How to get the orientation vector of the camera given its rotation matrix / quaternion?

Question

When I have the rotation matrix or quaternion representation of a camera's pose, is there a way to obtain the orientation vector of the camera?

Here the orientation vector means a 3D vector in the world coordinate (WC) that represents an orientation.

I read through the commonly used representations like euler angles and axis-angle, but I didn't find any representations that can represent the orientation of the camera in WC.

Could anyone help? Thank you!

Answer 1

You probably want the 3x1 Rodrigues vector. Just plug in the SO(3) rotation matrix of the camera orientation in world coordinates, and you will get a vector representation. Just to be clear, pose and orientation are different. Pose is orientation + position. If you want the position as well, that can be represented as a 3x1 vector of t = [x y z]' (using Matlab notation).

A typical representation of the pose is a 4x4 matrix in SE(3) (Special Euclidean Group), which is just:

T = [R t; 0 0 0 1]

Where R is the rotation matrix in SO(3).