D. Van De Ville, T. Blu, M. Unser, W. Philips, I. Lemahieu and R. Van de Walle, Hex-splines: a novel spline family for hexagonal lattices, IEEE Transactions on Image Processing, Vol. 13, No. 6, pp. 758-772, 2004.
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http://bigwww.epfl.ch/publications/vandeville0402.pdf
Code/Data:
http://bigwww.epfl.ch/demo/hexsplines/
BibTeX:
http://bigwww.epfl.ch/publications/vandeville0402.html
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http://bigwww.epfl.ch/publications/vandeville0402.html
Abstract:
This 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.
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