Rodrigues' Rotation Formula

Sources: 1 2 3

I stumbled upon this when checking my camera calibration. I could see that depending on the angle of the camera upon the X axis, a stationary ArUco mark would fluctuate a lot on it’s Z-axis position. This is related to camera backward projection, SeaClear.

The issue was fixed through Rodrigues’ Rotation Formula in opencv:

rmat, _ = cv2.Rodrigues(rvec)  
rmat_inv = rmat.T  
tvec_inv = -np.dot(rmat_inv, tvec.T)  
rvec_inv, _ = cv2.Rodrigues(rmat_inv)  
return rvec_inv, tvec_inv.T

So, I want to document this algorithm and see what exactly it does and why it fixed the issue. From what I understood, it succeeds in computing the camera pose camera backward projection and not the ArUco marker’s pose. (I could definitely phrase that better)

TO DO!