[Insight-users] Versor3DRegistration and the masks of meanSquareMetric

[Martin Urschler]

> I may be wrong here, but is there any reason to optimize both the center 
> and the translation ...
> 
> For the VersorRigid3DTransform which may be re-written as
> 
> p' = R(p-C) + C + T = Rp +  C(I-R) + T
> 
> If you were to optimize just R and T and specify a default center, you 
> should still be able to arrive at an equivalent translation that rotates 
> about any other center, if the optimizer does a good job.

I see your argument and basically agree with it. But thinking about that 
I ask myself why there exist Euler3DTransform and 
CenteredEuler3DTransform separately. The latter one explicitly take the 
center of rotation as optimization parameters as well, right? Since 
AffineTransforms (or some of the others for which Centered versions 
exist) are derived from MatrixOffsetBaseTransform (defining the same 
basic behaviour VersorRigid3DTransform is showing), what are the 
Centered versions good for in addition? Or am I mixing up something here?

regards,
Martin