Detecting critical configuration of six points

When space points and camera optical center lie on a twisted cubic, no matter how many corresponding pairs there are from space points to their image points, camera projection matrix cannot be uniquely determined, in other words, the configuration of camera and space points in this case is critical for camera parameter estimation. In practice, it is important to detect; this critical configuration before the estimated camera parameters are used. In this work, a new method is introduced to detect this critical configuration, which is based on an effective criterion function constructed from an invariant relationship between six space points and their corresponding image points. The advantage of this method is that no explicit computation on camera projection matrix or optical center is needed. Simulations show it is quite robust and stable against noise. Experiments on real data, show the criterion function can be faithfully trusted for camera parameter estimation.