[Insight-developers] Nonuniform spacing transform

[brian avants]

   hmm. i wasnt actually proposing anyone try to make every image
filter in itk work on meshes, though working on point sets with
topological neighborhoods would encapsulate most of the non-uniform
cases i've seen discussed ... + in the context of the image
refactoring stuff, it seems a similar problem.   that is, in
permitting a non-uniform neighborhood connection, the data object
becomes very similar to a mesh.   if you want to know how to do a
mathematical operation on a mesh (or an image with a non-uniform
neighborhood) there are new implementation questions that come up.
for instance, the field of finite elements was largely developed in
order to deal, in a general way, with domain representations that are
non-uniform.   that is, finite difference solutions break down in
those domains.   when i look at this page (
http://www.itk.org/Wiki/ITK_Release_4/Image_Class_Hierarchy_Refactoring
) ,  i see many filters listed at the bottom of the page that need to
be "fixed" to deal with non-linearities in spacing.    it's just not
clear how that can be done without using FEM or some other systematic
approach to model the regular-to-irregular grid transformations.
alternatively, if you first apply a transformation to an image that
factors out the nonlinearity, then you are ok with most of the
standard operations that exist it itk.    you can then transform the
output of the linear-space filter operation back to the nonlinear
space.   maybe this is a reasonable alternative to trying to fix each
filter to work with some unknown amount of nonlinearity in spacing?