Hex-splines : a novel spline family for hexagonal lattices
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...
| Veröffentlicht in: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 1992. - 13(2004), 6 vom: 23. Juni, Seite 758-72 |
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| 1. Verfasser: | |
| Weitere Verfasser: | , , , , |
| Format: | Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2004
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society |
| Schlagworte: | Comparative Study Evaluation Study Journal Article Research Support, Non-U.S. Gov't |
| Zusammenfassung: | 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 |
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| Beschreibung: | Date Completed 10.02.2005 Date Revised 10.12.2019 published: Print Citation Status MEDLINE |
| ISSN: | 1941-0042 |