问题
I'm trying to obtain a 3x3 rotation matrix and a focal length parameter in a constrained projection camera model:
formula to relate pixel coordinates to real world coordinates:
The 3x4 matrix that describe both intrinsic and extrinsic parameters
so in my constrained camera model, u0 and v0 are set to 1, Tx, Tv, Tz are set to 0, so the DOF of this is reduced 4 DOF (3 DOF from rotation matrix + 1 DOF for the focal length (au, av)).
My problem is, although I know the rotation matrix is orthogonal and each columns / rows are related to each other so that the 3x3 matrix although have 9 elements but have only 3 DOF, I would like to know how I can get all the 9 elements of the rotational matrix and the focal length paramters (au, av) by using just 4 equations of 2 known [u,v] and [X,Y,Z] pairs.
I apologize this sounds more of a math question than a programming one, but I'm try to achieve this using numpy linear algebra solving functions. Can anyone show me any example or guide me to a direction about how I can achieve this? I have stuck on this for a few days and I don't seem to find a way accomplish this. Thanks.
来源：https://stackoverflow.com/questions/31498095/solving-the-3-dof-rotation-in-a-simplified-camera-model