[Insight-users] MI Registration example translation parameters
David Wikler
dwikler@ulb.ac.be
Fri, 14 Mar 2003 10:16:26 +0100 (MET)
Dear Lydia,
>Actually, the MultiResMIRegistration application actually doesn't use
>image origin information. The first preprocessing step it does is to
>artificially place the origin in the center of each of the images. This
>is equivalent to align the images at their center. Additionally any
>rotation is with respect to the center of the image.
>
I have seen this in the code and that was the substrate for my
correction of the physical translation parameters using the
relative distance between the image centers. Does your remark
make this computation irrelevant or just makes Luis proposal
to tweak the original images origins impossible with this code ?
>You should also note that the "final quaternion parameters" are respect
>to the origin at the image center - but the display of the overall
>matrix and translation is reposition so that the image origin for both
>images is at the [0,0,0] pixel.
>
>Since the output matrix has some rotation in it - the position of the
>center of rotation comes into play and hence the output translation is a
>mixture of your introduced translation and the center of rotation.
Could we formalize it with a formula to add the rotation contribution
to the translations numbers ?
using
1. the rotation matrix
2. the volume center coordinates
We would end with someting like
T(mm) = T(physical) - D - d
where D = (PET_volume_center(physical)-MR_volume_center(physical))/2
which is the relative distance between the centers of images
where d = PET_volume_center(physical) - RotationMatrix * PET_volume_center(physical)
[d would be zero for a null rotation whicj makes sense]
For my case, I would end with
For Z: 86.6143 - (63*2.4- 50*1.3)/2 - dz = 43.5 mm - dz
For Y: 31.1387 - (128*2.57- 256*1.05)/2 - dy = 1.06 mm - dy
For X: 36.6828 - (128*2.57- 256*1.05)/2 - dx = 6.6 mm - dx
with dx = 0.6885, dy = -0.7060, dz = 0.0495
and I would end with a translation of
(6.55, 1,766, 42.81)
which still makes sense according to my visual evaluation but as
my rotation quasi null, I can't be 100% sure of my formulas.
I don't currently have a dataset with more rotation to check this
better. Can you tell me whether you think my math development
looks allright according to your comments.
Thank you all.
David
>> -----Original Message-----
>> From: Luis Ibanez [mailto:luis.ibanez@kitware.com]
>> Sent: Thursday, March 13, 2003 11:01 AM
>> To: David Wikler
>> Cc: insight-users@public.kitware.com
>> Subject: Re: [Insight-users] MI Registration example translation
>> parameters
>>
>> Hi David,
>>
>> The origin of the physical coordinate system
>> for the volumes should be taken into account
>> during the registration process.
>>
>> Your analysis looks right. It makes sense to
>> first discount the relative distance between
>> the image centers.
>>
>> In general, simply creating a diagram of the
>> images in a common coordinate system in physical
>> space should clarify the discrepancy.
>>
>> In any case, if the resampled images are aligned
>> correctly, you can be confident that the only
>> difficulty is the intrepretation of the transform
>> in a common coordinate system.
>>
>> --
>>
>> If the resampled images are not aligned correctly,
>> then we could suspect that the registration method
>> didn't converge as expected.
>>
>> ---
>>
>> An easy and quick test is to tweak the origin
>> values of your images and verify that the
>> changes are reflected in the final registration.
>> For example, if you add (13,17,19) to x,y,z of one
>> of the images origin, the registration should
>> report a variation of (13,17,19) in the translation
>> offset.
>>
>>
>>
>> Luis
>>
>>
>> ---------------------
>> David Wikler wrote:
>> > Dear Luis,
>> >
>> > I think your comments helped me to understand
>> > my numbers a bit better. I focused on my numeral (3)
>> >
>> >
>> >>3. The registration result I get with datasets oriented
>> >>Head to Feet along the z axis is
>> >>
>> >>Overall transform matrix:
>> >>0.999868 -0.0144369 0.00750628
>> >>0.0144862 0.999874 -0.00655476
>> >>-0.0074107 0.00666263 0.99995
>> >>
>> >>Overall transform offset:
>> >>36.6828 31.1387 86.6143
>> >
>> >
>> > What I actually did was flip the images along the Z axis
>> > so the head goes to feet and vice-versa. I actually also
>> > did flip Anterio-posterior but this is not relevant for
>> > the following.
>> >
>> > I said to you that I estimated the Z translation to
>> > about 40.8 mm. Actually I can also estimate X and Y
>> > translation being of the order of less than 10mm.
>> >
>> > After reading your comments about physical space vs
>> > voxels space, I imagined the dicrepancy could come
>> > from the centers of volumes translations when going
>> > from voxel space to physical space.
>> > We could then write
>> >
>> > Tz(slices) = slicethickness *( Tz(physical) - D)
>> > and
>> > Tz(mm) = Tz(physical) - D
>> >
>> > where D = (PET_volume_Zcenter(physical)-MR_volume_Zcenter(physical))
>/2
>> > which is the translation in physical space between volume centers
>> > (for Z coordinate)
>> >
>> > In my case:
>> >
>> > For Z: 86.6143 - (63*2.4- 50*1.3)/2 = 43.5 mm
>> > For Y: 31.1387 - (128*2.57- 256*1.05)/2 = 1.06 mm
>> > For X: 36.6828 - (128*2.57- 256*1.05)/2 = 6.6 mm
>> >
>> > which is now compatible with my estimation.
>> > I still have got to check with other cases but
>> > I think it could be the solution, what is your
>> > impression ?
>> >
>> > Thank a lot for your quick help.
>> >
>> > David
>> >
>> > David Wikler, Ir
>> > ULB - Erasme Hospital - PET Scan
>> > 808 route de Lennik - B1070 Brussels - Belgium
>> > Phone: 32 2 5556603 - Fax: 32 25556631
>> > Email: dwikler@ulb.ac.be
>> > _______________________________________________
>> > Insight-users mailing list
>> > Insight-users@public.kitware.com
>> > http://public.kitware.com/mailman/listinfo/insight-users
>> >
>>
>>
>>
>>
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>
David Wikler, Ir
ULB - Erasme Hospital - PET Scan
808 route de Lennik - B1070 Brussels - Belgium
Phone: 32 2 5556603 - Fax: 32 25556631
Email: dwikler@ulb.ac.be