[Insight-users] Direction of the transform in the registration framework

[Luis Ibanez]

Hi Anja,

Thanks for sharing your findings.


Regarding your remaining question:

Please consider the following simple case of resampling:

A) Fixed image
    Size 100 x 100 pixels
    Spacing 1.0mm x 1.0 mm
    Origin    0.0, 0.0
    Direction: Identity Matrix

B) Moving image

    Size 50 x 50 pixels
    Spacing 2.0mm x 2.0 mm
    Origin    0.0, 0.0
    Direction: Identity Matrix

C) Transform: Identity


If you do the resampling by visiting all pixels from
the Moving image, and finding their corresponding
pixels in the Fixed image, you will visit

                 50 x 50 = 2,500 pixels,

and will find destinations for them and store there
the appropriate intensities.

The fixed image, however, has

              100 x 100 = 10,000 pixels.

So clearly there will be 7,500 pixels that will not
receive an intensity value. Those are the "holes"
to which we are referring in the ITK Software Guide.

This is the reason why resampling must be done
by visiting the pixels of the destination image.


      Regards,


            Luis


---------------------------------
On Wed, Mar 24, 2010 at 8:11 PM, Anja Ende <anja.ende at googlemail.com> wrote:
> Hello,
>
> I think I now see how this would work. Had missed that the resampler
> would iterate through all the voxels in the fixed image grid and
> assign the transformed them intensity values interpolated from the
> moving image. Now, I can see how this would result in a translation in
> the opposite direction after the resampling.
>
> However, one last question in the same vein. The guide says:
> "If we have used the Transform that maps coordinates from the moving
> image physical space into the fixed image physical space, then the
> resampling process could not guarantee that every pixel in the grid of
> the fixed image was going to receive one and only one value. In other
> words, the resampling will have resulted in an image with holes and
> with redundant or overlapped pixel values."
>
> Is this true for even simple transforms as I mentioned before. I am
> having difficulty seeing how this would be the case for affine or
> rigid transforms. Here every voxel sould map to a unique position in
> space, right? Can someone give an example or explain when this might
> occur?
>
> Thanks,
>
> Anja
>
> On 24 March 2010 23:39, Anja Ende <anja.ende at googlemail.com> wrote:
>> Hello,
>>
>> This is discussed in the software guide but I wam having a bit of
>> trouble understanding why the transform that is optimized is the one
>> that takes you from points fixed image to points in moving imge.
>>
>> The guide says:
>>
>> "What tends to create confusion is the fact that when the Transform
>> shifts a point on the positive X direction, the visual effect of this
>> mapping, once the moving image is resampled, is equivalent to manually
>> shifting the moving image along the negative X direction".
>>
>> I am struggling to see how this is. Say as an example,the optimized
>> transformation from fixed to moving image is a simple translation by 5
>> mm. So, my deformation field is where every point is shifted by 5 mm.
>> How does the resampler use this information and how is equivalant to
>> shifting the moving image by -5 mm? If someone could help me
>> understand what happens say at a chosen point..it would help me a lot.
>> I think I am not understanding how the resampler would effect the
>> moving image given that the transformation is:
>>
>> 1 0 0 5
>> 0 1 0 0
>> 0 0 1 0
>> 0 0 0 1
>>
>> I would be really grateful if someone could illustrate this to me...
>>
>> Many thanks!
>>
>> Cheers,
>>
>> Anja
>>
>
>
>
> --
> Cheers,
>
> Anja
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