[vtkusers] optimized thin-plate-spline in VTK ?

[Khaldoun Zine El Abidine]

Hi,

Thanks for the response.

As far as I know FMM is an evaluation method, it doesn't compute the TPS
coefficients themselves. Yet FastRBF indeed does both - that is,
solution of the TPS equation as well as evaluation of the TPS over some
given points. However I do not intend to buy FastRBF (too expensive for
me, unfortunately) so there is no point trying it ...

Again thanks for the answer though.

Khaldoun.

-----Original Message-----
From: vtkusers-admin at vtk.org [mailto:vtkusers-admin at vtk.org] On Behalf
Of Liao Qinghu
Sent: 18 décembre 2003 12:40
To: Khaldoun Zine El Abidine; vtk users
Subject: Re: [vtkusers] optimized thin-plate-spline in VTK ?

hi, 

you mean the Fast Multipole Method (FMM). there is a trial version of
the fast radial method. FastRBF

http://www.farfieldtechnology.com/products/toolbox/


On Thu, 2003-12-18 at 09:22, Khaldoun Zine El Abidine wrote:
>  
> 
> Hello everybody,
> 
>  
> 
>  
> 
>  
> 
> I am interested in an “optimized” Thin Plate Spline (TPS)
> interpolation/smoothing algorithm (in 2D). It seems to me that VTK’s
> implementation uses the direct method (i.e. one that inverts a N*N
> matrix). If that is the case, VTK’s implementation has a O (N^2)
> memory usage and a O (N^3) computational complexity, which is
> impractical for N > 5000 when execution time requirements are strict
> (no more than a few seconds on a regular PC). Algorithms in O (N log
> N) complexity exist in the literature (see for example “Fast Solution
> Of The Radial Basis Function Interpolation Equations: Domain
> Decomposition Methods, R. K. BEATSON, W. A. LIGHT, AND S. BILLINGS, in
> Society for Industrial and Applied Mathematics, Vol. 22, No. 5, pp.
> 1717–1740, 2000”, among others). Is anyone aware of a working
> implementation of this algorithm? Is it, or will it be, available in
> present/future versions of VTK ?
> 
>  
> 
>  
> 
> Thank you in advance for you help.
> 
>  
> 
>  
> 
>  
> 
> Khaldoun.
> 
>  
-- 
Qinghu Liao
Department of Computer Engineering,
Polytechnique, University of Montreal
CANADA

qing-hu.liao at polymtl.ca
qhliaok at hotmail.com


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