[Insight-developers] Nonuniform spacing transform

[brian avants]

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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