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Three-directional box-splines: characterization and efficient evaluation

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2 Author(s)
Condat, L. ; Lab. of Images & Signals, Inst. Nat. Polytech. de Grenoble ; Van De Ville, D.

We propose a new characterization of three-directional box-splines, which are well adapted for interpolation and approximation on hexagonal lattices. Inspired by a construction already applied with success for exponential splines and hex-splines, we characterize a box-spline as a convolution of a generating function, which is a Green function of the spline's associated differential operator, and a discrete filter that plays the role of a localization operator. This process leads to an elegant analytical expression of three-directional box-splines. It also brings along a particularly efficient implementation

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Signal Processing Letters, IEEE  (Volume:13 ,  Issue: 7 )