[Insight-users] Resampling the moving image?

[Luis Ibanez]

Hi Motes,

If you have a Fixed image "F" and a Moving image "M",
and the output of your registration process is the transform
"T",

Then applying "T" to the *points* of the image F will give you
the coordinates of the corresponding points in the image M.

Following your example,
if the transform turns out to be a translation:

                                      T = (1,5)

That means that if we take a point P from the Fixed image
space, and P has coordinates P=(x,y), then we can find the
coordinates of its corresponding point Q in the Moving image
by the following operation:

                        Q = T(P) = ( x+1, y+5 )

The expression T(F) could be interpreted as "mapping all
the points from the fixed image".

T is indeed the transform that is used for resampling the
Moving image M into the coordinates of the Fixed image F.


The way resampling works, is by:

    A)  visiting all the pixels of the Fixed image,
    A.1) for each pixel, compute its physical coordinates
           in the space of the Fixed image
    A.2) Use the transform T to compute the corresponding
            point Q = T(P) in the moving image space
    A.3) convert Q from the physical coordinates of the moving
            image into the grid coordinates of the moving image
    A.4)  Apply an interpolator as needed.

Please note that in the resampling process we DO NOT
NEGATE the transform T.    We use exactly the SAME
transform that is the result of the registration process.

That transform is always the one that maps points from
the physical space of the Fixed image, into the physical
space of the Moving image.


The best way to understand this is to truly try to
writer a resampler from scratch. This exercise
will make evident to you, why is that the direction
of the Transform must go from the Fixed image space
to the Moving image space.


       Regards,


              Luis


---------------------------------------------------------------------------------
On Wed, Nov 4, 2009 at 6:55 AM, motes motes <mort.motes at gmail.com> wrote:
> I am current reading section 8.3 Features of the Registration
> Framework of the itkSoftwareGuide.
>
> The image registration method returns a set of final parameters that
> maps the fixed image into the moving image space:
>
>  F = original fixed image.
>  M = original moving image.
>  T = final transform parameters
>
>  T(F) = M' = currently best known alignment wih the moving image.
>
> So when T is applied to F a "best" approximate to the M is computed.
>
>
>  Its possible to use T to compute (in the resampling process RS) the
> "registered" image R which is the original moving image M mapped into
> the fixed image space:
>
>  RS = resampler
>  RS(M,T) = R
>
>
> But I don't understand how that works. Assume that a translation
> transform T = (1,5)   is returned from the image registration process.
> This means that translating all points in F with (x,y) = (1,5) gives a
> pretty good approximation to M.
>
>
>
> Now in the resampler is T simply negated meaning that T=(-1,-5) is
> applied instead of T=(1,5)?
>
> I don't think it makes much sense to apply T directly to M since that
> would just further move M.
>
> But I guess I am misunderstanding some basic stuff here.
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