I have two affine transformations $A_1$ and $A_2$ consisting only of a rotation matrix $R_i$ and a translation vector $\overrightarrow{t_i}$ (all in 3D space):
$$A_i = \left[ \begin{array}{ccc|c} \, & R_i & & \vec{t_i} \ \\ 0 & \ldots & 0 & 1 \end{array} \right]$$
Now I want to measure how much "change" occurs between $A_1$ and $A_2$, or put differently how similar $A_1$ and $A_2$ are.
I thought of calculating the relative transformation $A'$ between $A_1$ and $A_2$ and apply the euclidean norm. The norm's difference from $1$ could be a measure of "similarity" $s$ :
$$A' = {A_1}^{-1} \cdot A_2$$ $$s = ||A'||_2-1$$
Is this a valid way? Is there a better (=numerically less sensitive and computationally less expensive) way which exploits the fact that $A_i$ only consists of rotation and translation?
