Extract Euler Angles from 3x3 rotation matrix resulted in matlab camera calibration process

How we can extract the the three angles of orientation from the Rotation matrix resulted in matlab extrinsic camera parameters. For example, if you given the following rotation matrix,

Rc_ext = [

       -0.012785     0.999906    -0.004886

        0.982489     0.011654    -0.185957

        -0.185883    -0.007178   -0.982546 
]

Find the three angles of orientation (around x-axis,y-axis and z-axis? And what is the order of orientation? for example (theta_x,theta_y, theta_z , theta_y,theta_x, theta_z , theta_z,theta_y, theta_x ..etc).

Thanks

Answer 1

[Mischa Kim]

The short answer is, it can be whatever you want it to be: the rotation matrix simply defines the orientation of the camera frame relative to some other frame.

In other words, if you decide that you want to describe the camera orientation relative to the other frame using for example a 3-2-1 (yaw-pitch-roll) rotation sequence about angles psi, theta, and phi then you end up with an overall rotation matrix as a function of these three angles.

R(psi, theta, phi) = R1(phi)R2(theta)R3(psi),

where

R3(psi)   = [ cos(psi) sin(psi) 0; 
             -sin(psi) cos(psi) 0; 
                     0        0 1]
R2(theta) = [cos(theta) 0 -sin(theta); 
                     0  1           0; 
             sin(theta) 0  cos(theta)]
R1(phi)   = [1        0          0; 
             0  cos(phi)  sin(phi);
             0 -sin(phi)  cos(phi)]

Given the numerical values of the matrix (Rc_ext) you can back out yaw, pitch, roll angles. For a different rotation sequence you would get a different set of rotation angles.