[Insight-users] Mean of transformation parameters

[Eve]

Thanks Luis. One more Q: could you please tell me how to compute the average
of rotation matrices?

i.e. M1 = {r1,.., r9} where r1, ..., r9 are the element of a 3x3 matrix
i.e. M2 = {s1,.., s9}, "   "    "
...

average of {M1, ... M2} = ?

Thanks,
Eve


Luis Ibanez wrote:
> 
> 
> Hi Eve,
> 
> 
> 1) No we can't guarantee that transform would not deviate from the mean.
>     If the optimizer has unstable parameters, a transform can end up very
>     far from a reasonable registration.
> 
>     If you need to guarrantee a certain bound, then, that restriction
>     must be added into the Transfrom or into the Optimizer.
> 
> 
> 2) You probably want to explore the concepts of robust-estimation,
>     http://en.wikipedia.org/wiki/Robust_statistics
>     http://mathworld.wolfram.com/RobustEstimation.html
>     where you first get rid of outliers, and then you use the remaining
>     results for generating a robust mean that is representative of the
>     stable population.
> 
> 3) If you use a set of Affine transforms, you are correct with the
>     intuition that you can only averaget their parameters *if* they
>     are using the same center of rotation.
> 
>     If the center of rotation is different on every case, then you
>     should compute the average of the offset, and the average of the
>     rotation matrix. In this way, the center of rotation will be fused
>     into the offset computation.
> 
> 
> 
>    Regards,
> 
> 
>        Luis
> 
> 
> -----------
> Eve wrote:
>> Hi Users,
>> 
>> Given N sets of transformation parameters, can we guarantee that any one
>> set
>> would not deviate much from the mean set? Say, if one obtains N
>> registration
>> results based on stochastic optimization, how can one report the average
>> result? Further, if an affine transform is used, how can we compute the
>> mean
>> parameters? Is it true that we simply compute the mean, as long as the
>> center of rotation is fixed in N registrations? What if the center of
>> rotations are different in each case?
>> 
>> Thanks,
>> Eve
>> 
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> 
> 

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