[Insight-users] Inverse of ScaleSkewVersor3DTransform

[Karthik Krishnan]

Karthik Krishnan wrote:

> Please correct me if I am wrong:
>
> A ScaleSkewVersor3DTransform is exactly the same as an 
> AffineTransform, with a more intuitive representation of parameters. 
> (ie the 3 scales and 6 skews in addition to the versor and translation)
>
> The inverse is then the inverse of the affine matrix, which is another 
> affine transform.
>
> I am pretty sure somebody has done the math to decompose an affine 
> transform into the scale, skew, Rotation matrix and translation 
> components. At least it sounds like something one would often want to 
> do to get a meaningful interpretation from an affine transform. If you 
> do find that, we could add it back into the class.
>
On second thought, this might be harder than it seems. Every 
ScaleSkewVersor3DTransform can be represented by an affine transform. 
The mapping

{ ScaleSkewVersor3DTransform }  ---- >  { AffineTransform }
 
is a many to one mapping. (3 scale +6 skew +3 versor parameters + 3 
translation parameters,,, all independent of each other) to represent  
the (12 parameters of the affine matrix).

So the inverse decomposition will not be unique.

> Regards
> karthik
>
> Ranjan, Sohan (Research) wrote:
>
>> I am doing registration using the ScaleSkewVersor3DTransform. As per ITK
>> registration convention, the transform returned is from the fixed 
>> image space to the moving image space. I am not using the resample 
>> filter for resampling
>> the moving image due to certain reasons, so I need to find an inverse 
>> of the
>> transform myself. But it looks like that the inverse for 
>> ScaleSkewVersor3DTransform
>> is not defined.
>>
>> Can someone suggest how should I go about constructing the inverse?
>>
>> Sohan
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>>  
>>
>