CAMERA CALIBRATION-PROBLEM - SOME NEW RESULTS

We consider the problem of determining the position and orientation in three-dimensional space of a camera knowing the locations of some (=N) points in the three-dimensional object space and their corresponding coordinates obtained by perspective projection onto the camera plane. A mathematically equivalent problem is that of the camera being attached to a vehicle which is moving in a 3D environment with landmarks at known locations and the goal being to guide this vehicle by observing images of these landmarks. (This is known as passive navigation.) We show that if N = 3, then in general there can be up to four solutions for the motion problem, though there can be infinitely many solutions in certain cases where the image points are collinear. Also, if N= 4 and the feature points are coplanar, we give conditions when there may be two or infinitely many solutions. In the cases where multiple solutions arise the image points are collinear, though the feature points themselves may not be. When N = 4 and the feature points are noncoplanar, the solution is generally unique, though there can be up to four solutions. We give several examples of multiple solutions obtained in each of these cases. © 1991.