[Insight-users] Thin-plate spline limitations?

[Blezek, Daniel J (Research)]

Hi,

  Just a bit of correction to Jim's statement.  While it is true that ITK
stores the N*D x N*D matrix, it is not needed for evaluation of the spline,
i.e. it's only an intermediate result.  For any of the splines in ITK, the
coefficients that need to be stored are N*D.  Perhaps this matrix could be
released, if it becomes an issue?

-dan

-----Original Message-----
From: Miller, James V (Research) [mailto:millerjv@crd.ge.com]
Sent: Tuesday, May 20, 2003 12:13 PM
To: 'Steve Boyd'; itk
Subject: RE: [Insight-users] Thin-plate spline limitations?


As Luis pointed out, the thin plate spline in ITK does not implement
the FMM approximation.

There are some differences between the ITK and VTK implementations of the
thin plate spline.  ITK allows a weight to be associated with each 
correspondence.  This loosens the requirement that the spline pass
exactly through the correspondence pair.  Essentially, this stiffens
the spline a bit such that low confidence correspondence pairs do
not overly influence the spline.

The ITK thin plate spline is also implemented in a general framework
that also supports the volume spline and the elastic body spline.
This generality, unfortunately, results in some additional overhead
for the thin plate spline case.  Let's assume you have N pairs of 
D-dimensional points that you want to define a thin plate spline. The 
internal storage for the spline is matrix that is N*D x N*D.  A matrix
of this size is needed to support the elastic body spline. But for a
thin plate spline, this matrix should only be NxN. I have meant to go
into the kernel spline code and adapt the implementation such that a
smaller matrix can be used under certain circumstances.

The upside of this generality, however, is that it will (someday) allow 
a covariance matrix to be assigned to each correspondence in a thin plate 
spline which will influence the spline's warp field such that
correspondences 
with low variance are given precedence over correspondences with high
variances. 
Again, this is way to stiffen the spline.




-----Original Message-----
From: Steve Boyd [mailto:skboyd@ucalgary.ca]
Sent: Tuesday, May 20, 2003 12:12 PM
To: itk
Subject: [Insight-users] Thin-plate spline limitations?



Hello,

Is there a limitation to the number of landmarks that can be used in the
thin-plate spline in ITK?  I understand that numerical problems may
occur if too many landmarks are used, and I believe this is the case in
the current VTK implementation.  To overcome this problem, there have
been publications that describe the use of the fast multipole method
(FMM) for approximations
(http://www.aranz.com/download/modelling/papers/siggraph01.pdf), but I'm
not sure if this has been implemented in ITK.  I'd love to use the
thin-plate splines method, but my needs for the algorithm would require
>200,000 landmarks.  

Has the FMM been implemented in ITK's thin-plate splines?

Sincerely,

Steve

-- 
Steven Boyd, PhD

Assistant Professor
Department of Mechanical and Manufacturing Engineering
University of Calgary
2500 University Drive, N.W.
Calgary, Alberta, Canada, T2N 1N4

tel. 1.403.220.4173  fax. 1.403.282.8406  skboyd@ucalgary.ca
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