[Insight-users] A quick question on combining displacement fields

[Anja Ende]

Hello,

This is a follow up to my earlier question. I have been thinking about
this and was wondering if someone could verify whether my line of
thinking is correct or now.

So, I have these three images A, B and C and I have the following
transformations and the displacement fields.

- Displacement field in the grid of B (fixed image) that maps each
point in image B to a point in image A. This is the result of
registering image A (moving image) to image B (fixed image). Let us
call this T1.

- Displacement field in the grid of C (fixed image) that maps each
point in image C to a point in image B. This is the result of
registering image B (moving image) to image C (fixed image). Let us
call this T2.

Now I want to to generate the displacement field that will map each
point in image C to each point in image A or equivalantly the result
of registering image A (moving image) to image C (fixed image). Can I
do the following:

- For each index (in mm) in image C, add the corresponding
displacement vector from T2 to get the corresponding position in image
B.
- Transform this position (in mm) in image B to the corresponding
voxel position in image B.
- Go to that voxel and get the displacement vector from T1 and add it
to the calculated physical (mm) position to get to the physical
position in image A.
- Compute the index position in image A from this physical position.

- Resample to compute the corresponding intensity value in the grid
position of image C.

Does that make sense or is it completely wrong. Is there a better way
to go about this?

I am sorry this is not a core ITK question but I want to make sure
that I understand what I am doing and not blindly use a filter without
knowing what it actually does.

Many thanks,
Anja

On 4 September 2010 14:17, Anja Ende <anja.ende at googlemail.com> wrote:
> Hello,
>
> I have a set of three images (say A, B and C) and my registration
> process is as follows:
>
> A (moving image) is registered to B (fixed image) rigidly. I take the
> transformation and generate a displacement or position field using the
> grid of the fixed image (B).
>
> B (moving image) is registered to C (fixed image) using non-rigid
> transformation. I can generate a similar displacement or position
> field using the grid of fixed image (C).
>
> Now, what I want to do is combine these two displacement or position
> fields and generate a composite field that I can use to resample A
> using the composite transformation in the space of C.
>
> However, I am not clear on how I should combine these displacement or
> position fields as the grid sizes of B and C may not be the same.
>
> One simple solution is to do two resampling: first one to resample A
> into the space of B and then resample the result using the second
> transformation into the space of C. However, I would like to avoid
> this multiple resampling, if possible.
>
> Does anyone have any idea on how I can go about this?
>
> I would really appreciate your help and comments.
>
> Thanks,
>
> Anja
>



-- 
Cheers,

Anja