CAF dataset for  Allen Reference Atlas:

1. Fetch AtlasAnnotation25.sva sparse volume file from  ABA Website.
2. Coordinates in this volume are expressed in  Mouse_ABAvoxel_1.0 (ABAvoxel, INCF:0100) SRS, in which units of measurements are voxels. In order to express coordinates in stereotaxic coordinates (with bregma point defined as origin of the coordinate system), the volume has to be transformed into  Mouse_ABAreference_1.0 SRS (ABAreference, INCF:0101).

3. Such transfomration is given by the  TransfomPOI INCF DAI service (ie.  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 following equation:

After all, matrix M is:

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]]

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