Camera calibration with coplanar conics: a unified explanation and ambiguity analysis

In this paper, we propose a two-step method to give a unified explanation of camera calibration with two coplanar conics. Various kinds of conics-based patterns in which often two parameters are unknown have been studied in previous literatures. The key in such algorithms is to adopt different strategies to compute the world-to-image projective transformation (also called 2D homography). In the first step of our method, we show that two unknown parameters can always be computed in general cases by utilizing the underlying constraints on all parameters through the projective transformation (mathematically called projective invariants). The accompanied ambiguity problem is that the solutions of the unknown parameters are multiple. In the second step, the four intersection points (real or complex) of two totally known conics are utilized to compute the homography. The ambiguity in this step arises from the point correspondence problem. This results in multiple possibilities of correspondences followed by the ambiguous homographies. After analyzing the reasons of the two kinds of ambiguities, we apply the Centre Circle constraint to completely remove them. Finally, the experiments are shown to validate the proposed technique.