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B.2 Contents of the DDT file

DDT file format, for each voxel, with vij the eigenvector entries and eigenvalues λ1 > λ2 > λ3, there are 12 values:

[ ] v1x v1y v1z v2x v2y v2z v3x v3y v3z λ 1 λ2 λ3

If you want to reconstruct the tensor D, use the following:

DE = EΛ
( ) Dxx Dxy Dxz ( Dyx Dyy Dyz) Dzx Dzy Dzz( ) v1x v2x v3x (v1y v2y v3y) v1z v2z v3z = ( ) v1x v2x v3x (v1y v2y v3y) v1z v2z v3z( ) λ1 0 0 ( 0 λ2 0 ) 0 0 λ3
and
DEET = D = EΛET
ETEΛ = Λ = ETDE.

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