Asymptotic error of cubic B-spline interpolation using prefiltering

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.