[Insight-developers] Nonuniform spacing transform

[Luis Ibanez]

Hi Brian


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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