== CAF dataset for [http://mouse.brain-map.org/launchviewer.do Allen Reference Atlas] ==

'''The following description is related to Allen Reference Atlas CAF dataset available with the following links: [http://www.3dbar.org:8080/getPreview?cafDatasetName=aba;structureName=Brain live preview], [http://www.3dbar.org:8080/getCafInfoPage?cafDatasetName=aba dataset details].''' The CAF dataset was created by Łukasz Wałejko and Piotr Majka.

Detailed description of volume preprocessing:

  1. Fetch `AtlasAnnotation25.sva` sparse volume file from [http://community.brain-map.org/confluence/download/attachments/525267/data.zip?version=1 ABA Website].
  2. Coordinates in this volume are expressed in  [http://incf-dev.crbs.ucsd.edu/aba/atlas?service=WPS&version=1.0.0&request=Execute&Identifier=ListSRSs Mouse_ABAvoxel_1.0] (`ABAvoxel, INCF:0100`) SRS, in which units of measurements are voxels. In order to express data in stereotaxic coordinates (with bregma point as origin of the coordinate system), the volume has to be transformed into [http://incf-dev.crbs.ucsd.edu/aba/atlas?service=WPS&version=1.0.0&request=Execute&Identifier=ListSRSs Mouse_ABAreference_1.0] SRS (`ABAreference, INCF:0101`).

  3. Such transformation is given by the [http://code.google.com/p/incf-dai/wiki/AtlasRequestInterfaceSpec#TransformPOI TransfomPOI] INCF DAI service (ie. [http://incf-dev.crbs.ucsd.edu/aba/atlas?service=WPS&version=1.0.0&request=Execute&Identifier=TransformPOI&DataInputs=transformationCode=Mouse_ABAvoxel_1.0_To_Mouse_ABAreference_1.0_v1.0;x=1;y=112;z=162 this request]).

  4. Tranformation may be calculated from 4 points in `ABAvoxel` SRS (`p1, p2, p3, p4`) and 4 corresponding point in `ABAreference` SRS (`p1', p2', p3', p4'`) by solving the following equation:

  [[Image(gif.latex.gif)]]

After all transformations, matrix '''M''' reads:
{{{

M=
[[  2.71693750e-02  -8.17542750e-05  -5.01197500e-04  -1.25701700e+00]
 [  8.92628250e-04   2.82020000e-02  -2.71143000e-04  -1.28628500e+00]
 [ -5.86774750e-04  -8.96920500e-04  -2.59281250e-02   6.04778000e+00]
 [  0.00000000e+00   1.73472348e-18   0.00000000e+00   1.00000000e+00]]
}}}


and '''M'''':
{{{
M'=
[[  1.00000000e+00  -2.89888217e-03  -1.93302640e-02  -1.25701700e+00]
 [  3.28542063e-02   1.00000000e+00  -1.04574858e-02  -1.28628500e+00]
 [ -2.15969175e-02  -3.18034359e-02  -1.00000000e+00   6.04778000e+00]
 [  0.00000000e+00   6.15106544e-17   0.00000000e+00   1.00000000e+00]]
}}}


{{{#!comment
\\

\mathbf{V}=\begin{bmatrix}
p_1[1] & p_2[1] & p_3[1] & p_4[1] \\ 
p_1[2] & p_2[2] & p_3[2] & p_4[2]\\ 
p_1[3] & p_2[3] & p_3[3] & p_4[3]\\ 
1 & 1 & 1 & 1 
\end{bmatrix}

\\
\\

\mathbf{V'}=\begin{bmatrix}
p'_1[1] & p'_2[1] & p'_3[1] & p'_4[1] \\ 
p'_1[2] & p'_2[2] & p'_3[2] & p'_4[2]\\ 
p'_1[3] & p'_2[3] & p'_3[3] & p'_4[3]\\ 
1 & 1 & 1 & 1 
\end{bmatrix}

\\

\mathbf{M} = \mathbf{V'} \mathbf{V^{-1}}

\\
\\

\textup{And normalizing so the all diagonal elements are equal to 1:}

\\

\mathbf{M_c} = \begin{bmatrix}
|\mathbf{M}_{1,1}|^{-1} & 0 & 0 & 0\\ 
0 & |\mathbf{M}_{2,2}|^{-1} & 0 & 0\\ 
0 & 0 & |\mathbf{M}_{3,3}|^{-1} & 0\\ 
0 & 0 & 0 & 1
\end{bmatrix}

\\

\mathbf{M'} =\mathbf{M} \mathbf{M_c} 

}}}

Then, an initial volume from `AtlasAnnotation25.sva` is transformed using '''M'''' and the resulting volume is used by the 3dBAR parser to create CAF dataset.

Below you may find comparison of brain outlines created using raw volume (dark gray) and volume after transformation (light gray):


  [[Image(ss1.png)]]

  [[Image(ss2.png)]]

  [[Image(ss3.png)]]