Suppose that I have two cameras. I don't know exactly the poses of these two cameras. So their rotation matrice denoted as R1 and R2, respectively, are unknown. But I know the relative angles of these cameras along three axes. I mean if the angles along three axes of the two camera are (alpha1, betta1, gamma1) and (alpha2, betta2, gamma2), then the relative angles of these camera (deltaX, deltaY, deltaZ)=(alpha2-alpha1, betta2-betta1, gamma2-gamma1) are known.
My question is that can we form a "relative" rotation matrix R12 so that R2=R12*R1?
Because there're many methods to construct a rotation matrix. And the results of these methods are different (I'm still don't understand why can a camera have different rotation matrices). In this case, I construct the rotation matrix by multiply three rotation matrix along three axes. More specifically, R=RzRyRx.
As I test with the code in Matlab,
R(alpha2, 0, 0)*R(alpha1, 0, 0)=R(alpha1+alpha2, 0, 0).
But
R(alpha2, betta2, gamma2)*R(alpha1, betta1, gamma1) != R(alpha1+alpha2, betta1+betta2, gamma1+gamma2).
Thanks!