[SciPy-user] Thin plates for a 3D deformation field

Zachary Pincus zpincus@stanford....
Sat Oct 27 18:01:57 CDT 2007

Hello Matthieu,

I don't know of any fast multipole solver or anything fancy like that  
for dealing with evaluating the splines rapidly, but for simple  
purposes, the rbf module in scipy.sandbox should do just fine.

Set the function to 'thin-plate', and you will get a thin-plate  
spline interpolator that can interpolate values of arbitrary  
dimension in spaces of arbitrary dimension. So it should naturally be  
able to interpolate a 3D deformation field in three dimensions, or  
any other combination you might want.

I haven't used the RBF module exclusively (I wrote my own thin-plate  
spline interpolator before it existed -- it's a very small amount of  
code), but I think that that module should be just right. One note:  
this sort of interpolation can be very slow if you're going to be  
interpolating the deformations over a fine grid -- for, say, using  
the deformation field for image warping. This is where one might  
start wanting a fast multipole solver. I find that in most cases, I  
can get away with interpolating the deformations on a relatively  
coarse grid, and then using linear interpolation to fill in the gaps.  
(The resizing methods in ndimage come in useful here -- just scale up  
the x, y, and z components of the deformation separately.)

Zach Pincus

On Oct 26, 2007, at 4:35 AM, Matthieu Brucher wrote:

> Hi,
> I wondered if someone knew of a package that allows the  
> interpolation of a 3D deformation field with thin plates (or in  
> fact with anything) based on a list of points and their associated  
> deformation field.
> If only 2D deformation field is supported by a package, I'll go for  
> it too ;)
> -- 
> French PhD student
> Website : http://miles.developpez.com/
> Blogs : http://matt.eifelle.com and http://blog.developpez.com/? 
> blog=92
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