Storage of Talairach Transformation
Document Actions
Submitted by bpittman.
on 2005-04-18 09:15.
An answer to a question from a loyal user, who was concerned about transforming ROI volumes calculated in Talairach space back to the original brain space.
How the Talairach Transformation is Stored in the .HEAD File
A linear warp is stored as 30 numbers in the THD_linear_mapping struct:
- mfor = 3x3 matrix (the forward matrix)
- mbac = 3x3 matrix (the backward matrix)
- bvec = 3-vector (forward transform is x_map = [mfor] * x_in - bvec)
- svec = 3-vector (backward transform is x_in = [mbac] * x_map - svec)
- bot = 3-vector (range of x vector values )
- top = 3-vector (to use for transformation)
#define W_RAS 0 /* right-anterior -superior mapping index */ #define W_LAS 1 /* left -anterior -superior */ #define W_RMS 2 /* right-medial -superior */ #define W_LMS 3 /* left -medial -superior */ #define W_RPS 4 /* right-posterior-superior */ #define W_LPS 5 /* left -posterior-superior */ #define W_RAI 6 /* right-anterior -inferior */ #define W_LAI 7 /* left -anterior -inferior */ #define W_RMI 8 /* right-medial -inferior */ #define W_LMI 9 /* left -medial -inferior */ #define W_RPI 10 /* right-posterior-inferior */ #define W_LPI 11 /* left -posterior-inferior */That is, the first 30 numbers correspond to the Right-Anterior-Superior region of the brain in Talairach coordinates; the next 30 for the Left-Anterior-Superior region of the brain; et cetera. Here are some numbers from a file, corresponding to the Right-Medial-Superior region (#2):
1.030303 0 0 0 0.8695359
0.06210971 0 -0.07029709 0.9841592 0.9705882
0 0 0 1.144201 -0.07220985
0 0.08172864 1.010938 0.4121149 -12.08224
-41.22271 -0.3999939 10.84782 42.66106 -9999
0 0 0 23 9999.9
Note that the last 6 numbers give the bot vector as [-9999,0,0]
and the top vector as [0,23,9999.9]. This indicates that this transformation
is valid for vectors [x,y,z] with
-9999 < x < 0 (the right of the brain),
0 < y < 23 (the medial region, between the AC and PC)
0 < z < 9999.9 (the superior region, above the AC-PC line)
Recall that AFNI (x,y,z) coordinates are in DICOM order:
-x = Right +x = Left
-y = Anterior +y = Posterior
-z = Inferior +z = Superior
In particular, x and y are sign-reversed with respect to SPM.
The "forward" transformation transforms (x,y,z) in +orig coordinates to +tlrc coordinates -- this corresponds to the mfor matrix. The "backward" transformation is the inverse of the forward, and corresponds to the mbac matrix. If you are counting volume in +tlrc coords, then you want to multiply by the determinant of the mbac matrix to scale to volume in +orig coords.
The regions for each transform are given in the bot and top vectors. These are fixed, though, for the AFNI +tlrc transform, at
Right = {x < 0} Left = {0 < x}
Anterior = {y < 0} Medial = {0 < y < 23} Posterior = {23 < y}
Superior = {0 < z} Inferior = {z < 0}
You could extract the 360 numbers from the WARP_DATA field using the command
3dAttribute WARP_DATA anat+tlrcfor example -- this writes to stdout, which I suppose you could pipe into another program to calculate the determinants you want.
