Unbiased Estimator for Distorted Conics in Camera Calibration

Chaehyeon Song, Jaeho Shin, Myung-Hwan Jeon, Jongwoo Lim, Ayoung Kim

Abstract: In the literature, points and conics have been major features for camera geometric calibration. Although conics are more informative features than points, the loss of the conic property under distortion has critically limited the utility of conic features in camera calibration. Many existing approaches addressed conic-based calibration by ig-noring distortion or introducing 3D spherical targets to cir-cumvent this limitation. In this paper, we present a novel formulation for conic-based calibration using moments. Our derivation is based on the mathematical finding that the first moment can be estimated without bias even under dis-tortion. This allows us to track moment changes during pro-jection and distortion, ensuring the preservation of the first moment of the distorted conic. With an unbiased estima-tor, the circular patterns can be accurately detected at the sub-pixel level and can now be fully exploited for an entire calibration pipeline, resulting in significantly improved cal-ibration. The entire code is readily available from https://github.com/ChaehyeonSong/discocal.