[Insight-users] LandmarkBasedTransformInitializer

[Karthik Krishnan]

Please find comments inlined.

Hari wrote:
> Hi all,
>
>   I am using the LandmarkBasedTransformInitializer to find the 
> transform from a set of correspondences. I want to specify the center 
> of rotation. I initialize the transform by setting this center. 
> However, after the LandmarkBasedTransformInitializer has run, the 
> center of rotation is changed. 
The class does not allow you to specify constraints on the final 
solution. It will analytically compute the optimal LeastSquares rigid 
transform given two point sets with point correspondances as outlined in

 Berthold K. P. Horn (1987), "Closed-form solution of absolute 
orientation using unit quaternions,"

> I have tried Euler2DTransform and CenteredRigid2DTransform. 
How did you manage to that with this class ?

I've mentioned clearly in the documentation of the class that it will 
work only with the VersorRigid3DTransform (in 3D) and Rigid2DTransform 
(in 2D).

I end up throwing an exception if any other transform is supplied as input.

> In both cases I get a center different from the one I initialized 
> with. Is there a way to keep the center of rotation constant and 
> estimate the other parameters based on that ?
No.

In any case your question is irrelevant. Let me explain..

The rigid transform computed by the class is mathematically represented 
as (let me deviate from the versor notation used in the class to matrix 
notation):

  p' = R (p - C)  + C  + T


where the point p is transformed to p'.
R = rotation matrix
C = center
T = translation.

Note that the number of terms is over-constrained. (In reality, you need 
just 6 parameters to represent a rigid transform, not 15 terms (9 
rotation + 3 center + 3 translation).


The class will find the optimal values of R, T and C.

Even if you constrained C, the class would end up computing an 
appropriate value of T so as to give you the same solution.

>
> Thanks,
> Hari
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Regards

--
Karthik Krishnan
R & D Engineer,
Kitware Inc,