Hex-Splines: A Novel Spline Family for Hexagonal Lattices

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.


Published in:
IEEE Transactions on Image Processing, 13, 6, 758–772
Year:
2004
Publisher:
IEEE
Keywords:
Other identifiers:
Laboratories:




 Record created 2005-11-30, last modified 2018-10-07

n/a:
Download fulltextPDF
External links:
Download fulltextURL
Download fulltextURL
Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)