[Insight-users] Preserving topology - image registration?

[Luis Ibanez]

Hi Motes,

It will be hard to speak for what other authors meant when they
used the term "preserving topology",...

but,
a reasonable interpretation is that the neighborhood relationships
between different objects in the image should be preserved by
the transform that maps one coordinate system to the other.

Most ITK transforms will preserve topology. In particular, any
rigid, similarity and affine Transform will preserve topology.

On the other hand, examples of Transforms that "may not"
preserve topology are:

* BSplineDeformable transform
* Kernel Transforms
* Dense deformation fields

and we say "may" because the circumstances in which the
topology is not preserved are when the Transform applies
the equivalent of a "folding".   This can, in principle, be
detected by computing the Determinant of the Jacobian of
the transformation and checking if it ever changes signs.

To put it short, unless you are using a deformable registration
method, such as Demons, or the BSplineDeformable transform,
you don't have to worry too much about the preservation of
topology.


     Regards,


          Luis


-----------------------------------------------------
On Sun, Oct 25, 2009 at 1:41 PM, motes motes <mort.motes at gmail.com> wrote:
> In various articles on image registration I have read the transforms
> must preserve topolgy. But what does "preserving topology" mean? The
> closest explanation I found was that artifacts like introduction of
> noice and edges in the image should not be allowed. But is there a
> more formal description on what preserving the topolgy means?
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