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Common pole-polar and common tangent properties of dual coplanar circles and their application in camera calibration

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Abstract

A novel linear calibration method for a camera using two coplanar circles as the calibration template is proposed. Under projective transformation, the common pole-polar and common tangent of coplanar circles maintain invariance and homogeneity, respectively. The two tangent points on the common tangent, the four intersections, and the line passing through the centers of the two coplanar circles can form two groups of vertical parallel lines. Considering duality, a common polar passes through the centers of two coplanar dual circles in various positions with their corresponding poles located at infinity. The common tangent problem was solved iteratively by employing a search algorithm. Further, in the camera model, the vanishing points are obtained by using three images including the two coplanar circle template. The internal parameters can be solved based on the constraint relationship between the imaged circular points and the imaged absolute conic(IAC). In the simulation experiment, the solution of the common tangent and the noise experiment of the internal parameters. In the real experiment, the internal parameters by each method are verified and the projection error is analyzed. The results show that the algorithm is feasible and effective.

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Funding

This study was supported in part by the National Natural Science Foundation of China (NSFC) (61663048 and 11861075), Programme for Innovative Research Team (in Science and Technology) in Universities of Yunnan Province, and the Key Joint Project of the Science and Technology Department of Yunnan Province and Yunnan University (2018FY001(-014)).

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  1. Institute of Mathematics and Statistics, Yunnan University, Cuihu, Kunming, 650091, China

    Sixin Liang & Yue Zhao

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  1. Sixin Liang
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  2. Yue Zhao
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Correspondence to Yue Zhao.

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Liang, S., Zhao, Y. Common pole-polar and common tangent properties of dual coplanar circles and their application in camera calibration. Multimed Tools Appl 83, 381–401 (2024). https://doi.org/10.1007/s11042-023-15684-4

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