[Insight-developers] [Insight-registration] vector transformation / reorientation

[brian avants]

Right.  The eigendecomposition approach is part of the "preservation of
principal directions" algorithm used when reorienting diffusion tensors.
 The idea is that, as long as your deformation is a diffeomorphism, you can
estimate it, locally, as an affine transformation.   Then you use the rigid
part of the affine transformation to reorient the tensor's eigenvectors.
 There are a few other steps, though.

My question, in part, is whether ITK's pixel types are specific enough to
uniquely specify the required reorientation.   Some examples:

A diffusion tensor may be reoriented by either PPD (above) or finite strain
estimates.   So this is a non-unique mapping from pixel type to
reorientation strategy.

When reorienting a vector, one may want to change its relative orientation
but not change its length, even under an affine transformation.  Also a
non-unique mapping from pixel type to reorientation strategy.

One approach (what we've done in the past) is to implement filters for each
of these strategies for DTI.  While having filters would be nice, I can see
this becoming confusing, in particular if some metrics/interpolators are
performing reorientation as well.
Matt, I look forward to seeing the strain filter.  Thans much!

Re: Tcon , when would you like to discuss?  Previously, we used 10 am
Tuesday for registration discussions.

Brian

On Nov 20, 2010 4:36 PM, "Luis Ibanez" <luis.ibanez at kitware.com> wrote:
> On Sat, Nov 20, 2010 at 7:14 PM, Matthew McCormick (thewtex) <
> matt at mmmccormick.com> wrote:
>
>> On Sat, Nov 20, 2010 at 6:07 PM, Luis Ibanez <luis.ibanez at kitware.com>
>> wrote:
>> >
>> >
>> > On Sat, Nov 20, 2010 at 7:00 PM, Matthew McCormick (thewtex)
>> > <matt at mmmccormick.com> wrote:
>> >>
>> >> >
>> >> > (b) Estimating the Rotational and Stress component of the
>> >> > deformation field at that pixel location and use it to correct
>> >> > the Vector (or covariant vector) accordingly. This is
>> >> > essentially based on the Jacobian matrix of the deformation
>> >> > field, estimated at the location of the pixel.
>> >> >
>> >>
>> >> I have a StrainImageFilter that calculates the strain tensor from a
>> >> deformation field if it would be of any help. I assume what is meant
>> >> by the 'Rotational and Stress component' are the same as the angles to
>> >> the principle strains and the principle strains. I intend on
>> >> submitting this filter to the Insight Journal in the next week or two
>> >> after I get another paper out and the following patch gets merged:
>> >>
>> >>
>> >>
>>
http://review.source.kitware.com/#q,status:open+project:ITK+branch:master+topic:BUG0010725_VTKTensors3,n,z
>> >>
>> >> Matt
>> >
>> >
>> > Excellent !
>> >
>> > Yes,
>> > that what I meant by the stress component.
>> >
>> > Do you see a way of deriving as well
>> > the rotational component of the Jacobian ?
>> >
>>
>> I was thinking just using
>>
>>
http://www.itk.org/Doxygen320/html/classitk_1_1SymmetricEigenAnalysis.html#_details
>>
>> And the eigenvectors determine the rotation, while the eigenvalues
>> (principle strains) determine the compression/expansion of the
>> components? Correct?
>>
>> Matt
>>
>
>
> Yes,
> That sound very reasonable to me.
>
>
> Luis
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