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.

中文翻译：

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使用共面圆锥的相机校准：统一的解释和歧义分析

在本文中，我们提出了一种分两步的方法来统一解释带有两个共面圆锥的摄像机标定。在先前的文献中，已经研究了各种基于圆锥曲线的模式，其中通常不知道两个参数。这种算法的关键是采用不同的策略来计算世界到图像的投影变换（也称为2D单应性）。在我们的方法的第一步中，我们证明了在一般情况下，总是可以通过投影变换（在数学上称为投影不变式）利用所有参数的基础约束来计算两个未知参数。伴随的歧义问题是未知参数的解是多重的。第二步 两个完全已知的圆锥形的四个交点（实点或复点）用于计算单应性。该步骤中的歧义由点对应问题引起。这导致对应的多重可能性，然后是模棱两可的单应性。在分析了两种歧义的原因之后，我们应用中心圆约束将其完全消除。最后，实验表明可以验证所提出的技术。