A robust method to recognize critical configuration for camera calibration

When space points and camera optical center lie on a twisted cubic, no matter how many pairs there are used from the space points to their image points, camera parameters cannot be determined uniquely. This configuration is critical for camera calibration. We set up invariant relationship between six space points and their image points for the critical configuration. Then based on the relationship, an algorithm to recognize the critical configuration of at least six pairs of space and image points is proposed by using a constructed criterion function, where no any explicit computation on camera projective matrix or optical center is needed. Experiments show the efficiency of the proposed method.