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.
>         >
>         >
>         >
>         >
>
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