[MINC-users] mincresample and linear 'deformations'

[Vladimir S. FONOV]

xfm2def samples forward deformation in the space of input image.
Then when you apply the transformation, mincresample will try to 
calculate the inverse (numerically) in the space of output image.
So, if your transformation is a shift of 30mm the forward transformation 
will have the same vector everywhere. However when inverse is 
calculated, mincresmple will reach the edge of the domain where vectors 
are defined and will take value of 0 for the translation outside of this 
domain - that's why you have a sudden jump in the result.

However, if you invert the original affine transformation,  and sample 
it for every voxel and then invert again (applying xfminvert to a 
non-linear transformation doesn't actually recompute the transform, only 
adds a flag that it have to be inverted), then when mincresample will 
run, it will again apply the inverse of the transform, on top of 
inverted transform , negating the need to actually numerically recompute 
the transformation.


On 2016-08-17 04:30 PM, Alex Zijdenbos wrote:
> Right - I am aware of that, but I don't think that explains any of this
> though?
>
> On Wed, Aug 17, 2016 at 3:21 PM, Vladimir S. FONOV <vladimir.fonov at gmail.com
>> wrote:
>
>> When you apply "simple" forward transform, mincresample have to invert it
>> internally.
>>
>> On Wed, Aug 17, 2016 at 1:50 PM, Alex Zijdenbos <zijdenbos at gmail.com>
>> wrote:
>>
>>> These were simple forward resamplings. I experimented a bit with various
>>> sequences of inversions, and found that this process:
>>>
>>> xfminvert( xfm2def( xfminvert( lin.xfm )))
>>>
>>> Yields a deformation grid that I can use in a forward resampling call and
>>> have it produce the same result as resampling using lin.xfm directly.
>>>
>>> Well I am puzzled.
>>>
>>> -- A
>>>
>>> For some more details, I tried these steps. Starting with
>>>
>>> param2xfm -translation 10 20 30 lsq3.xfm
>>> mincresample -use_input_sampling -transform lsq3_D.xfm in.mnc res.mnc
>>>
>>> I had done this:
>>>
>>> xfm2def -float [lattice from input volume] lsq3.xfm lsq3_D.xfm
>>> mincresample -use_input_sampling -transform lsq3_D.xfm in.mnc res_D.mnc
>>>
>>> which "fails". Similarly, this:
>>>
>>> xfminvert lsq3_D.xfm lsq3_D_inv.xfm
>>> mincresample -use_input_sampling -transform lsq3_D_inv.xfm -invert in.mnc
>>> res_D_inv.mnc
>>>
>>> reproduces res_D.mnc (the "bad" result). Note that the xfminvert call in
>>> this case only sets the "Invert" flag in the xfm, it doesn't actually
>>> invert the deformation field. But now, this:
>>>
>>> xfminvert lsq3.xfm lsq3_inv.xfm
>>> xfm2def -float [lattice from input volume] lsq3_inv.xfm lsq3_inv_D.xfm
>>> mincresample -use_input_sampling -transform lsq3_inv_D.xfm -invert in.mnc
>>> res_inv_D.mnc
>>>
>>> Exactly reproduces res.mnc (the "good" result). So inverting the linear
>> xfm
>>> first, then converting it to a deformation and resampling with inversion,
>>> somehow does the right thing. Then this:
>>>
>>> xfminvert lsq3.xfm lsq3_inv.xfm
>>> xfm2def -float [lattice from input volume] lsq3_inv.xfm lsq3_inv_D.xfm
>>> xfminvert lsq3_inv_D.xfm lsq3_inv_D_inv.xfm
>>> mincresample -use_input_sampling -transform lsq3_inv_D.xfm in.mnc
>>> res_inv_D_inv.mnc
>>>
>>> also does the right thing.
>>>
>>>
>>> On Wed, Aug 17, 2016 at 12:28 PM, Vladimir S. FONOV <
>>> vladimir.fonov at gmail.com> wrote:
>>>
>>>> It looks like it's a problem of finding an inverse of the
>> transformation
>>>> outside of the domain where it's defined.
>>>>
>>>> When you apply the transform do you apply it directly or with
>>>> -invert_transformation ?
>>>>
>>>>
>>>> On 2016-08-17 11:54 AM, Alex Zijdenbos wrote:
>>>>
>>>>> Hi all,
>>>>>
>>>>> I was always under the impression that one could turn a linear xfm
>> into
>>> a
>>>>> deformation field (using xfm2def), and that the application of the
>>>>> resulting deformation would be equivalent to using the linear xfm.
>>>>> However,
>>>>> mincresample disagrees.
>>>>>
>>>>> In the attached image, I've created a simpe lsq3 (param2xfm
>> -translation
>>>>> 10
>>>>> 20 30) linear xfm, generated a 'deformation' field out of that using
>>>>> xfm2def (same lattice as the input volume), and resampled the input
>>> volume
>>>>> with both xfms. Clearly, in the case of a 'deformation' xfm, the
>> volume
>>> is
>>>>> filled with unmodified voxels where I didn't expect them.
>>>>>
>>>>> This is tied to the sampling lattice of the deformation field, which
>> in
>>>>> this example is the same as the input volume. The resamplings are done
>>>>> using -use_input_sampling btw. The two bottom rows show the resampling
>>>>> using a padded input volume (no change), and using a 'deformation'
>> grid
>>>>> with a larger extent (generated on a lattice that is 10 voxels larger
>>> all
>>>>> around).
>>>>>
>>>>> To pre-empt Vladimir, itk_resample behaves the same way ;-)
>>>>>
>>>>> Bug, or feature? I'd say the former.
>>>>>


-- 
Best regards,

  Vladimir S. FONOV ~ vladimir.fonov <at> gmail.com