Abstract
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.
Highlights
Conic as an important image primitive has been studied very well in the early 1990s [1,2,3]
For most of the classes, we find that the quadrangle formed by four intersection points has different shapes and degrees of freedom (DOF)
Different pairs of coplanar conics may have the same projective invariants that will result in the ambiguity of solving unknown parameters
Summary
Conic as an important image primitive has been studied very well in the early 1990s [1,2,3]. Rothwell et al use four intersection points of two conics to obtain homography which results in the solution of relative motion and pose [5]. The methods of computing homography in [1, 5] are not suitable for calibration because the proposed posterior rules of removing the correspondence ambiguity are only effective when the intrinsic parameters of the camera are given. Wang et al [15] propose an algorithm which is efficient and easy to estimate the pose of camera based on the conic correspondences from world plane to image plane system. The key of camera calibration based on two coplanar conics is how to obtain homography using partial. We analyze the correspondence ambiguity of four intersection points of conics
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