B-Spline Interpolation

Dear Newsgroup

  when using B-Splines for interpolation purposes, we have to prefilter 
the image (signal) to get B-Spline coefficients. This is done 
efficiently by using a cascade of first-order causal and anti-causal 
recursive filters. Once we have this coefficients, the interpolation 
itself works similar to standard convolution based interpolation (eg 
cubic convolution, sinc, ...).
(refering to the masters of image interpolation: Michael Unser, Erik 
Meijering, Philippe Thévenaz)

Question 1: if we only want to interpolate few points of the image, the 
prefiltering is a computational overkill. Is there an efficient method 
when only interpolating few samples using B-Splines?

Question 2 & 3: the B-spline coefficients are of type <double> after 
prefiltering. if our input image is of type <byte> (8 bit), we need 8 
times more memory (double == 64 bit). Is there somewhere an evaluation 
available which gives the computational error, if we only use - lets say 
- 16 bit to represent the spline coefficients?

And what's the error if we only use blocks of a big image - eg 512x512 - 
 and perform the interpolation there? Because of the digital 
prefiltering (causal, anticausal) the spline coeffients will change, 
when performing a block-processing.

Thanks, Roland Perko

--
DI Roland Perko - Computer Graphics and Vision
Graz University of Technology, Inffeldgasse 16/II, 8010 Graz, Austria
Phone: +43/316/873-5028, Fax: +43/316/873-5050, Room: E3.19
WWW: http://www.icg.tu-graz.ac.at/~perko