Recompose a 3D shape from 2 sub matrix

I am looking for a way to align 3D shapes and thus recompose a matrix. I have 3 matrix AB, A and B which contain each a 3D item and AB is composed of A and B.

I would like to find the rotation, translation needed for A and B to rebuild AB.

Do you have any methodology, or useful functions that could help me ?

Regards.

[Matt J]

Explain what "AB is composed of A and B" means. Do you mean that AB is the sum of roto-translated versions of A and B? So you have 6 degrees of freedom in A and another 6 dof in B?

Which of your data are matrices (2D) and which of your data are 3D arrays?

[ocelote]

"So you have 6 degrees of freedom in A and another 6 dof in B" yes exactly.

It is as if AB was separated in 2 different pieces that are each independant. Each matrix AB, A and B are 3D (stack of 2D images).

I might to detect 1 of the two flat surfaces of AB to find how A should be rotated/translated to stick this surface and do the same for B with the other flat surface of AB.