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|a (DE-627)NLM153094427
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|a (NLM)15648867
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|a DE-627
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|c DE-627
|e rakwb
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|a eng
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|a Van De Ville, Dimitri
|e verfasserin
|4 aut
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|a Hex-splines
|b a novel spline family for hexagonal lattices
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|c 2004
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|a Text
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|a ohne Hilfsmittel zu benutzen
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|2 rdamedia
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|a Date Completed 10.02.2005
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|a Date Revised 10.12.2019
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|a published: Print
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|a Citation Status MEDLINE
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|a 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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|a Comparative Study
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|a Evaluation Study
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|a Journal Article
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|a Research Support, Non-U.S. Gov't
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|a Blu, Thierry
|e verfasserin
|4 aut
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|a Unser, Michael
|e verfasserin
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|a Philips, Wilfried
|e verfasserin
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|a Lemahieu, Ignace
|e verfasserin
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|a Van de Walle, Rik
|e verfasserin
|4 aut
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|i Enthalten in
|t IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
|d 1992
|g 13(2004), 6 vom: 23. Juni, Seite 758-72
|w (DE-627)NLM09821456X
|x 1941-0042
|7 nnns
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|g volume:13
|g year:2004
|g number:6
|g day:23
|g month:06
|g pages:758-72
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|d 13
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|e 6
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|h 758-72
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