Hi Martin,

Thanks for your quick response.

I think I am understanding you correctly. For clarification... Say, we have original points (x, y, z) in a given space and we'd like to transform it to a difference space:

x-translation: x' = x + p y' = y z'= z y-translation: x' = x y' =y +q z'= z x-translation: x' = x y' = y x' = x = r

Then:

[image: affinematrix.png]

The top left 3x3 submatrix in the last line above is equivalent to the left 3x3 submatrix of the matrix from talairach.xfm, and the very right column in the matrix from talairach.xfm is equivalent to : [p] [q] [r]

Am I understanding you correctly?

Thank you.

Best, Lisa ______________________________ Lisa F. Akiyama Research Study Assistant Institute for Learning & Brain Sciences (I-LABS) University of Washington Portage Bay Building, BOX 357988 Seattle, WA 98195-7988 U.S.A. E-mail: lrisa87@uw.edu

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On Thu, Nov 4, 2010 at 11:09 AM, Martin Reuter mreuter@nmr.mgh.harvard.eduwrote:

Hi Lisa,

this is an affine transformation. Usually there is a 4th row containing 0 0 0 1

A point at position x,y,z is mapped to the target location via

M * (x,y,z,1)^t where M is the 4x4 matrix and (x,y,z,1)^T is the column vector of the coordinates of the point with a 1 in the 4th row.

The top left 3x3 sub matrix of M is a linear transformation (rotation,scaling, sheering combined) and the last column is the translation.

Take a look here to review http://en.wikipedia.org/wiki/Transformation_matrix

So you cannot directly extract scaling factors and rotation from the 3x3 submatrix.

Best, Martin

On Thu, 2010-11-04 at 10:51 -0700, Lisa F. Akiyama wrote:

...

Hello,

Could someone inform me what each value of the 3x4 talairach transformation matrix signifies (e.g. translation, rotation in specific directions)? Here's an example of an talairach.xfm output.

    MNI Transform File
    % tkregister2

    Transform_Type = Linear;
    Linear_Transform =
       1.05550623    0.03465762   -0.08214028   -3.92954969
       0.02312534    1.03939676    0.38879746  -13.37033176
       0.00010875   -0.35171938    1.10944259  -10.23139286

Thank you.

Best, Lisa ______________________________ Lisa F. Akiyama Research Study Assistant Institute for Learning & Brain Sciences (I-LABS) University of Washington

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On Tue, Nov 2, 2010 at 2:59 PM, Lisa F. Akiyama lrisa87@uw.edu wrote: Hello,

    Are there any documentations on the details of the
    talairach_avi command
    and the 3x4 matrix (talairach.xfm) output?


    Thank you.


    Best,
    Lisa Akiyama
     ______________________________
    Lisa F. Akiyama
    Research Study Assistant
    Institute for Learning & Brain Sciences (I-LABS)
    University of Washington


    P Please consider the environment before printing this e-mail.

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Hi Martin,

Thanks for the detailed explanation! I think I've got it down now.

Best, Lisa ______________________________ Lisa F. Akiyama Research Study Assistant Institute for Learning & Brain Sciences (I-LABS) University of Washington

lrisa87@uw.edu

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On Thu, Nov 4, 2010 at 12:48 PM, Martin Reuter mreuter@nmr.mgh.harvard.eduwrote:

Basically yes, but the 3x3 submatrix can be more than just rotation and scaling (there can be shearing in a 9 degree of freedom linear transform).

So the 12 DOFs are 3 rotation, 3scaling,3 shearing,3 translation. Only the translation parameters can be read directly from the matrix (as you correctly detailed below).

Best, Martin

On Thu, 2010-11-04 at 11:59 -0700, Lisa F. Akiyama wrote:

...

Hi Martin,

Thanks for your quick response.

I think I am understanding you correctly. For clarification... Say, we have original points (x, y, z) in a given space and we'd like to transform it to a difference space:

x-translation: x' = x + p enorm y' = y z'= z y-translation: x' = x y' =y +q z'= z x-translation: x' = x y' = y x' = x = r

Then:

affinematrix.png

The top left 3x3 submatrix in the last line above is equivalent to the left 3x3 submatrix of the matrix from talairach.xfm, and the very right column in the matrix from talairach.xfm is equivalent to : [p] [q] [r]

Am I understanding you correctly?

Thank you.

Best, Lisa ______________________________ Lisa F. Akiyama Research Study Assistant Institute for Learning & Brain Sciences (I-LABS) University of Washington Portage Bay Building, BOX 357988 Seattle, WA 98195-7988 U.S.A. E-mail: lrisa87@uw.edu

P Please consider the environment before printing this e-mail.

On Thu, Nov 4, 2010 at 11:09 AM, Martin Reuter mreuter@nmr.mgh.harvard.edu wrote: Hi Lisa,

    this is an affine transformation. Usually there is a 4th row
    containing
    0 0 0 1

    A point at position x,y,z is mapped to the target location via

    M * (x,y,z,1)^t
    where M is the 4x4 matrix and (x,y,z,1)^T is the column vector
    of the
    coordinates of the point with a 1 in the 4th row.

    The top left 3x3 sub matrix of M is a linear transformation
    (rotation,scaling, sheering combined) and the last column is
    the
    translation.

    Take a look here to review
    http://en.wikipedia.org/wiki/Transformation_matrix

    So you cannot directly extract scaling factors and rotation
    from the 3x3
    submatrix.

    Best, Martin



    On Thu, 2010-11-04 at 10:51 -0700, Lisa F. Akiyama wrote:
    > Hello,
    >
    > Could someone inform me what each value of the 3x4 talairach
    > transformation matrix signifies (e.g. translation, rotation
    in
    > specific directions)?
    > Here's an example of an talairach.xfm output.
    >
    >
    >         MNI Transform File
    >         % tkregister2
    >
    >         Transform_Type = Linear;
    >         Linear_Transform =
    >            1.05550623    0.03465762   -0.08214028
    -3.92954969
    >            0.02312534    1.03939676    0.38879746
     -13.37033176
    >            0.00010875   -0.35171938    1.10944259
     -10.23139286
    >
    > Thank you.
    >
    >
    > Best,
    > Lisa
    >  ______________________________
    > Lisa F. Akiyama
    > Research Study Assistant
    > Institute for Learning & Brain Sciences (I-LABS)
    > University of Washington
    >
    >
    >
    > P Please consider the environment before printing this
    e-mail.
    >
    >
    >
    > On Tue, Nov 2, 2010 at 2:59 PM, Lisa F. Akiyama
    <lrisa87@uw.edu>
    > wrote:
    >         Hello,
    >
    >         Are there any documentations on the details of the
    >         talairach_avi command
    >         and the 3x4 matrix (talairach.xfm) output?
    >
    >
    >         Thank you.
    >
    >
    >         Best,
    >         Lisa Akiyama
    >          ______________________________
    >         Lisa F. Akiyama
    >         Research Study Assistant
    >         Institute for Learning & Brain Sciences (I-LABS)
    >         University of Washington
    >
    >
    >         P Please consider the environment before printing
    this e-mail.
    >
    >
    >
    >

    > _______________________________________________
    > Freesurfer mailing list
    > Freesurfer@nmr.mgh.harvard.edu
    > https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer

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