[Insight-users] Preserving topology - image registration?

[Luis Ibanez]

Hi Motes,

Here is a way of visualizing what "folding" means.

Imagine the image of Lenna:
http://en.wikipedia.org/wiki/Lenna

Let's say that the distance between the centers
of her eyes is 50 pixels.

Then imagine that we apply to this image a
deformation field that move her left eye (the eye
that we see in the right side of the image),
10 pixels to the right, while at the same time
moves her right eye (the eye that we see in the
left side of the image) by 65 pixels to the right,
and compound that with the assumption that
almost everywhere else, the deformation field
is close to zero.


Such transformation will swap the left-right
relationships of the eyes and will require that
the central part of the face will be flipped.
Her right eye will end up in the left side of
her face, at 5 pixels from her left eye, which
now will be on the right side of her face.


That's what a folding will look like, and
what could be described as non-preserving
the topology.


     Regards,


              Luis


-------------------------------------------------------------
On Tue, Oct 27, 2009 at 7:33 PM, motes motes <mort.motes at gmail.com> wrote:
> I am using the BSplineDeformableTransform. You write that when the
> topology is not preserved it appears as a "folding". But what does a
> "folding" look like and what might cause it?
>
>
>
> On Sun, Oct 25, 2009 at 11:00 PM, Luis Ibanez <luis.ibanez at kitware.com> wrote:
>> 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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>