[MINC-users] mincresample and linear 'deformations'

Alex Zijdenbos zijdenbos at gmail.com
Thu Aug 18 20:38:53 EDT 2016 

Hi Bert,

Agreed on carefully testing. I would argue that implementationally this
would be the correct behaviour of evaluate_grid_volume() though. "0
displacement" and "cannot compute displacement" are two very different
things, and it should be up to the caller to decide how to interpret these.

-- A

On Thu, Aug 18, 2016 at 11:36 AM, Robert D. Vincent <
robert.d.vincent at mcgill.ca> wrote:

> Hi Alex,
>
> Sure, it's possible, but I would have to be careful about the unintended
> consequences. My biggest issue is how the change might affect some of the
> clients of the transform functions. At the very least the change would be
> the effect on some of the libminc tests - several would have to be modified
> to account for the change in behavior of general_transform_point() and its
> ilk.
>
>     -bert
>
> On Thu, Aug 18, 2016 at 11:00 AM, Alex Zijdenbos <zijdenbos at gmail.com>
> wrote:
>
> > Hi all,
> >
> > Thanks for all your input. I'm still trying to figure out how to do what
> I
> > want, which is really to convert an arbitrary xfm into a deformation
> field
> > and have everything "just work", but I have some ideas that I'll pursue.
> >
> > Bert, whatever the "right thing" is for mincresample, I'm pretty sure we
> > don't want to change its current behaviour; however, do you think it
> would
> > be feasible to add an option to it to control this? Would require
> > implementing what you suggest, and then adding a mincresample option to
> > insert the fill value as opposed to assuming '0 displacement'.
> >
> > -- A
> >
> >
> >
> > On Thu, Aug 18, 2016 at 10:37 AM, Robert D. Vincent <
> > robert.d.vincent at mcgill.ca> wrote:
> >
> > > Hi all,
> > >
> > > The core of the issue from an implementation perspective is the
> function
> > > evaluate_grid_volume(), which is responsible for evaluating the grid
> > > transform for a point in world space. If the point lies outside the
> grid,
> > > this function silently returns zero for all of the displacements, so
> the
> > > point is not transformed and the original data is copied.
> > >
> > > It is trivial to modify this function to return an error indication if
> > the
> > > point is outside the grid, so that the resampling process could "do the
> > > right thing", whatever that is...
> > >
> > >     -bert
> > >
> > > On Wed, Aug 17, 2016 at 8:38 PM, Andrew Janke <a.janke at gmail.com>
> wrote:
> > >
> > > > Note that xfm2def does not have to calculate the sampling of the grid
> > > > from the input volume. You can define this output grid transform
> > > > sampling however you choose. This will solve your current problem,
> but
> > > > not all problems like this as the input xfm can be any xfm, which
> > > > itself may have a defined sampling (eg: def grid)
> > > >
> > > > I'd argue that what you are seeing is correct behaviour, I use this
> > > > feature of mincresample regularly when doing resampling of large (TB
> > > > scale) microscopy data. In this case you perform the registration on
> > > > chunks and then perform some magic to smoothly interpolate the
> > > > resulting deformation grids at the edges. Move edges, repeat,
> iterate.
> > > >
> > > >
> > > > a
> > > >
> > > > On 18 August 2016 at 08:05, Alex Zijdenbos <zijdenbos at gmail.com>
> > wrote:
> > > > > Thanks, Louis, Vlad!
> > > > >
> > > > > I was getting to the same conclusion as Vlad's explanation; but
> that
> > > > still
> > > > > leaves me with the problem that two conceptually the same
> operations
> > > > > generate very different output:
> > > > >
> > > > > 1) voxel-wise transformation inversion fails (due to lack of
> support)
> > > =>
> > > > 0
> > > > > deformation => insert source image value
> > > > > 2) voxel-wise transformation ok/no inversion needed, points outside
> > > input
> > > > > image => insert 0 (or fill value).
> > > > >
> > > > > Not sure how to deal with this, unless by adding an option to
> > > > mincresample
> > > > > that would insert a 0 (fill value) when the transformation
> inversion
> > > > fails,
> > > > > as opposed to treating that as '0 transformation'. E.g.,
> > > > -fill_def_missing
> > > > > or some such.
> > > > >
> > > > > Alternatively, pad or transform the deformation grid lattice to
> allow
> > > for
> > > > > the inversion to work?
> > > > >
> > > > > -- A
> > > > >
> > > > >
> > > > >
> > > > > On Wed, Aug 17, 2016 at 5:24 PM, Vladimir S. FONOV <
> > > > vladimir.fonov at gmail.com
> > > > >> wrote:
> > > > >
> > > > >> 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
> > > > >> _______________________________________________
> > > > >> MINC-users at bic.mni.mcgill.ca
> > > > >> http://www.bic.mni.mcgill.ca/mailman/listinfo/minc-users
> > > > >>
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