[Insight-developers] Nonuniform spacing transform

[brian avants]

Luis

I agree with both (A) and (B) ... one thing we are assuming in the
revised transform classes is that each transform has a GetInverse()
function (even the deformation field transforms).   In that case, I
would still create a NuToU2 filter but would  invoke its inverse.
Sorry for being unclear.

Another approach to solve this problem generally would be to represent
images as point-sets / meshes ... and then make sure that all filters
work properly on them where the spacing between "voxels" is controlled
by edge distance.

B

> A) Shouldn't
>
>      Image1 => NuToU1 =>  Affine =>  NuToU2 => Image2
>
>      rather be:
>
>      Image1 => NuToU1 =>  Affine =>  UToNU2 => Image2
>
>      where UToNU2 :  UniformToNonUniformTransform
>
>
> B) As long as NuTU and UToNU are one-to-one mappings,
>      this approach seems to be generic enough.
>
>
> It may be convenient for the purpose of the software
> implementation to distinguish between non-uniform
> spacing (variable spacing) and non-orthogonal grids.
>
>
>    Luis
>
>
> -------------------------------------------------------
> On Fri, Oct 15, 2010 at 11:07 PM, brian avants <stnava at gmail.com> wrote:
>>
>> There seems to be significant interest in dealing  with images that have
>> irregular spacing or that exist in non-rectangular spaces, e.g. projective
>> or spherical coordinates ....
>>
>> in general, the way we like to deal with these initially nonlinear
>> problems is to choose a mapping that linearizes the space.  that is, undo
>> the nonlinearity before we solve the problem with registration.   e.g. if
>> the image coordinates are cylindrical we would first want to map the voxel
>> coordinates to cylindrical coordinates ----  ( i , j ) =>   ( radius , theta
>> ) .
>>
>>  so, for the moment, let's suppose we define a transform called
>>
>> itkNonuniformToUniformSpacingTransform
>>
>> or somesuch which can be concatenated with any other transform via the
>> CompositeTransform class ( which we hope to push to Gerritt soon ).
>>
>> The idea is that the NonuniformToUniformSpacingSpacingTransform would map
>> the regular grid positions of a standard itk image to the correct physical
>> space.    In practice, of course, this may be a deformation field, b-spline
>> , parametric model or whatever ... It's difficult to predict what
>> transformation would be needed , but if it's implemented as a standard
>> transform, then we can easily add it to the CompositeTransform which can
>> also contain other transforms.  So, one example registration might be as
>> follows:
>>
>> Image1 => NuToU1 =>  Affine =>  NuToU2 => Image2
>>
>> where we map between two image with nonuniform spacing by an affine
>> transform.
>>
>> does this make sense?  do people have an idea of what cases would not be
>> handled by this approach?
>>
>>
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