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| == Transformations between Freesurfer Surfaces and TrackVis == * FreeSurferTrackVisTransforms |
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| == 1.0 Coordinate System Overview Disclaimer: The stuff below may or may not be correct. == | == Use Cases == |
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| '''''Disclaimer:''''' The stuff below may or may not be correct.Use the info above instead. | Below are several cases in which someone has a coordinate in one coordinate system and wants to transform it to some other coordinate system (eg, a point on the surface to MNI305 space). Each computation shows the matrices needed and how to get them as well as a check using tkmedit/tksurfer. The equations are based on those in '''[[attachment:fscoordinates.ppt|FS Coordinates (PowerPoint)|&do=get]]'''. The checks assume you have run tkmedit and tksurfer in the following way: |
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| Freesurfer uses at least 4 voxel coordinate systems and 4 "RAS" coordinate systems. {{{ 0. Stored in volume file original volume ========> RAS ("scanner RAS", c_(r,a,s)!=0 in general) | | | 1. calculated | identity | | V 2. calculated V conformed volume ========> RAS (to have the same c_(r,a,s) as above) L^3 with S mm voxel | | | | identity | 3. calculated (translation) | | V 4. fixed(standard) V conformed volume ========> SurfaceRAS with c_(r,a,s) = 0 L^3 with S mm voxel }}} |
tkmedit subject orig.mgz -reg register.dat -ov mov.nii -surfs |
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| The functional analysis stream uses another coordinate system to map from the src volume. | tksurfer subject lh inflated -reg register.dat -ov mov.nii |
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| {{{ original volume ========> RAS ("scanner RAS", c_(r,a,s) != 0 in general) | | | identity | calculated V 5. fixed("standard") V original volume ========> tkregRAS where c_(r,a,s) = 0 | | | 6. calculated | mri2fmri (registration will give this) | | V 7. fixed("standard") V overlay volume ========> fRAS where c_(r,a,s) = 0 }}} All these coordinate systems make it a rather difficult task to trace to the original source volume voxel index from surface or functional index. If you can follow the arrows, you can get the necessary transforms easily. |
Note on Talairach: FreeSurfer does not report true "Talairach" coordinates. The coordinates listed unter "Talairach" are actually based on Matthew Brett's 10/8/98 non-linear transform from MNI305 space (see http://www.mrc-cbu.cam.ac.uk/Imaging/mnispace.html). FreeSurfer also reports "Talairach MNI" coordinates. These are MNI305 space. |
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| The transform 2 (CORONAL coordinates) is calculated so that the following equation holds. That is, the direction cosine part is fixed, but not the translation part. In this way, the conformed volume always in the CORONAL orientation. | |
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| {{{ [-1 0 0 s1][S 0 0 0][L/2] [c_r] s1 = c_r + S*L/2 [ 0 0 1 s2][0 S 0 0][L/2] = [c_a] ==> s2 = c_a - S*L/2 [ 0 -1 0 s3][0 0 S 0][L/2] [c_s] s3 = c_s + S*L/2 [ 0 0 0 1][0 0 0 1][ 1 ] [ 1 ] }}} where c_(r,a,s) is from the "scanner RAS". This "scanner RAS" has the physical meaning of "Right-Anterior-Superior" directions of the head. |
== Transforms within a subject's anatomical space == |
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| The transform 4 (surface``RAS``From``Conformed``Voxel) is fixed as | ------------------------------------------------------------------ 1. I have a point on the surface and want to compute the CRS for voxel in the orig.mgz that corresponds to this point: |
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| {{{ [-1 0 0 S*L/2][S 0 0 0] [ 0 0 1 -S*L/2][0 S 0 0] [ 0 -1 0 S*L/2][0 0 S 0] [ 0 0 0 1 ][0 0 0 1] }}} |
VoxCRS = inv(Torig)*[tkrR tkrA tkrS 1]' |
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| The transform 1 (conformed``Voxel``From``Voxel) is calculated by (in a matrix sense) | where [tkrR tkrA tkrS] is your point on the RAS on the surface is in the "tkregister space" (eg, the "Volume coordinate" in tksurfer) and Torig is the Vox2tkrRAS obtained from "mri_info --vox2ras-tkr orig.mgz" (note: this is the same for all orig volumes). |
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| {{{ xform1 = inv(xform2) * xform0 = [1/S 0 0 0][-1 0 0 s1] * xform0 [ 0 1/S 0 0][ 0 0 -1 s3] [ 0 0 1/S 0][ 0 1 0 -s2] [ 0 0 0 1][ 0 0 0 1 ] }}} The transform 3(Surface``RAS``From``RAS) is calculated by (in a matrix sense). Note that it is independent of conformed voxel size S and the length L: |
Test: click on a point in tksurfer. Use "Vertex RAS" to compute Vox2CRS. Round Vox2CRS to the nearest integer. Hit Save Point in tksurfer. In tkmedit, Goto Saved Point. Compare VoxCRS to "Volume Index". Note: you may need to use the "Volume RAS" from tkmedit in the computation above to get an exact match. |
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| {{{ xform3 = xform4 * inv(xform2) = [ 1 0 0 -c_r] [ 0 1 0 -c_a] [ 0 0 1 -c_s] [ 0 0 0 1 ] }}} Because of the xform3 (changing only translation part), it is easy to calculate Surface``RAS``From``Voxel (xform3*xform0) and is given by |
------------------------------------------------------------------ 2. I have a point on the surface and want to compute the MNI305 RAS that corresponds to this point: |
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| {{{ SurfaceRASFromVoxel = [ 3x3 part (t1 - c_r)] [ same as (t2 - c_a)] [ xform0 (t3 - c_s)] [ 0 1 ] }}} where t1,t2,t3 are the translation part of xform0. |
MNI305RAS = TalXFM*Norig*inv(Torig)*[tkrR tkrA tkrS 1]' TalXFM: subject/orig/transforms/talairach.xfm Norig: mri_info --vox2ras orig.mgz Torig: mri_info --vox2ras-tkr orig.mgz |
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| The transform 5 and the transform 7 are calculated by the requirement | Test: click on a point in tksurfer. Use "Vertex RAS" to compute MNI305RAS. Compare MNI305RAS to "Vertex MNI Talairach". Also, hit Save Point in tksurfer. In tkmedit, Goto Saved Point, compare MNI305RAS to "MNI Coordinates". Note: you may need to use the "Volume RAS" from tkmedit in the computation above to get an exact match. |
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| {{{ [-1 0 0 s1][xsize 0 0 0][width/2 ] [0] [ 0 0 1 s2][ 0 ysize 0 0][height/2] = [0] [ 0 -1 0 s3][ 0 0 zsize 0][depth/2 ] [0] [ 0 0 0 1][ 0 0 0 1][ 1 ] [1] }}} Here the name "RAS" lost the meaning completely. This "RAS" is just to be used for alignment purpose only. The width/height/depth are for the appropriate volume. The reason is that the original volume could be sagittal or horizontal. |
------------------------------------------------------------------ 3. I have a point on the surface and want to compute the Scanner RAS from the point in orig.mgz that corresponds to this point: |
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| == 2.0 Relationship between lores and hires surfaceRAS == {{{ conformed vol -------------> surfRAS | | | | surfRASToRAS V V high res ------------> RAS | | | | Xfm V V low res ------------> RAS | | | | RASToSurfRAS V V conformed vol -------------> surfRAS }}} Therefore, the map from the high res surfaceRAS to the low res surfaceRAS is given by |
ScannerRAS = Norig*inv(Torig)*[tkrR tkrA tkrS 1]' Norig: mri_info --vox2ras orig.mgz Torig: mri_info --vox2ras-tkr orig.mgz |
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| {{{ highresSurfRASTolowresSurfRAS = RASTosurfRAS(lowres) * Xfm * sufRASToRAS(highres) }}} which is not equal to Xfm. In fact, |
Test: click on a point in tksurfer. Use "Vertex RAS" to compute ScannerRAS. Save Point. In tkmedit, Goto Saved Point, compare ScannerRAS to "Volume Scanner Coordinates". |
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| {{{ RASTosurfRAS(lowres) = 1 0 0 -c_r(lowres) surfRASTORAS(highres) = 1 0 0 c_r(highres) 0 1 0 -c_a(lowres) 0 1 0 c_a(highres) 0 0 1 -c_s(lowres) 0 0 1 c_s(highres) 0 0 0 1 0 0 0 1 }}} |
---------------------------------------------------------------- 4. I have a CRS from a voxel in the orig.mgz volume and want to compute the RAS in surface space (tkrRAS) for this point: |
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| or write these as {{{ RASToSurfRAS(lowres) = [ 1 -C(lowres)] surfRASToRAS(highres) = [ 1 C(highres)] [ 0 1 ] [ 0 1 ] |
tkrRAS = Torig*[C R S 1]' Torig: mri_info --vox2ras-tkr orig.mgz |
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| Xfm = [ R T ] [ 0 1 ] }}} Then, {{{ highresSurfRASTolowresSurfRAS = [ 1 -C(lowres)] x [ R T ] x [ 1 C(highres)] [ 0 1 ] [ 0 1 ] [ 0 1 ] |
Test: click on a point in tkmedit very close to the left hemi white surface. Use the "Volume index" to compute tkrRAS. It "Save Point" in tkmedit. In tksurfer, Goto Saved Point. Compare tkrRAS to "Vertex RAS". It might not be exactly the same because you might not have clicked exactly on a vertex in tkmedit. |
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| = [ R R*C(highres)-C(lowres) + T ] [ 0 1 ] }}} The conclusion is that the transform is non-trivial. Even when R = 1 and T = 0 (no rotation), we have |
== Transforms within subject across imaging modalities == |
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| {{{ highresSurfRASTolowresSurfRAS = [ 1 C(highres)-C(lowres)] [ 0 1 ] }}} Therefore, when translating highres vertex positions into lowres vertex position, we must make sure that c_(ras) for highres and lowres must match exactly. |
------------------------------------------------------------------ 5. I have a point on the surface and want to compute the CRS for the corresponding voxel in my functional/diffusion/ASL/rawavg/etc "mov" volume: |
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| == 3.0 FreeSurferTalairach == * FreeSurferTalairach |
movCRS = inv(Tmov)*Reg*[tkrR tkrA tkrS 1]' Tmov: mri_info --vox2ras-tkr mov.nii Reg: register.dat tkregister2 --mov mov.nii --reg register.dat |
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| == 4.0 Direction cosines == The direction cosines tell you about how the acquired volume x, y, z axes correspond to the R(right), A(anterior), S(superier) axes. You can see this info by running the command, [[mri_info]] <volume>. For example, x_r = -1, x_a = 0, x_s = 0 means that the x axis points to the left (-1) of the R axis (no components along A and S axes). The '''CORONAL''' orientation, which is by the way the default freesurfer volume orientation, has x_r = -1, x_a = 0, x_s = 0, y_r = 0, y_a = 0, y_s = -1, z_r = 0, z_a = 1, z_s = 0. This means that the x axis points to the left, the y axis points to the inferior, and the z axis points to the anterior direction. The "c_ras" values specify where the volume center sits in the RAS coordinate system. That is, c_r, c_a. c_s are the RAS coordinate values of a voxel point (width/2, height/2, depth/2). Note that we use the convention of the voxel coordinate such that the center of a voxel corresponds to the integer voxel coordinate position. This is not the usual convention taken by the graphics software like OpenGL. You have to watch out for this 1/2 voxel position shift. |
Test: click on a point in tksurfer and hit Save Point. Compute movCRS using the "Vertex RAS". Round movCRS to the nearest integer. In tkmedit, Goto Saved Point. Compare movCRS to "Functional Overlay Index Coordinates". |
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| Each volume format stores this direction cosine information in each own way. COR volume (COR-001, ...) stores it in COR-.info file. [[DICOM]] stores it in the file. Note that Analyze file (.img)stores it in .mat file, meanwhile bflort (.bfloat or .bshort) stores it in .bhdr file. For these formats it is essential to have these files. | -------------------------------------------------------------- 6. I have a CRS from a voxel in my functional/diffusion/ASL/rawavg/etc "mov" volume and want to compute the CRS for the corresponding point in the orig.mgz: |
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| == 5.0 MNI Talairach in tkmedit == [[tkmedit]] shows a non-identity Talairach even though talairach.xfm is an identity matrix. The reason is described in [[http://www.mrc-cbu.cam.ac.uk/Imaging/Common/mnispace.shtml|Cambride Imagers-MNI space]]. [[tkmedit]] uses Approach 2 described in the web page. |
origCRS = Torig * inv(Reg) * inv(Tmov) * [movC movR movS 1]' Torig: mri_info --vox2ras-tkr orig.mgz Tmov: mri_info --vox2ras-tkr mov.nii Reg: register.dat tkregister2 --mov mov.nii --reg register.dat |
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| There are two talairach transformed used in [[tksurfer]]. One is MNI talairach and the other is modified talairach. The modified talairach is done in `tksurfer.c conv_initialize()`: | Test: click on a point in tkmedit very close to the left hemi white surface. Use the "Functional Overlay Index Coordinates" to compute origCRS (round to the nearest integer). Compare origCRS to the "Volume index". Note: you may need to use the "Volume RAS" from tkmedit in the computation above to get an exact match. |
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| {{{ For Z < 0: |
-------------------------------------------------------------- 7. I have a CRS from a voxel in my functional/diffusion/ASL/rawavg/etc "mov" volume and want to compute the tkrRAS for the corresponding point on the surface: |
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| conv_mnital_to_tal_m_ltz = MatrixIdentity (4, NULL); stuff_four_by_four (conv_mnital_to_tal_m_ltz, 0.99, 0, 0, 0, 0.00, 0.9688, 0.042, 0, 0.00, -0.0485, 0.839, 0, 0.00, 0, 0, 1); }}} |
tkrRAS = inv(Reg) * Tmov * [movC movR movS 1]' Tmov: mri_info --vox2ras-tkr mov.nii Reg: register.dat tkregister2 --mov mov.nii --reg register.dat |
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| {{{ For Z > 0: conv_mnital_to_tal_m_gtz = MatrixIdentity (4, NULL); stuff_four_by_four (conv_mnital_to_tal_m_gtz, 0.99, 0, 0, 0, 0.00, 0.9688, 0.046, 0, 0.00, -0.0485, 0.9189, 0, 0.00, 0, 0, 1); }}} == 6.0 Transformations between Freesurfer Surfaces and TrackVis == * FreeSurferTrackVisTransforms |
Test: click on a point in tkmedit very close to the left hemi white surface. Use the "Functional Overlay Index Coordinates" to compute tkrRAS. Hit "Save Point" in tkmedit. In tksurfer, hit "Goto Saveed Point". Compare tkrRAS to "Vertex RAS". It might not be exactly the same because you might not have clicked exactly on a vertex in tkmedit. |
FreeSurfer Coordinate Systems
The "official" FreeSurfer Coordinate definitions can be found in the following power-points slides (SEE THESE FIRST):
or PDF:
This also includes a little intro to Affine Transformations.
See also: VOX2RAS(PDF)
Transformations between Freesurfer Surfaces and TrackVis
Also see: TrackVis Transforms <--- !!!
Use Cases
Below are several cases in which someone has a coordinate in one coordinate system and wants to transform it to some other coordinate system (eg, a point on the surface to MNI305 space). Each computation shows the matrices needed and how to get them as well as a check using tkmedit/tksurfer. The equations are based on those in FS Coordinates (PowerPoint). The checks assume you have run tkmedit and tksurfer in the following way:
tkmedit subject orig.mgz -reg register.dat -ov mov.nii -surfs
tksurfer subject lh inflated -reg register.dat -ov mov.nii
Note on Talairach: FreeSurfer does not report true "Talairach" coordinates. The coordinates listed unter "Talairach" are actually based on Matthew Brett's 10/8/98 non-linear transform from MNI305 space (see http://www.mrc-cbu.cam.ac.uk/Imaging/mnispace.html). FreeSurfer also reports "Talairach MNI" coordinates. These are MNI305 space.
Transforms within a subject's anatomical space
1. I have a point on the surface and want to compute the CRS for voxel in the orig.mgz that corresponds to this point:
VoxCRS = inv(Torig)*[tkrR tkrA tkrS 1]'
where [tkrR tkrA tkrS] is your point on the RAS on the surface is in the "tkregister space" (eg, the "Volume coordinate" in tksurfer) and Torig is the Vox2tkrRAS obtained from "mri_info --vox2ras-tkr orig.mgz" (note: this is the same for all orig volumes).
Test: click on a point in tksurfer. Use "Vertex RAS" to compute Vox2CRS. Round Vox2CRS to the nearest integer. Hit Save Point in tksurfer. In tkmedit, Goto Saved Point. Compare VoxCRS to "Volume Index". Note: you may need to use the "Volume RAS" from tkmedit in the computation above to get an exact match.
2. I have a point on the surface and want to compute the MNI305 RAS that corresponds to this point:
MNI305RAS = TalXFM*Norig*inv(Torig)*[tkrR tkrA tkrS 1]'
- TalXFM: subject/orig/transforms/talairach.xfm Norig: mri_info --vox2ras orig.mgz Torig: mri_info --vox2ras-tkr orig.mgz
Test: click on a point in tksurfer. Use "Vertex RAS" to compute MNI305RAS. Compare MNI305RAS to "Vertex MNI Talairach". Also, hit Save Point in tksurfer. In tkmedit, Goto Saved Point, compare MNI305RAS to "MNI Coordinates". Note: you may need to use the "Volume RAS" from tkmedit in the computation above to get an exact match.
3. I have a point on the surface and want to compute the Scanner RAS from the point in orig.mgz that corresponds to this point:
ScannerRAS = Norig*inv(Torig)*[tkrR tkrA tkrS 1]'
- Norig: mri_info --vox2ras orig.mgz Torig: mri_info --vox2ras-tkr orig.mgz
Test: click on a point in tksurfer. Use "Vertex RAS" to compute ScannerRAS. Save Point. In tkmedit, Goto Saved Point, compare ScannerRAS to "Volume Scanner Coordinates".
4. I have a CRS from a voxel in the orig.mgz volume and want to compute the RAS in surface space (tkrRAS) for this point:
tkrRAS = Torig*[C R S 1]'
- Torig: mri_info --vox2ras-tkr orig.mgz
Test: click on a point in tkmedit very close to the left hemi white surface. Use the "Volume index" to compute tkrRAS. It "Save Point" in tkmedit. In tksurfer, Goto Saved Point. Compare tkrRAS to "Vertex RAS". It might not be exactly the same because you might not have clicked exactly on a vertex in tkmedit.
Transforms within subject across imaging modalities
5. I have a point on the surface and want to compute the CRS for the corresponding voxel in my functional/diffusion/ASL/rawavg/etc "mov" volume:
movCRS = inv(Tmov)*Reg*[tkrR tkrA tkrS 1]'
- Tmov: mri_info --vox2ras-tkr mov.nii Reg: register.dat
- tkregister2 --mov mov.nii --reg register.dat
Test: click on a point in tksurfer and hit Save Point. Compute movCRS using the "Vertex RAS". Round movCRS to the nearest integer. In tkmedit, Goto Saved Point. Compare movCRS to "Functional Overlay Index Coordinates".
6. I have a CRS from a voxel in my functional/diffusion/ASL/rawavg/etc "mov" volume and want to compute the CRS for the corresponding point in the orig.mgz:
origCRS = Torig * inv(Reg) * inv(Tmov) * [movC movR movS 1]'
- Torig: mri_info --vox2ras-tkr orig.mgz Tmov: mri_info --vox2ras-tkr mov.nii Reg: register.dat
- tkregister2 --mov mov.nii --reg register.dat
Test: click on a point in tkmedit very close to the left hemi white surface. Use the "Functional Overlay Index Coordinates" to compute origCRS (round to the nearest integer). Compare origCRS to the "Volume index". Note: you may need to use the "Volume RAS" from tkmedit in the computation above to get an exact match.
7. I have a CRS from a voxel in my functional/diffusion/ASL/rawavg/etc "mov" volume and want to compute the tkrRAS for the corresponding point on the surface:
tkrRAS = inv(Reg) * Tmov * [movC movR movS 1]'
- Tmov: mri_info --vox2ras-tkr mov.nii Reg: register.dat
- tkregister2 --mov mov.nii --reg register.dat
Test: click on a point in tkmedit very close to the left hemi white surface. Use the "Functional Overlay Index Coordinates" to compute tkrRAS. Hit "Save Point" in tkmedit. In tksurfer, hit "Goto Saveed Point". Compare tkrRAS to "Vertex RAS". It might not be exactly the same because you might not have clicked exactly on a vertex in tkmedit.