Shearing Matrix in Affine Transform

[o-fares]

Hello,

I want to apply an affine transform on a 3D MRI volume and recover the parameters used with the affine matrix, such as:

• translation (tx, ty, tz)
• rotation (rx, ry, rz)
• shearing (sx, sy, sz)
• scaling (hx, hy, hz)

I am struggling with the shearing matrix, that is usually defined with 6 coefficients:
[1 sxy sxz]
[syx 1 syz]
[szx szy 1]

But I can only recover the initial coefficients with the initial matrix if the shearing is applied only on one direction in each place (syx = szx = szy = 0). Then the shearing matrix is written this way :
[1 sxy sxz]
[0 1 syz]
[0 0 1]

I wanted to used the AffineDTI3DTransform to get directly the shearing coefficients, but then the matrix used is of the form:

[1 sx*sz sx]
[sy 1 0]
[0 sz 0]

Do you know how the shearing is applied with the Affine Transform matrix (3 shearing parameters or 6 parameters) ? Do you know if the AffineDTITransform could be suitable for other MRI images ? Do you know the order of the transormations (translation, rotation, scaling, shearing) in the Affine Transform ?

Thank you.