Numerical Algorithms

, Volume 70, Issue 1, pp 191–203

Asymptotic error of cubic B-spline interpolation using prefiltering

Open Access
Original Paper


A popular class of reconstruction filters that are used in signal and image processing is based on cubic B-splines. One reason for their popularity is the fact that they can be efficiently implemented. This is specifically true with modern GPUs where cubic B-spline filtering can be implemented by means of linearly interpolating texture fetches so that the actual number of memory accesses can be significantly reduced. The curve obtained from filtering with the cubic B-spline does in general not interpolate the original data set. The latter can however be achieved by applying a prefiltering step that transforms the original data set. We study the asymptotic behavior of the reconstruction error of the cubic B-spline interpolation filter using a state of the art method that is based on a Taylor series expansion and that was carefully adjusted to accommodate the infinite support of this reconstruction filter.


Splines Reconstruction Asymptotic error 

Copyright information

© The Author(s) 2014

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  1. 1.Chair of Computer ScienceUniversity of CologneCologneGermany

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