Intrinsic and extrinsic parameters

When both intrinsic and extrinsic camera parameters are known, the full camera projection matrix is determined. In this case a Euclidean reconstruction is obtained immediately by back-projecting the points.

In the case of known relative position and orientation of the cameras, the first view can be aligned with the world frame without loss of generality. If only the (relative) orientation and the intrinsic parameters are known, the first $3 \times 3$ part of the camera projection matrices is known and it is still possible to linearly obtain the transformation which upgrades the projective reconstruction to metric.