, nonseparable 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.
